WEBVTT 00:00:00.000 --> 00:00:02.408 align:middle line:90% [SQUEAKING] 00:00:02.408 --> 00:00:03.839 align:middle line:90% [RUSTLING] 00:00:03.839 --> 00:00:07.178 align:middle line:90% [CLICKING] 00:00:07.178 --> 00:00:11.280 align:middle line:90% 00:00:11.280 --> 00:00:13.820 align:middle line:84% HAZHIR RAHMANDAD: OK, let's get started. 00:00:13.820 --> 00:00:16.720 align:middle line:84% So today, we have the Ponzi model. 00:00:16.720 --> 00:00:20.720 align:middle line:84% Basically, interestingly enough, we kind of 00:00:20.720 --> 00:00:28.560 align:middle line:84% asked Yvonne and Ryan to basically work 00:00:28.560 --> 00:00:34.480 align:middle line:84% on this Ponzi model a while back as part of their PhD admission 00:00:34.480 --> 00:00:35.680 align:middle line:90% process. 00:00:35.680 --> 00:00:37.840 align:middle line:84% So they are familiar with the problem 00:00:37.840 --> 00:00:39.520 align:middle line:84% as well, although kind of the version we 00:00:39.520 --> 00:00:43.440 align:middle line:84% gave them was a little bit different but largely similar. 00:00:43.440 --> 00:00:49.200 align:middle line:84% And the basic prompt is to build a model of the Ponzi, 00:00:49.200 --> 00:00:51.220 align:middle line:84% try to stay grounded in the case, 00:00:51.220 --> 00:00:54.640 align:middle line:84% but also think of a more generic version 00:00:54.640 --> 00:00:58.360 align:middle line:84% that can apply to other settings, Ponzi-like schemes 00:00:58.360 --> 00:01:03.020 align:middle line:84% or schemes that may not be nefarious as Ponzi was but maybe 00:01:03.020 --> 00:01:08.820 align:middle line:84% even legal as long as you are not deceiving the investors, 00:01:08.820 --> 00:01:09.640 align:middle line:90% it is fine. 00:01:09.640 --> 00:01:14.260 align:middle line:84% So let's start with what we did in the previous sessions 00:01:14.260 --> 00:01:19.060 align:middle line:84% as well, which is what were your common challenges 00:01:19.060 --> 00:01:21.040 align:middle line:90% and take it from there. 00:01:21.040 --> 00:01:25.820 align:middle line:84% So what were some of the common challenges 00:01:25.820 --> 00:01:30.080 align:middle line:84% that you were facing as you were trying to build the Ponzi model? 00:01:30.080 --> 00:01:33.340 align:middle line:90% 00:01:33.340 --> 00:01:36.660 align:middle line:84% And folks online, please unmute yourself and chime in 00:01:36.660 --> 00:01:39.620 align:middle line:90% and don't wait for us. 00:01:39.620 --> 00:01:41.940 align:middle line:84% AUDIENCE: I think I'm just approaching it fundamentally 00:01:41.940 --> 00:01:47.300 align:middle line:84% the wrong way, but I was having challenges with the timing of-- 00:01:47.300 --> 00:01:49.340 align:middle line:84% like if they had more trust, there's the chance 00:01:49.340 --> 00:01:52.300 align:middle line:84% that they [INAUDIBLE] they continue their lease 00:01:52.300 --> 00:01:54.300 align:middle line:90% and their payout is different. 00:01:54.300 --> 00:01:58.500 align:middle line:84% And it's more dependent on what the rate of return was promised, 00:01:58.500 --> 00:02:00.440 align:middle line:84% and maybe I was just overcomplicating it 00:02:00.440 --> 00:02:03.560 align:middle line:84% and couldn't make any sense [INAUDIBLE]. 00:02:03.560 --> 00:02:10.400 align:middle line:84% HAZHIR RAHMANDAD: How to make the timing of investment 00:02:10.400 --> 00:02:18.520 align:middle line:84% versus expectations of return to work. 00:02:18.520 --> 00:02:21.040 align:middle line:84% It's an interesting question because you think about it 00:02:21.040 --> 00:02:23.880 align:middle line:84% at an individual level, it becomes a messier problem 00:02:23.880 --> 00:02:27.600 align:middle line:84% that, for each individual, I was promised three months ago 00:02:27.600 --> 00:02:29.880 align:middle line:90% with a 50% return. 00:02:29.880 --> 00:02:32.360 align:middle line:84% Am I getting that or not and so on? 00:02:32.360 --> 00:02:35.440 align:middle line:90% What else? 00:02:35.440 --> 00:02:37.160 align:middle line:84% AUDIENCE: So there's the element of trust 00:02:37.160 --> 00:02:39.400 align:middle line:90% of customers in this scene. 00:02:39.400 --> 00:02:44.960 align:middle line:84% I was a little bit unsure how visible the business 00:02:44.960 --> 00:02:47.680 align:middle line:84% is to the customers, but how much information they 00:02:47.680 --> 00:02:49.760 align:middle line:90% have from inside the business. 00:02:49.760 --> 00:02:53.340 align:middle line:84% I went with full visibility, but I wasn't very comfortable. 00:02:53.340 --> 00:02:56.810 align:middle line:90% 00:02:56.810 --> 00:02:58.560 align:middle line:84% HAZHIR RAHMANDAD: Very important question. 00:02:58.560 --> 00:03:03.380 align:middle line:84% So if they have no visibility, then 00:03:03.380 --> 00:03:05.660 align:middle line:84% the only signal anybody would get 00:03:05.660 --> 00:03:11.540 align:middle line:84% is when the Ponzi fails to pay off. 00:03:11.540 --> 00:03:15.260 align:middle line:84% Then you can assume there might be investigations or people talk 00:03:15.260 --> 00:03:18.860 align:middle line:84% about it and analyze what his story is versus how viable 00:03:18.860 --> 00:03:21.420 align:middle line:84% that the story is, and they start to build some visibility 00:03:21.420 --> 00:03:24.660 align:middle line:90% into what might be happening. 00:03:24.660 --> 00:03:27.780 align:middle line:84% And the bigger than the gap between what he's saying 00:03:27.780 --> 00:03:35.220 align:middle line:84% and what he's doing creates a more serious perception problem 00:03:35.220 --> 00:03:37.500 align:middle line:90% in the public. 00:03:37.500 --> 00:03:39.740 align:middle line:84% Good, so that's another important piece 00:03:39.740 --> 00:03:41.280 align:middle line:84% of the model how to think about it 00:03:41.280 --> 00:03:45.060 align:middle line:84% and how much do you want to model trust explicitly 00:03:45.060 --> 00:03:47.380 align:middle line:90% and how do you deal with that. 00:03:47.380 --> 00:03:51.720 align:middle line:90% Other issues, other challenges? 00:03:51.720 --> 00:03:57.400 align:middle line:90% 00:03:57.400 --> 00:04:01.560 align:middle line:84% AUDIENCE: Mine was, [INAUDIBLE], if I'm 00:04:01.560 --> 00:04:04.840 align:middle line:84% trying to do that in an individual level 00:04:04.840 --> 00:04:08.880 align:middle line:84% or an agent-based model, and the running time 00:04:08.880 --> 00:04:10.860 align:middle line:90% is just a crazy number. 00:04:10.860 --> 00:04:14.940 align:middle line:84% HAZHIR RAHMANDAD: So it became expensive computationally. 00:04:14.940 --> 00:04:15.440 align:middle line:90% Yes. 00:04:15.440 --> 00:04:22.920 align:middle line:90% 00:04:22.920 --> 00:04:25.120 align:middle line:90% It's an interesting example. 00:04:25.120 --> 00:04:25.978 align:middle line:90% Go ahead. 00:04:25.978 --> 00:04:27.520 align:middle line:84% AUDIENCE: No, I was just going to say 00:04:27.520 --> 00:04:28.895 align:middle line:84% I find it difficult to generalize 00:04:28.895 --> 00:04:32.565 align:middle line:84% the exact same model between Ponzi and Social Security, 00:04:32.565 --> 00:04:33.940 align:middle line:84% even though they're very similar. 00:04:33.940 --> 00:04:37.843 align:middle line:84% But I was trying to [INAUDIBLE] for a while and then give up. 00:04:37.843 --> 00:04:39.260 align:middle line:84% HAZHIR RAHMANDAD: OK, that's fair. 00:04:39.260 --> 00:04:48.940 align:middle line:90% 00:04:48.940 --> 00:04:49.440 align:middle line:90% Great. 00:04:49.440 --> 00:04:52.120 align:middle line:90% 00:04:52.120 --> 00:04:56.480 align:middle line:90% Any other issues? 00:04:56.480 --> 00:05:00.100 align:middle line:84% So as we go through it, we will try to touch on some of these, 00:05:00.100 --> 00:05:02.040 align:middle line:90% I think, more explicitly. 00:05:02.040 --> 00:05:05.490 align:middle line:84% I think these are good problems to have in mind 00:05:05.490 --> 00:05:07.240 align:middle line:84% because they are important and tough ones. 00:05:07.240 --> 00:05:11.640 align:middle line:84% So I guess when I'm looking at the Ponzi model-- 00:05:11.640 --> 00:05:14.500 align:middle line:84% and I think actually Yvonne brought up an important question 00:05:14.500 --> 00:05:16.540 align:middle line:84% that we usually don't ask in this class 00:05:16.540 --> 00:05:19.860 align:middle line:84% that what level of aggregation in terms 00:05:19.860 --> 00:05:21.720 align:middle line:90% do you go all the way to agents? 00:05:21.720 --> 00:05:24.700 align:middle line:84% And we have been building aggregate models in the class 00:05:24.700 --> 00:05:26.480 align:middle line:84% pretty much for all of the cases, 00:05:26.480 --> 00:05:29.980 align:middle line:84% but I think also for everything, we 00:05:29.980 --> 00:05:34.540 align:middle line:84% could have gone a significant level of detail 00:05:34.540 --> 00:05:38.860 align:middle line:84% at a lower level of detail to individuals 00:05:38.860 --> 00:05:44.540 align:middle line:84% or to individual houses in the retrofit model 00:05:44.540 --> 00:05:50.660 align:middle line:84% or in the predator-prey for individual predator or prey. 00:05:50.660 --> 00:05:56.400 align:middle line:84% So you could have built very detailed models. 00:05:56.400 --> 00:05:58.840 align:middle line:84% Part of it is that we are focused here 00:05:58.840 --> 00:06:02.260 align:middle line:84% on some of the more aggregate modeling challenges, 00:06:02.260 --> 00:06:04.340 align:middle line:84% and part of it is the computational cost. 00:06:04.340 --> 00:06:08.520 align:middle line:84% Even though the costs with increased computational powers 00:06:08.520 --> 00:06:11.980 align:middle line:84% are increasingly, for a single simulation, trivial, 00:06:11.980 --> 00:06:14.080 align:middle line:84% not really something to worry about. 00:06:14.080 --> 00:06:17.960 align:middle line:84% But as soon as you want to do more serious analysis, which 00:06:17.960 --> 00:06:20.280 align:middle line:84% includes calibration specifically, 00:06:20.280 --> 00:06:21.900 align:middle line:90% things will be different. 00:06:21.900 --> 00:06:25.120 align:middle line:84% That is, if you need hundreds of thousands or millions 00:06:25.120 --> 00:06:28.800 align:middle line:84% of simulation for a simple calibration run, 00:06:28.800 --> 00:06:33.840 align:middle line:84% then simulation times that go beyond a second 00:06:33.840 --> 00:06:37.240 align:middle line:90% will be terribly slow. 00:06:37.240 --> 00:06:44.140 align:middle line:84% And again, your computational resources are important. 00:06:44.140 --> 00:06:47.400 align:middle line:84% So that can change some of the analysis, some 00:06:47.400 --> 00:06:48.930 align:middle line:90% of the trade-offs. 00:06:48.930 --> 00:06:53.890 align:middle line:84% There are two other significant trade-offs that come to my mind. 00:06:53.890 --> 00:06:59.710 align:middle line:84% One is that when you go into building agent-based models, 00:06:59.710 --> 00:07:01.930 align:middle line:84% it is actually very intuitive in the sense 00:07:01.930 --> 00:07:05.330 align:middle line:84% that the concepts are concepts you deal with in the real world 00:07:05.330 --> 00:07:06.390 align:middle line:90% more closely. 00:07:06.390 --> 00:07:09.350 align:middle line:84% So we think of a person, we think of an animal, 00:07:09.350 --> 00:07:13.060 align:middle line:84% we think of a house as a very concrete object. 00:07:13.060 --> 00:07:15.310 align:middle line:84% And as soon as you are building a model of that thing, 00:07:15.310 --> 00:07:17.370 align:middle line:84% that's the first thing that comes to mind. 00:07:17.370 --> 00:07:19.610 align:middle line:84% And sometimes, that means you may 00:07:19.610 --> 00:07:24.710 align:middle line:84% lock into that level of aggregation just out of habit, 00:07:24.710 --> 00:07:27.650 align:middle line:84% out of simplicity, rather than by thinking 00:07:27.650 --> 00:07:31.170 align:middle line:84% whether that is the right choice for your problem. 00:07:31.170 --> 00:07:34.730 align:middle line:84% And therefore, it has this kind of an attractor 00:07:34.730 --> 00:07:38.250 align:middle line:84% in the space of possibilities that you may converge to 00:07:38.250 --> 00:07:39.550 align:middle line:90% without enough thinking. 00:07:39.550 --> 00:07:41.570 align:middle line:84% It doesn't mean it is the wrong choice. 00:07:41.570 --> 00:07:43.690 align:middle line:90% It's just that there is a risk. 00:07:43.690 --> 00:07:45.770 align:middle line:84% There is a kind of a psychological risk 00:07:45.770 --> 00:07:50.870 align:middle line:84% of locking into that level of aggregation, where it is not 00:07:50.870 --> 00:07:51.950 align:middle line:90% the right choice. 00:07:51.950 --> 00:07:55.310 align:middle line:84% And then you have basically not thought 00:07:55.310 --> 00:07:56.810 align:middle line:90% through the process correctly. 00:07:56.810 --> 00:08:01.070 align:middle line:84% So that's a subtle but, I think, actually a very important 00:08:01.070 --> 00:08:02.170 align:middle line:90% feature of this. 00:08:02.170 --> 00:08:06.110 align:middle line:84% And to add to that, there is also 00:08:06.110 --> 00:08:08.390 align:middle line:84% kind of demand side pressures that 00:08:08.390 --> 00:08:11.070 align:middle line:84% may push you towards that level of more 00:08:11.070 --> 00:08:12.570 align:middle line:90% detailed level of aggregation. 00:08:12.570 --> 00:08:15.790 align:middle line:84% That is, people get impressed when you show them 00:08:15.790 --> 00:08:19.370 align:middle line:84% graphics with some agents moving around, 00:08:19.370 --> 00:08:25.070 align:middle line:84% or deers and wolves kind of attacking each other 00:08:25.070 --> 00:08:29.370 align:middle line:84% or whatever that might come out of an agent-based model. 00:08:29.370 --> 00:08:36.030 align:middle line:84% It is kind of cool, and cool is going to increase demand 00:08:36.030 --> 00:08:40.090 align:middle line:84% from your audiences to see something like that, 00:08:40.090 --> 00:08:43.150 align:middle line:84% or you get applauded for showing something like that. 00:08:43.150 --> 00:08:47.970 align:middle line:84% And then that increases the kind of behavioral bias 00:08:47.970 --> 00:08:51.210 align:middle line:84% we may have towards that level of aggregation-- again, 00:08:51.210 --> 00:08:52.550 align:middle line:90% very explicit. 00:08:52.550 --> 00:08:55.790 align:middle line:84% It doesn't mean sometimes that is not the right choice, 00:08:55.790 --> 00:08:58.930 align:middle line:84% but it means there is a built in bias in favor of that 00:08:58.930 --> 00:09:01.850 align:middle line:84% level of aggregation you need to be aware of. 00:09:01.850 --> 00:09:06.650 align:middle line:84% So that's one set of questions or issues 00:09:06.650 --> 00:09:09.610 align:middle line:84% beyond computational question that we talked about. 00:09:09.610 --> 00:09:12.710 align:middle line:84% Then there is a third set of issues. 00:09:12.710 --> 00:09:17.010 align:middle line:84% And that is about understanding where the behavior comes from. 00:09:17.010 --> 00:09:19.810 align:middle line:84% So we emphasize, even though we haven't 00:09:19.810 --> 00:09:22.270 align:middle line:84% done as much deep analysis in this course, 00:09:22.270 --> 00:09:24.610 align:middle line:84% but we emphasize building a relationship 00:09:24.610 --> 00:09:26.890 align:middle line:84% between the structure that generates 00:09:26.890 --> 00:09:29.190 align:middle line:84% the behavior and the behaviors that we are observing. 00:09:29.190 --> 00:09:31.890 align:middle line:84% If we don't understand where the behavior is coming from, 00:09:31.890 --> 00:09:35.150 align:middle line:84% we are saying, that's just not going to cut it. 00:09:35.150 --> 00:09:37.070 align:middle line:84% You're not generating much insight. 00:09:37.070 --> 00:09:40.530 align:middle line:84% You can't tell whether it is a bug or a feature 00:09:40.530 --> 00:09:45.430 align:middle line:84% of the simulation that you are learning from or being 00:09:45.430 --> 00:09:46.670 align:middle line:90% misled by. 00:09:46.670 --> 00:09:50.070 align:middle line:84% So you really need to make that connection. 00:09:50.070 --> 00:09:52.550 align:middle line:84% And basically, when you have thousands 00:09:52.550 --> 00:09:56.670 align:middle line:84% and thousands or millions of interacting objects 00:09:56.670 --> 00:09:59.750 align:middle line:84% in an obscure code, obscure in the sense of you 00:09:59.750 --> 00:10:03.430 align:middle line:84% can't delve deeper as easily to see 00:10:03.430 --> 00:10:06.510 align:middle line:84% what are the causal chains that create those macro outcomes you 00:10:06.510 --> 00:10:09.530 align:middle line:84% care about, it is much, much harder, 00:10:09.530 --> 00:10:13.830 align:middle line:84% even with the kind of deterministic, differential 00:10:13.830 --> 00:10:17.090 align:middle line:84% equation models with just a handful of state variables, 00:10:17.090 --> 00:10:18.450 align:middle line:90% the stock variables. 00:10:18.450 --> 00:10:20.250 align:middle line:84% We have a hard time explaining them. 00:10:20.250 --> 00:10:24.210 align:middle line:84% I think we have seen a few of those examples in this class, 00:10:24.210 --> 00:10:27.250 align:middle line:84% but more generally, this is a pretty hard problem, 00:10:27.250 --> 00:10:29.350 align:middle line:84% and that is why it is a very active research 00:10:29.350 --> 00:10:31.870 align:middle line:84% area to just-- what are the best ways 00:10:31.870 --> 00:10:33.710 align:middle line:84% to make the connection between the structure 00:10:33.710 --> 00:10:37.830 align:middle line:84% and behavior in the much, much simpler case 00:10:37.830 --> 00:10:42.350 align:middle line:84% of deterministic models with few interacting parts. 00:10:42.350 --> 00:10:44.250 align:middle line:84% Now you go to a stochastic models 00:10:44.250 --> 00:10:48.250 align:middle line:84% with orders of magnitude more interacting parts. 00:10:48.250 --> 00:10:50.767 align:middle line:90% The problem becomes really hard. 00:10:50.767 --> 00:10:52.350 align:middle line:84% I mean, I'm not saying it is hopeless, 00:10:52.350 --> 00:10:55.010 align:middle line:84% but there is not even a serious literature trying 00:10:55.010 --> 00:10:57.730 align:middle line:90% to do that in a systematic way. 00:10:57.730 --> 00:11:00.810 align:middle line:84% So then you end up with all these kind 00:11:00.810 --> 00:11:02.810 align:middle line:84% of very detailed models that people 00:11:02.810 --> 00:11:04.870 align:middle line:90% say, yes, this is the behavior. 00:11:04.870 --> 00:11:08.030 align:middle line:84% And then you say, why is that behavior happening? 00:11:08.030 --> 00:11:10.550 align:middle line:84% And they say, oh, it is an emergent behavior. 00:11:10.550 --> 00:11:11.990 align:middle line:90% What do you mean by emergent? 00:11:11.990 --> 00:11:14.450 align:middle line:84% Basically, it means I don't understand what's happening. 00:11:14.450 --> 00:11:17.090 align:middle line:84% So not that emergence doesn't exist 00:11:17.090 --> 00:11:20.970 align:middle line:84% as a construct of microlevel interactions 00:11:20.970 --> 00:11:24.930 align:middle line:84% can create counterintuitive macrolevel outcomes, 00:11:24.930 --> 00:11:31.490 align:middle line:84% but as a way to push aside understanding, 00:11:31.490 --> 00:11:34.350 align:middle line:90% that is a bad concept to use. 00:11:34.350 --> 00:11:38.870 align:middle line:84% So those are three of the reasons I'm usually 00:11:38.870 --> 00:11:42.510 align:middle line:84% trying to push myself to think hard at the beginning, what's 00:11:42.510 --> 00:11:45.370 align:middle line:84% the right choice in terms of the level of aggregation, 00:11:45.370 --> 00:11:48.550 align:middle line:84% rather than going down the trajectory of building 00:11:48.550 --> 00:11:52.590 align:middle line:84% a very detailed model and then being 00:11:52.590 --> 00:11:55.590 align:middle line:84% disappointed for any of these reasons that we discussed. 00:11:55.590 --> 00:11:59.150 align:middle line:90% 00:11:59.150 --> 00:12:02.728 align:middle line:84% So very generally, when is it a good idea to use an ABM? 00:12:02.728 --> 00:12:04.270 align:middle line:84% I've heard something that if you want 00:12:04.270 --> 00:12:06.510 align:middle line:84% to look at the distribution of something across regions, 00:12:06.510 --> 00:12:07.010 align:middle line:90% it's good. 00:12:07.010 --> 00:12:09.410 align:middle line:84% So distributions are potentially important. 00:12:09.410 --> 00:12:14.670 align:middle line:84% So you need more details to get the distributions well. 00:12:14.670 --> 00:12:20.310 align:middle line:84% And there are interactions-- for example, network structure, 00:12:20.310 --> 00:12:22.350 align:middle line:90% how it impacts outcomes. 00:12:22.350 --> 00:12:25.250 align:middle line:84% To capture that, you really need to go one level deeper. 00:12:25.250 --> 00:12:28.550 align:middle line:84% And sometimes that is really important. 00:12:28.550 --> 00:12:30.710 align:middle line:84% In diffusion models, when you're looking 00:12:30.710 --> 00:12:34.210 align:middle line:84% at local diffusion, sexually-transmitted diseases, 00:12:34.210 --> 00:12:35.550 align:middle line:90% they go through local networks. 00:12:35.550 --> 00:12:39.750 align:middle line:84% Modeling those at the network level adds value. 00:12:39.750 --> 00:12:43.325 align:middle line:84% Now that once you understand how it works at that level, 00:12:43.325 --> 00:12:45.450 align:middle line:84% you could actually build more aggregate models that 00:12:45.450 --> 00:12:50.730 align:middle line:84% capture the features of that more detailed model as well. 00:12:50.730 --> 00:12:52.850 align:middle line:84% So sometimes, it is actually a way 00:12:52.850 --> 00:12:55.530 align:middle line:84% to discover what is the mechanism that you 00:12:55.530 --> 00:12:58.210 align:middle line:84% need to capture at a higher level of aggregation. 00:12:58.210 --> 00:13:02.130 align:middle line:84% So many of the kind of good agent-based modelers 00:13:02.130 --> 00:13:05.850 align:middle line:84% kind go between these levels because they say, sometimes, I 00:13:05.850 --> 00:13:09.230 align:middle line:84% need to actually go very deep, build all of these things, 00:13:09.230 --> 00:13:12.170 align:middle line:84% and then I'll discover that there are two or three core 00:13:12.170 --> 00:13:15.890 align:middle line:84% mechanisms that need to be accounted for in the more 00:13:15.890 --> 00:13:17.430 align:middle line:90% aggregate version of the model. 00:13:17.430 --> 00:13:19.930 align:middle line:84% Then I can build a more aggregate version of the model 00:13:19.930 --> 00:13:21.722 align:middle line:90% that has those features. 00:13:21.722 --> 00:13:23.430 align:middle line:84% But at the beginning, I didn't know that. 00:13:23.430 --> 00:13:25.890 align:middle line:90% So that's another way. 00:13:25.890 --> 00:13:28.510 align:middle line:84% There is a kind of another possibility, 00:13:28.510 --> 00:13:31.570 align:middle line:84% and that is when policy levers are 00:13:31.570 --> 00:13:34.750 align:middle line:84% very customized at the kind of level of individual. 00:13:34.750 --> 00:13:38.270 align:middle line:84% And you need to see the impact of those policy levers 00:13:38.270 --> 00:13:40.110 align:middle line:84% that are kind of differentiated based 00:13:40.110 --> 00:13:43.330 align:middle line:84% on very detailed characteristics of actors. 00:13:43.330 --> 00:13:45.730 align:middle line:90% So that's another area. 00:13:45.730 --> 00:13:47.750 align:middle line:90% So those are some examples. 00:13:47.750 --> 00:13:50.210 align:middle line:84% AUDIENCE: Just a general questions, 00:13:50.210 --> 00:13:51.550 align:middle line:90% which I think is related. 00:13:51.550 --> 00:13:54.150 align:middle line:84% Then how do people understand the behavior 00:13:54.150 --> 00:13:57.870 align:middle line:84% of ABMs because, surely, some people do it [INAUDIBLE]? 00:13:57.870 --> 00:14:01.630 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so I think 00:14:01.630 --> 00:14:05.550 align:middle line:84% the best practice is they try their best at the level of agent 00:14:05.550 --> 00:14:07.210 align:middle line:90% to make sure it is very robust. 00:14:07.210 --> 00:14:09.070 align:middle line:84% So all of the extreme condition thinking 00:14:09.070 --> 00:14:10.990 align:middle line:84% that we bring to our equations, they 00:14:10.990 --> 00:14:14.350 align:middle line:84% run through that for the individual agent. 00:14:14.350 --> 00:14:19.770 align:middle line:84% And so that with the range of inputs that it can get, 00:14:19.770 --> 00:14:22.390 align:middle line:84% it behaves meaningfully and reasonably. 00:14:22.390 --> 00:14:25.730 align:middle line:84% So that way, you make sure the model is generally robust, 00:14:25.730 --> 00:14:29.950 align:middle line:84% and at least you are not looking at noise or kind of error 00:14:29.950 --> 00:14:33.450 align:middle line:84% in code or something, but it doesn't fully 00:14:33.450 --> 00:14:37.370 align:middle line:84% explain what is generating the behavior. 00:14:37.370 --> 00:14:43.210 align:middle line:84% Then it is basically we went through the kind of hypothesis 00:14:43.210 --> 00:14:44.870 align:middle line:90% testing by cutting loops. 00:14:44.870 --> 00:14:47.510 align:middle line:84% So you have a hypothesis for what is generating things. 00:14:47.510 --> 00:14:49.090 align:middle line:84% And then you cut the loops, and you 00:14:49.090 --> 00:14:51.010 align:middle line:84% see whether that behavior goes away. 00:14:51.010 --> 00:14:54.310 align:middle line:84% You can do that type of deep analysis with an ABM. 00:14:54.310 --> 00:14:57.130 align:middle line:84% That is, whenever you see a behavior, 00:14:57.130 --> 00:15:00.290 align:middle line:84% you should come up with a hypothesis for explaining it. 00:15:00.290 --> 00:15:03.490 align:middle line:84% Then go through cutting that mechanism 00:15:03.490 --> 00:15:05.530 align:middle line:84% and seeing whether that behavior goes away. 00:15:05.530 --> 00:15:08.290 align:middle line:84% So that scientific method of testing 00:15:08.290 --> 00:15:11.490 align:middle line:84% applies to ABMs as well as any other model as well as bigger 00:15:11.490 --> 00:15:13.130 align:middle line:90% problems, other problems. 00:15:13.130 --> 00:15:16.450 align:middle line:90% So that's the channel typically. 00:15:16.450 --> 00:15:18.850 align:middle line:84% What happens in practice is that it 00:15:18.850 --> 00:15:22.730 align:middle line:84% is harder to do, so you usually end up with models that 00:15:22.730 --> 00:15:25.890 align:middle line:84% are dynamically simpler-- that is, they have fewer feedback 00:15:25.890 --> 00:15:29.130 align:middle line:84% mechanisms and interacting parts, 00:15:29.130 --> 00:15:31.630 align:middle line:84% conceptually interacting parts, but then 00:15:31.630 --> 00:15:35.910 align:middle line:84% much more detail within the components that you have. 00:15:35.910 --> 00:15:41.390 align:middle line:84% So you may have agents that are people interacting. 00:15:41.390 --> 00:15:44.510 align:middle line:84% And in our setting, it might normally-- 00:15:44.510 --> 00:15:47.670 align:middle line:84% in an aggregate model, you may have just a reinforcing loop 00:15:47.670 --> 00:15:49.370 align:middle line:90% of a Bass diffusion model. 00:15:49.370 --> 00:15:52.730 align:middle line:84% And you say, OK, this is a very simple model. 00:15:52.730 --> 00:15:54.750 align:middle line:84% Let me add this and that and that. 00:15:54.750 --> 00:15:57.650 align:middle line:84% In that ABM formulation, you may stick with that, 00:15:57.650 --> 00:16:02.230 align:middle line:84% but then you start to say, OK, what is the tail of distribution 00:16:02.230 --> 00:16:04.630 align:middle line:84% of adoption doing to the rest, or how 00:16:04.630 --> 00:16:06.950 align:middle line:90% it is changing the dynamics. 00:16:06.950 --> 00:16:11.050 align:middle line:84% And then you would incrementally add complexity and understand. 00:16:11.050 --> 00:16:12.490 align:middle line:90% So those are ways to do it. 00:16:12.490 --> 00:16:17.950 align:middle line:84% But none of those are kind of algorithmic automated ways 00:16:17.950 --> 00:16:20.790 align:middle line:90% of doing deep analysis. 00:16:20.790 --> 00:16:25.330 align:middle line:84% So going back to the question of-- 00:16:25.330 --> 00:16:31.800 align:middle line:90% 00:16:31.800 --> 00:16:34.090 align:middle line:84% I would be typically looking at when 00:16:34.090 --> 00:16:42.270 align:middle line:84% I'm looking at the Ponzi model, so this is about investment. 00:16:42.270 --> 00:16:45.450 align:middle line:84% So you have people who are investing in Ponzi 00:16:45.450 --> 00:16:48.330 align:middle line:84% or in whatever the scheme you're talking about. 00:16:48.330 --> 00:16:51.790 align:middle line:84% There is money that they bring in and then is paid to people. 00:16:51.790 --> 00:16:54.910 align:middle line:84% So there's kind of the stock of money that matters. 00:16:54.910 --> 00:16:58.470 align:middle line:84% And then there is liabilities, what Ponzi owes people. 00:16:58.470 --> 00:17:00.190 align:middle line:84% And these two are conceptually different, 00:17:00.190 --> 00:17:01.898 align:middle line:84% even though they are close to each other. 00:17:01.898 --> 00:17:04.650 align:middle line:84% And if you don't make that conceptual distinction, 00:17:04.650 --> 00:17:07.869 align:middle line:84% and you try to mix them together, things don't work out. 00:17:07.869 --> 00:17:09.569 align:middle line:84% So that's one of the first places 00:17:09.569 --> 00:17:13.050 align:middle line:84% that sometimes people have trouble with this problem. 00:17:13.050 --> 00:17:17.089 align:middle line:84% Then there are the dynamics of investor acquisition and people 00:17:17.089 --> 00:17:20.490 align:middle line:84% leaving the scheme and what drives that. 00:17:20.490 --> 00:17:23.290 align:middle line:84% I think kind of there are basic formulations 00:17:23.290 --> 00:17:27.710 align:middle line:84% you can use from standard methods like Bass diffusion 00:17:27.710 --> 00:17:30.710 align:middle line:84% model with word of mouth, with saturation. 00:17:30.710 --> 00:17:35.130 align:middle line:84% But then there is this risk and reward considerations. 00:17:35.130 --> 00:17:37.870 align:middle line:84% How do you decide what is the infectivity 00:17:37.870 --> 00:17:41.110 align:middle line:84% or what is the adoption rate at any point in time 00:17:41.110 --> 00:17:44.090 align:middle line:84% or the withdrawal rate at any point in time? 00:17:44.090 --> 00:17:46.110 align:middle line:84% And that goes to the question of reputation 00:17:46.110 --> 00:17:48.030 align:middle line:90% that has some brought up. 00:17:48.030 --> 00:17:50.230 align:middle line:84% How do you make good formulations 00:17:50.230 --> 00:17:52.690 align:middle line:84% for reputation that are operational? 00:17:52.690 --> 00:17:57.830 align:middle line:84% You can connect it to risk and reward very closely. 00:17:57.830 --> 00:17:59.750 align:middle line:84% They are well-balanced in the sense 00:17:59.750 --> 00:18:06.730 align:middle line:84% that when you formulate the model for initial condition, 00:18:06.730 --> 00:18:09.090 align:middle line:84% whatever is kind of ponzi's initial condition, 00:18:09.090 --> 00:18:10.163 align:middle line:90% it works with that. 00:18:10.163 --> 00:18:11.830 align:middle line:84% But then you can think about the extreme 00:18:11.830 --> 00:18:15.950 align:middle line:84% when everybody now trusts Ponzi or the other extreme when 00:18:15.950 --> 00:18:20.290 align:middle line:84% everybody has lost trust in him and his scheme, 00:18:20.290 --> 00:18:21.370 align:middle line:90% the model should behave. 00:18:21.370 --> 00:18:23.630 align:middle line:84% That trust formulation or reputation formulation 00:18:23.630 --> 00:18:26.690 align:middle line:90% should work well. 00:18:26.690 --> 00:18:31.250 align:middle line:84% And then all kinds of robustness to extreme conditions 00:18:31.250 --> 00:18:32.550 align:middle line:90% are important as well. 00:18:32.550 --> 00:18:34.970 align:middle line:84% So those are questions when I'm entering, 00:18:34.970 --> 00:18:37.630 align:middle line:84% looking at these models in the back of my mind. 00:18:37.630 --> 00:18:39.990 align:middle line:84% I'm just kind of highlighting what is happening. 00:18:39.990 --> 00:18:43.330 align:middle line:84% So now is a good time to switch to the models. 00:18:43.330 --> 00:18:47.010 align:middle line:84% And I think we have a dozen of them. 00:18:47.010 --> 00:18:49.850 align:middle line:90% So let me bring them. 00:18:49.850 --> 00:18:53.010 align:middle line:90% Let's go through a few of them. 00:18:53.010 --> 00:18:57.690 align:middle line:84% So let's first look at how the stocks and flows are structured 00:18:57.690 --> 00:18:58.950 align:middle line:90% across different ones. 00:18:58.950 --> 00:19:01.250 align:middle line:84% So this is, in a way, the first session 00:19:01.250 --> 00:19:05.190 align:middle line:84% we have a more open-ended problem. 00:19:05.190 --> 00:19:08.170 align:middle line:84% So I expect a lot more variance in this one compared 00:19:08.170 --> 00:19:10.730 align:middle line:84% to the previous ones because the previous ones 00:19:10.730 --> 00:19:17.210 align:middle line:84% we had a lot of detail in how the problem was defined already. 00:19:17.210 --> 00:19:19.390 align:middle line:90% So this is by Ross. 00:19:19.390 --> 00:19:23.230 align:middle line:84% And here, we have investors stocks and flows, 00:19:23.230 --> 00:19:29.910 align:middle line:84% so new investors and investors at maturity. 00:19:29.910 --> 00:19:33.450 align:middle line:84% And I assume, by investors at maturity, 00:19:33.450 --> 00:19:37.710 align:middle line:84% Ross means people who are basically 00:19:37.710 --> 00:19:39.830 align:middle line:90% have invested with Ponzi. 00:19:39.830 --> 00:19:42.950 align:middle line:84% They have reached maturity of their notes. 00:19:42.950 --> 00:19:46.190 align:middle line:84% They should either get their money back 00:19:46.190 --> 00:19:50.610 align:middle line:90% or reinvest into Ponzi. 00:19:50.610 --> 00:19:53.230 align:middle line:84% And that's kind of what it is structured here. 00:19:53.230 --> 00:19:55.970 align:middle line:84% Conceptually, those are good categories to have. 00:19:55.970 --> 00:19:59.110 align:middle line:84% There is a question-- do you need a stock for investors 00:19:59.110 --> 00:20:01.310 align:middle line:84% at maturity, or it is fast enough 00:20:01.310 --> 00:20:07.430 align:middle line:84% that process that this is really the flow of people leaving 00:20:07.430 --> 00:20:08.810 align:middle line:90% or going through maturing? 00:20:08.810 --> 00:20:10.930 align:middle line:84% And then at that point, they split. 00:20:10.930 --> 00:20:15.190 align:middle line:84% They decide which path they take. 00:20:15.190 --> 00:20:18.590 align:middle line:84% It is an interesting question, which 00:20:18.590 --> 00:20:21.230 align:middle line:84% I think, in the Ponzi's case, this is also 00:20:21.230 --> 00:20:24.180 align:middle line:84% a good idea, potentially, to have that explicitly, 00:20:24.180 --> 00:20:28.480 align:middle line:84% but it may be a bit of an overkill. 00:20:28.480 --> 00:20:32.600 align:middle line:84% Then you have the principle that is owed, principle invest, 00:20:32.600 --> 00:20:35.260 align:middle line:90% and interest owed at maturity. 00:20:35.260 --> 00:20:37.660 align:middle line:84% So that's how much these people are owed. 00:20:37.660 --> 00:20:40.440 align:middle line:90% And then you have money at hand. 00:20:40.440 --> 00:20:43.700 align:middle line:84% And then you can, for accounting purposes, 00:20:43.700 --> 00:20:45.480 align:middle line:84% look at the money that was collected. 00:20:45.480 --> 00:20:47.060 align:middle line:84% So I like these stocks and flows. 00:20:47.060 --> 00:20:48.560 align:middle line:90% You have people. 00:20:48.560 --> 00:20:51.080 align:middle line:90% You have money that-- 00:20:51.080 --> 00:20:52.060 align:middle line:90% liabilities. 00:20:52.060 --> 00:20:55.720 align:middle line:84% This is money owed and then actual money. 00:20:55.720 --> 00:20:58.140 align:middle line:90% Let's see how others have this. 00:20:58.140 --> 00:21:04.520 align:middle line:90% So this is what we just opened. 00:21:04.520 --> 00:21:07.120 align:middle line:90% This one is Jason's. 00:21:07.120 --> 00:21:11.080 align:middle line:84% So Jason has also peoples, but this 00:21:11.080 --> 00:21:16.940 align:middle line:84% is closer to assignment 4, so people who are not interested, 00:21:16.940 --> 00:21:21.180 align:middle line:84% then potential investors, new investors, mature investors, 00:21:21.180 --> 00:21:24.980 align:middle line:90% and former investors. 00:21:24.980 --> 00:21:31.520 align:middle line:84% And then you have new funds and mature funds 00:21:31.520 --> 00:21:35.600 align:middle line:84% which go with mature investors, if I'm understanding correctly. 00:21:35.600 --> 00:21:39.180 align:middle line:84% But what does the meaning of the new versus mature investors 00:21:39.180 --> 00:21:40.100 align:middle line:90% mean here? 00:21:40.100 --> 00:21:46.980 align:middle line:84% AUDIENCE: The thought was, in reality, the money 00:21:46.980 --> 00:21:48.980 align:middle line:84% that everyone brings in ages with them 00:21:48.980 --> 00:21:54.820 align:middle line:84% as they go through the fund, but their returns will only 00:21:54.820 --> 00:21:58.950 align:middle line:84% mature if investors earn returns, which 00:21:58.950 --> 00:22:00.700 align:middle line:84% are coming from the total funds that we're 00:22:00.700 --> 00:22:05.980 align:middle line:84% taking from the new people total fund divided 00:22:05.980 --> 00:22:07.600 align:middle line:90% by the mature population. 00:22:07.600 --> 00:22:09.917 align:middle line:90% 00:22:09.917 --> 00:22:12.500 align:middle line:84% HAZHIR RAHMANDAD: So what is the definition of mature investor 00:22:12.500 --> 00:22:13.680 align:middle line:90% versus new investor? 00:22:13.680 --> 00:22:16.340 align:middle line:84% I just want to understand what's the distinction. 00:22:16.340 --> 00:22:18.440 align:middle line:84% Is it the people-- so mature investors 00:22:18.440 --> 00:22:22.280 align:middle line:84% are similar to Ross's, people whose investment 00:22:22.280 --> 00:22:23.460 align:middle line:90% has reached maturity? 00:22:23.460 --> 00:22:23.640 align:middle line:90% AUDIENCE: Yeah. 00:22:23.640 --> 00:22:24.600 align:middle line:90% HAZHIR RAHMANDAD: OK, got it. 00:22:24.600 --> 00:22:26.420 align:middle line:84% AUDIENCE: After a year, you're not earning anything. 00:22:26.420 --> 00:22:26.600 align:middle line:90% And then-- 00:22:26.600 --> 00:22:28.767 align:middle line:84% HAZHIR RAHMANDAD: It's actually 45 days or something 00:22:28.767 --> 00:22:31.680 align:middle line:90% when they get into the maturity. 00:22:31.680 --> 00:22:36.400 align:middle line:84% But then these guys can't reinvest, so they don't go back. 00:22:36.400 --> 00:22:39.360 align:middle line:84% So that's the assumption in this model. 00:22:39.360 --> 00:22:42.180 align:middle line:90% This one is from Alban. 00:22:42.180 --> 00:22:46.800 align:middle line:90% 00:22:46.800 --> 00:22:51.420 align:middle line:84% So Alban also has an-- oh, actually, the previous one. 00:22:51.420 --> 00:22:55.380 align:middle line:84% Does it have money separated from what is owed? 00:22:55.380 --> 00:23:01.480 align:middle line:84% So this is money or what-- they are the liabilities? 00:23:01.480 --> 00:23:03.720 align:middle line:84% AUDIENCE: I don't have the liability explicitly-- 00:23:03.720 --> 00:23:06.280 align:middle line:84% HAZHIR RAHMANDAD: So that probably 00:23:06.280 --> 00:23:08.760 align:middle line:84% will create some problems, although we 00:23:08.760 --> 00:23:10.920 align:middle line:90% should look at it to be sure. 00:23:10.920 --> 00:23:16.160 align:middle line:84% Then Alban has this structure with investors 00:23:16.160 --> 00:23:20.440 align:middle line:84% that are potential investors active, waiting to be paid. 00:23:20.440 --> 00:23:24.340 align:middle line:84% So this is very similar to Ross's structure. 00:23:24.340 --> 00:23:27.660 align:middle line:84% And then investors that have left. 00:23:27.660 --> 00:23:29.460 align:middle line:84% Then you have the liability or debt, 00:23:29.460 --> 00:23:31.040 align:middle line:84% and you have the cash in the scheme. 00:23:31.040 --> 00:23:34.700 align:middle line:84% So this is kind of similar architecture 00:23:34.700 --> 00:23:37.560 align:middle line:90% that we saw with Ross's model. 00:23:37.560 --> 00:23:41.780 align:middle line:84% And I think it's a good set of options to have. 00:23:41.780 --> 00:23:45.140 align:middle line:90% This one is search-ins. 00:23:45.140 --> 00:23:50.540 align:middle line:84% And we have investors potential versus those 00:23:50.540 --> 00:23:53.140 align:middle line:90% that are current investors. 00:23:53.140 --> 00:23:56.060 align:middle line:84% Then you have money that is owed, 00:23:56.060 --> 00:23:59.900 align:middle line:84% and then you have money available. 00:23:59.900 --> 00:24:06.540 align:middle line:84% So this is separating cash and liability, and then 00:24:06.540 --> 00:24:09.780 align:middle line:90% total defaulted payment. 00:24:09.780 --> 00:24:11.860 align:middle line:84% So you're capturing something that 00:24:11.860 --> 00:24:17.520 align:middle line:84% can be traced into basically trust reputation based 00:24:17.520 --> 00:24:19.120 align:middle line:90% on defaults. 00:24:19.120 --> 00:24:23.660 align:middle line:84% So that's one way to capture the trust dynamics. 00:24:23.660 --> 00:24:27.760 align:middle line:90% So that's this model. 00:24:27.760 --> 00:24:36.480 align:middle line:84% AUDIENCE: We have Hesam's here with cash, liability, 00:24:36.480 --> 00:24:42.520 align:middle line:84% and so Hesam is formulating people rather than people 00:24:42.520 --> 00:24:48.140 align:middle line:84% as how much money they can bring into the scheme. 00:24:48.140 --> 00:24:49.460 align:middle line:90% And that's OK. 00:24:49.460 --> 00:24:50.662 align:middle line:90% I think that's also-- 00:24:50.662 --> 00:24:52.120 align:middle line:84% HAZHIR RAHMANDAD: I didn't consider 00:24:52.120 --> 00:24:54.320 align:middle line:90% [INAUDIBLE] maturity period. 00:24:54.320 --> 00:24:57.920 align:middle line:84% That's something I thought investors can cash their money 00:24:57.920 --> 00:24:58.880 align:middle line:90% and profit-- 00:24:58.880 --> 00:25:00.500 align:middle line:90% At any point in time, yeah. 00:25:00.500 --> 00:25:03.580 align:middle line:90% That's not too bad. 00:25:03.580 --> 00:25:08.320 align:middle line:84% I think it could work fine for as-- it's a good first order 00:25:08.320 --> 00:25:09.100 align:middle line:90% approximation. 00:25:09.100 --> 00:25:10.580 align:middle line:90% So we could talk about that. 00:25:10.580 --> 00:25:16.880 align:middle line:84% So this is kind of the fairly simple but has similar ideas. 00:25:16.880 --> 00:25:20.320 align:middle line:84% And as long as you are in the recruited funds, 00:25:20.320 --> 00:25:22.240 align:middle line:90% you are reinvesting potentially. 00:25:22.240 --> 00:25:24.800 align:middle line:84% So the reinvestment is not separated, 00:25:24.800 --> 00:25:26.040 align:middle line:90% if I understand correctly. 00:25:26.040 --> 00:25:28.660 align:middle line:90% 00:25:28.660 --> 00:25:32.340 align:middle line:90% Then we have Cathy's. 00:25:32.340 --> 00:25:38.680 align:middle line:84% So we have the investors, those who are not willing to invest, 00:25:38.680 --> 00:25:41.180 align:middle line:84% those who are potential investors, 00:25:41.180 --> 00:25:44.180 align:middle line:84% and those who are the current investors. 00:25:44.180 --> 00:25:47.920 align:middle line:84% There is a flow back to not willing. 00:25:47.920 --> 00:25:51.740 align:middle line:84% There is a flow back to not willing from most of the stocks. 00:25:51.740 --> 00:25:55.480 align:middle line:84% And then reinvesting can be captured here as well. 00:25:55.480 --> 00:26:01.140 align:middle line:90% Then you have cash. 00:26:01.140 --> 00:26:04.660 align:middle line:90% Then you have trust. 00:26:04.660 --> 00:26:06.320 align:middle line:90% You don't have liabilities. 00:26:06.320 --> 00:26:09.320 align:middle line:84% You have something about failure. 00:26:09.320 --> 00:26:12.960 align:middle line:84% This is just accounting, not really having any feedback 00:26:12.960 --> 00:26:14.260 align:middle line:90% into the rest of the system. 00:26:14.260 --> 00:26:17.220 align:middle line:84% So the trust is the more important part, 00:26:17.220 --> 00:26:19.560 align:middle line:90% if I understand correctly. 00:26:19.560 --> 00:26:21.320 align:middle line:90% OK, good. 00:26:21.320 --> 00:26:23.700 align:middle line:84% So this is also missing the liability part, 00:26:23.700 --> 00:26:26.900 align:middle line:90% which could prove important. 00:26:26.900 --> 00:26:30.600 align:middle line:90% 00:26:30.600 --> 00:26:39.440 align:middle line:84% This one-- Gerardo's model has delay. 00:26:39.440 --> 00:26:41.460 align:middle line:84% I don't know what that delay is about. 00:26:41.460 --> 00:26:50.720 align:middle line:84% So it's the investment goes into this and then comes out and-- 00:26:50.720 --> 00:26:53.140 align:middle line:84% we need to look at it more closely to understand that. 00:26:53.140 --> 00:26:55.880 align:middle line:84% But it seems to be money that is-- 00:26:55.880 --> 00:26:58.560 align:middle line:90% what's that? 00:26:58.560 --> 00:27:01.920 align:middle line:84% AUDIENCE: [INAUDIBLE] structure to captured 00:27:01.920 --> 00:27:05.120 align:middle line:84% the effect of the debt visibility 00:27:05.120 --> 00:27:08.820 align:middle line:84% on the credibility of the investor. 00:27:08.820 --> 00:27:15.040 align:middle line:84% So it's a really bad name, delay, but this is the sense. 00:27:15.040 --> 00:27:18.680 align:middle line:84% And there is another page just for the [INAUDIBLE]. 00:27:18.680 --> 00:27:19.680 align:middle line:90% HAZHIR RAHMANDAD: I see. 00:27:19.680 --> 00:27:20.180 align:middle line:90% I see. 00:27:20.180 --> 00:27:24.260 align:middle line:84% So this is more about the credibility, this part. 00:27:24.260 --> 00:27:31.940 align:middle line:84% And then you have the money at hand, available liquidity. 00:27:31.940 --> 00:27:33.080 align:middle line:90% That's the money at hand. 00:27:33.080 --> 00:27:36.180 align:middle line:84% I don't know if you have the-- and then 00:27:36.180 --> 00:27:39.220 align:middle line:84% you have the Bass diffusion type for investors 00:27:39.220 --> 00:27:41.980 align:middle line:90% versus potential investors. 00:27:41.980 --> 00:27:44.680 align:middle line:84% And then [INAUDIBLE] has nothing. 00:27:44.680 --> 00:27:50.020 align:middle line:90% 00:27:50.020 --> 00:27:50.640 align:middle line:90% Great. 00:27:50.640 --> 00:27:53.360 align:middle line:90% And let's see next one. 00:27:53.360 --> 00:27:57.340 align:middle line:90% 00:27:57.340 --> 00:28:01.180 align:middle line:90% This one is Jake's. 00:28:01.180 --> 00:28:09.560 align:middle line:84% So we have investors that are scheme seem susceptible, yes, 00:28:09.560 --> 00:28:11.980 align:middle line:90% scheme susceptible population. 00:28:11.980 --> 00:28:15.720 align:middle line:84% This is-- can go into investors and then 00:28:15.720 --> 00:28:19.040 align:middle line:90% go into formally invested. 00:28:19.040 --> 00:28:23.680 align:middle line:84% And then if they're unpaid, they wouldn't go back. 00:28:23.680 --> 00:28:27.862 align:middle line:90% Then you have the money and-- 00:28:27.862 --> 00:28:29.320 align:middle line:84% AUDIENCE: The way I thought about-- 00:28:29.320 --> 00:28:31.920 align:middle line:84% I mean, my liabilities is a simpler one, 00:28:31.920 --> 00:28:34.863 align:middle line:84% where it's just desired money in terms of if I know somebody soon 00:28:34.863 --> 00:28:36.280 align:middle line:84% I'm going to have to pay out, then 00:28:36.280 --> 00:28:41.600 align:middle line:84% I go and hastily try to recruit two more to or multiple more 00:28:41.600 --> 00:28:42.460 align:middle line:90% to Venmo. 00:28:42.460 --> 00:28:43.460 align:middle line:90% HAZHIR RAHMANDAD: I see. 00:28:43.460 --> 00:28:47.080 align:middle line:84% So we can revisit kind of the formulations 00:28:47.080 --> 00:28:48.900 align:middle line:90% there in the next round. 00:28:48.900 --> 00:28:54.150 align:middle line:84% And then I think this is the last one, Ali's. 00:28:54.150 --> 00:28:55.560 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:28:55.560 --> 00:28:59.200 align:middle line:84% HAZHIR RAHMANDAD: So this is similar to the sum-- 00:28:59.200 --> 00:29:01.620 align:middle line:90% funds, liabilities, and cash. 00:29:01.620 --> 00:29:04.300 align:middle line:84% So you guys coordinate with each other. 00:29:04.300 --> 00:29:07.252 align:middle line:90% But that's all right. 00:29:07.252 --> 00:29:07.960 align:middle line:90% That's all right. 00:29:07.960 --> 00:29:10.680 align:middle line:90% 00:29:10.680 --> 00:29:13.540 align:middle line:90% So now kind of big picture-- 00:29:13.540 --> 00:29:18.300 align:middle line:84% we had these three, four categories of people. 00:29:18.300 --> 00:29:21.140 align:middle line:84% You could break it down based on whether they 00:29:21.140 --> 00:29:24.620 align:middle line:84% are potential investors from scratch or unwilling 00:29:24.620 --> 00:29:28.320 align:middle line:84% and then become potential and then become investors. 00:29:28.320 --> 00:29:30.780 align:middle line:84% I think capturing unwilling population 00:29:30.780 --> 00:29:32.340 align:middle line:90% is an interesting idea. 00:29:32.340 --> 00:29:35.020 align:middle line:84% I think a lot of investments, people 00:29:35.020 --> 00:29:37.260 align:middle line:90% start with being very skeptical. 00:29:37.260 --> 00:29:40.180 align:middle line:84% But you could also capture that skepticism 00:29:40.180 --> 00:29:42.520 align:middle line:84% through some mechanism about trust. 00:29:42.520 --> 00:29:45.780 align:middle line:84% That is, everybody is a potential investor 00:29:45.780 --> 00:29:49.760 align:middle line:84% is just that they are very skeptical at the beginning. 00:29:49.760 --> 00:29:52.440 align:middle line:84% That is, the priors, the initial perception, 00:29:52.440 --> 00:29:56.980 align:middle line:84% if you hear somebody is promising 50% return in 45 days 00:29:56.980 --> 00:29:59.140 align:middle line:84% is like, this is a scam, I'm not going 00:29:59.140 --> 00:30:02.760 align:middle line:84% to look at it even or think about it. 00:30:02.760 --> 00:30:04.740 align:middle line:84% So there are these two different ways. 00:30:04.740 --> 00:30:08.440 align:middle line:84% But if you are going with the second way of using trust 00:30:08.440 --> 00:30:11.360 align:middle line:84% to model that, you need a machinery 00:30:11.360 --> 00:30:14.000 align:middle line:84% for modeling trust, that probably needs a stock 00:30:14.000 --> 00:30:15.740 align:middle line:90% variable somewhere there. 00:30:15.740 --> 00:30:17.140 align:middle line:90% So that it changes over time. 00:30:17.140 --> 00:30:20.520 align:middle line:84% That is, you need to put an initial value for the trust 00:30:20.520 --> 00:30:24.580 align:middle line:84% level or kind of expected return or something along those lines. 00:30:24.580 --> 00:30:29.300 align:middle line:84% Then we have the liability and the cash. 00:30:29.300 --> 00:30:31.720 align:middle line:84% Those are pretty physical, clear as well. 00:30:31.720 --> 00:30:34.840 align:middle line:84% Then the fourth stock and flow is about trust. 00:30:34.840 --> 00:30:38.000 align:middle line:84% Now whether you capture it as explicit stock and flow 00:30:38.000 --> 00:30:39.740 align:middle line:90% or not is a choice. 00:30:39.740 --> 00:30:42.560 align:middle line:84% And I think most of you have simpler versions 00:30:42.560 --> 00:30:47.200 align:middle line:84% based on return rate of whether you are able to pay back-- 00:30:47.200 --> 00:30:48.620 align:middle line:90% your formulating that. 00:30:48.620 --> 00:30:54.640 align:middle line:84% Now let's start doing deep dives into perhaps the liability 00:30:54.640 --> 00:30:55.620 align:middle line:90% and cash part. 00:30:55.620 --> 00:30:59.000 align:middle line:84% It is kind of instructive because they're not 00:30:59.000 --> 00:31:06.540 align:middle line:84% super complicated, but they have enough interesting pieces 00:31:06.540 --> 00:31:09.080 align:middle line:84% to make it worth taking a look at them. 00:31:09.080 --> 00:31:12.060 align:middle line:90% So this is Ali's. 00:31:12.060 --> 00:31:15.300 align:middle line:84% We can just look at this one as a starter point. 00:31:15.300 --> 00:31:22.380 align:middle line:84% So when you recruit investors, you are issuing liability. 00:31:22.380 --> 00:31:26.020 align:middle line:84% And this is in the units of people-- 00:31:26.020 --> 00:31:29.160 align:middle line:84% oh, sorry, funds because you guys are modeling it as funds. 00:31:29.160 --> 00:31:33.300 align:middle line:84% So that simplifies your life that way. 00:31:33.300 --> 00:31:35.580 align:middle line:84% So the liability goes there and the same amount 00:31:35.580 --> 00:31:36.960 align:middle line:90% goes into your incoming cash. 00:31:36.960 --> 00:31:39.460 align:middle line:90% So that's straightforward. 00:31:39.460 --> 00:31:46.120 align:middle line:84% Then, at the end of the period, so you have a delivery time-- 00:31:46.120 --> 00:31:48.740 align:middle line:90% I'm sorry, let me see. 00:31:48.740 --> 00:31:50.400 align:middle line:90% How does the exit happen? 00:31:50.400 --> 00:31:52.240 align:middle line:90% So you have people who are-- 00:31:52.240 --> 00:31:55.260 align:middle line:90% 00:31:55.260 --> 00:31:57.500 align:middle line:90% so there is a indicated-- 00:31:57.500 --> 00:31:59.920 align:middle line:84% AUDIENCE: You have a confidence in the business, which is 00:31:59.920 --> 00:32:01.320 align:middle line:90% characterized by [INAUDIBLE]. 00:32:01.320 --> 00:32:03.000 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:32:03.000 --> 00:32:06.040 align:middle line:84% So you are assuming-- so this is actually an important assumption 00:32:06.040 --> 00:32:11.240 align:middle line:84% here, that this confidence is cash divided by a liability plus 00:32:11.240 --> 00:32:16.180 align:middle line:84% some small number so that you don't have overflow when you 00:32:16.180 --> 00:32:16.680 align:middle line:90% get-- 00:32:16.680 --> 00:32:18.605 align:middle line:84% AUDIENCE: People know that how much cash-- 00:32:18.605 --> 00:32:20.480 align:middle line:84% HAZHIR RAHMANDAD: Yes, so the assumption here 00:32:20.480 --> 00:32:21.460 align:middle line:90% is very important. 00:32:21.460 --> 00:32:23.460 align:middle line:84% So there are two assumptions that are important. 00:32:23.460 --> 00:32:26.120 align:middle line:84% The first one is the bigger one is that people know what 00:32:26.120 --> 00:32:28.600 align:middle line:90% is the cash that Ponzi has. 00:32:28.600 --> 00:32:30.780 align:middle line:84% That is usually not a good assumption. 00:32:30.780 --> 00:32:36.960 align:middle line:84% I mean, we could debate, but most of the businesses 00:32:36.960 --> 00:32:41.100 align:middle line:84% don't have all of their detail financials visible, 00:32:41.100 --> 00:32:43.460 align:middle line:84% at least not the ones that are not publicly traded. 00:32:43.460 --> 00:32:46.720 align:middle line:84% Now, publicly-traded companies have a lot more requirements 00:32:46.720 --> 00:32:47.580 align:middle line:90% for visibility. 00:32:47.580 --> 00:32:49.620 align:middle line:84% And part of it is exactly these dynamics. 00:32:49.620 --> 00:32:52.840 align:middle line:84% That is, once you remove that visibility, 00:32:52.840 --> 00:32:56.360 align:middle line:84% the balancing feedback loops go away, 00:32:56.360 --> 00:33:00.210 align:middle line:90% and things can get really messy. 00:33:00.210 --> 00:33:07.770 align:middle line:84% So I would be OK as long as you understand 00:33:07.770 --> 00:33:09.730 align:middle line:84% that you're making a strong assumption here 00:33:09.730 --> 00:33:12.870 align:middle line:84% and have a way to get out of that strong assumption. 00:33:12.870 --> 00:33:15.330 align:middle line:84% That is, you can say, OK, I have this switch that 00:33:15.330 --> 00:33:19.170 align:middle line:84% says how much this confidence matters versus 00:33:19.170 --> 00:33:24.010 align:middle line:84% some other version of confidence that is not reliant on this cash 00:33:24.010 --> 00:33:26.270 align:middle line:90% to liability ratio. 00:33:26.270 --> 00:33:30.910 align:middle line:84% I mean, you could even have that ratio raised to some power. 00:33:30.910 --> 00:33:34.410 align:middle line:84% And if that power is 0, basically, you 00:33:34.410 --> 00:33:38.690 align:middle line:84% get to there is no effect from this side 00:33:38.690 --> 00:33:40.690 align:middle line:90% or something along those lines. 00:33:40.690 --> 00:33:46.250 align:middle line:84% So right now, if liability is much bigger than the cash, 00:33:46.250 --> 00:33:48.550 align:middle line:84% then indicated withdrawal goes up. 00:33:48.550 --> 00:33:51.050 align:middle line:84% The way it is formulated is liability 00:33:51.050 --> 00:33:54.370 align:middle line:84% multiplied by deserting factor multiplied 00:33:54.370 --> 00:33:56.270 align:middle line:90% by 1 minus confidence. 00:33:56.270 --> 00:34:01.630 align:middle line:84% So deserting factor is just a factor 00:34:01.630 --> 00:34:03.410 align:middle line:90% that takes care of the units. 00:34:03.410 --> 00:34:08.230 align:middle line:84% So 5% of people leave every day as soon as-- 00:34:08.230 --> 00:34:11.230 align:middle line:84% assuming that there is no confidence, looking back 00:34:11.230 --> 00:34:13.389 align:middle line:90% at this formulation. 00:34:13.389 --> 00:34:18.110 align:middle line:90% But let's be a little bit-- 00:34:18.110 --> 00:34:20.210 align:middle line:84% this is cash divided by liability. 00:34:20.210 --> 00:34:24.150 align:middle line:84% So if cash divided by liability-- then as long as cash 00:34:24.150 --> 00:34:27.150 align:middle line:84% exceeds liability, this number should 00:34:27.150 --> 00:34:32.590 align:middle line:84% be above 1 which leads to negative values for 1 00:34:32.590 --> 00:34:34.550 align:middle line:90% minus confidence. 00:34:34.550 --> 00:34:37.590 align:middle line:84% And negative values for 1 minus confidence 00:34:37.590 --> 00:34:41.469 align:middle line:84% are not a good idea because, then, your settling liability 00:34:41.469 --> 00:34:44.710 align:middle line:90% thingy will go negative. 00:34:44.710 --> 00:34:48.030 align:middle line:84% AUDIENCE: So the assumption is that this is a scheme. 00:34:48.030 --> 00:34:49.830 align:middle line:84% HAZHIR RAHMANDAD: No, so that's not-- yeah, 00:34:49.830 --> 00:34:52.030 align:middle line:84% but you shouldn't build assumptions 00:34:52.030 --> 00:34:54.710 align:middle line:84% like that hidden inside equations. 00:34:54.710 --> 00:35:00.570 align:middle line:84% So the key thing here is let's go with the first assumption 00:35:00.570 --> 00:35:04.010 align:middle line:84% that people can see the confidence or can see the cash 00:35:04.010 --> 00:35:06.050 align:middle line:84% and can calculate the confidence. 00:35:06.050 --> 00:35:09.330 align:middle line:84% Still, the confidence should not go above 1 00:35:09.330 --> 00:35:11.810 align:middle line:84% in the next part of the equations. 00:35:11.810 --> 00:35:13.670 align:middle line:90% Maximum confidence is 1. 00:35:13.670 --> 00:35:19.450 align:middle line:84% So as such, you want this to be minimum of 1 and this ratio 00:35:19.450 --> 00:35:22.390 align:middle line:90% rather than the ratio alone. 00:35:22.390 --> 00:35:26.850 align:middle line:84% Otherwise, you create the risk of settling liability 00:35:26.850 --> 00:35:27.630 align:middle line:90% going negative. 00:35:27.630 --> 00:35:31.690 align:middle line:84% And then that breaks down the whole model. 00:35:31.690 --> 00:35:36.290 align:middle line:84% And yes, in practice, this model cash is always below liability 00:35:36.290 --> 00:35:42.010 align:middle line:84% unless you have situations where you are investing, actually, 00:35:42.010 --> 00:35:44.450 align:middle line:84% or you bring your own money into it. 00:35:44.450 --> 00:35:47.110 align:middle line:84% And both of those are not impossible. 00:35:47.110 --> 00:35:51.370 align:middle line:90% 00:35:51.370 --> 00:35:55.290 align:middle line:84% Now what I like about this is how simple it is. 00:35:55.290 --> 00:35:57.510 align:middle line:84% That is, you're just saying a fraction of people 00:35:57.510 --> 00:36:02.830 align:middle line:84% will leave the scheme if they are not confident 00:36:02.830 --> 00:36:11.870 align:middle line:84% that things are working and then as soon as they leave-- 00:36:11.870 --> 00:36:14.590 align:middle line:84% I mean, as soon as the confidence goes down. 00:36:14.590 --> 00:36:19.550 align:middle line:84% Now, deliverable cash is kind of a maximum rate 00:36:19.550 --> 00:36:26.230 align:middle line:84% that you can impose on how much withdrawal you could have. 00:36:26.230 --> 00:36:29.210 align:middle line:90% And how are you accounting for-- 00:36:29.210 --> 00:36:31.750 align:middle line:90% 00:36:31.750 --> 00:36:34.230 align:middle line:84% so you're accounting for growth in liability 00:36:34.230 --> 00:36:35.730 align:middle line:90% using this compounding rate. 00:36:35.730 --> 00:36:40.750 align:middle line:84% So basically, interest rate goes into compounding interest. 00:36:40.750 --> 00:36:44.970 align:middle line:84% And so this is also a nice, simple way of doing it. 00:36:44.970 --> 00:36:46.150 align:middle line:90% Now you have this-- 00:36:46.150 --> 00:36:48.710 align:middle line:84% AUDIENCE: The reason for this is that the Ponzi 00:36:48.710 --> 00:36:50.010 align:middle line:90% person is getting caught. 00:36:50.010 --> 00:36:54.330 align:middle line:84% So the liability cannot go grow forever. 00:36:54.330 --> 00:37:01.215 align:middle line:84% HAZHIR RAHMANDAD: So that's actually an interesting point. 00:37:01.215 --> 00:37:02.090 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:37:02.090 --> 00:37:03.590 align:middle line:84% HAZHIR RAHMANDAD: Yeah, I don't like 00:37:03.590 --> 00:37:06.770 align:middle line:84% the way you have formulated it by just cash bigger than one 00:37:06.770 --> 00:37:08.490 align:middle line:90% or some kind of ad hoc thing. 00:37:08.490 --> 00:37:11.650 align:middle line:84% So even if you want to put some kind of a switch that 00:37:11.650 --> 00:37:16.330 align:middle line:84% says scheme going bust, and then if scheme going bust 00:37:16.330 --> 00:37:19.130 align:middle line:84% has not happened, you continue with this accumulation 00:37:19.130 --> 00:37:24.370 align:middle line:84% of liability, otherwise you wouldn't, rather than build it 00:37:24.370 --> 00:37:26.150 align:middle line:84% inside the equation, it's the same idea, 00:37:26.150 --> 00:37:28.530 align:middle line:84% but it's kind of being built into the equation that 00:37:28.530 --> 00:37:29.682 align:middle line:90% doesn't work. 00:37:29.682 --> 00:37:31.890 align:middle line:84% AUDIENCE: So this is also saying that a confidence is 00:37:31.890 --> 00:37:33.778 align:middle line:90% when people never withdraw. 00:37:33.778 --> 00:37:36.070 align:middle line:84% HAZHIR RAHMANDAD: It is saying that if confidence is 1, 00:37:36.070 --> 00:37:37.195 align:middle line:90% people will never withdraw. 00:37:37.195 --> 00:37:37.810 align:middle line:90% Exactly. 00:37:37.810 --> 00:37:41.290 align:middle line:90% So is that a good assumption? 00:37:41.290 --> 00:37:42.350 align:middle line:90% Probably not. 00:37:42.350 --> 00:37:47.410 align:middle line:84% That is, people would not leave their assets 00:37:47.410 --> 00:37:49.650 align:middle line:90% for eternity with the scammers. 00:37:49.650 --> 00:37:53.770 align:middle line:84% At some point, they want to use that investment. 00:37:53.770 --> 00:37:57.350 align:middle line:84% So as such, the formulation for indicated withdrawal 00:37:57.350 --> 00:38:00.830 align:middle line:84% perhaps should have a scaling factor 00:38:00.830 --> 00:38:04.390 align:middle line:84% that goes from a maximum withdrawal rate 00:38:04.390 --> 00:38:09.150 align:middle line:84% when there is no confidence to a minimum withdrawal rate. 00:38:09.150 --> 00:38:14.270 align:middle line:84% That is when everybody thinks this is very legit, no risk. 00:38:14.270 --> 00:38:17.610 align:middle line:84% But at some point, I would like to take out my money. 00:38:17.610 --> 00:38:20.110 align:middle line:84% And so there is a kind of a maximum residence 00:38:20.110 --> 00:38:21.650 align:middle line:84% time and a minimum residence time, 00:38:21.650 --> 00:38:26.195 align:middle line:84% which are the 1 over those deserting factors. 00:38:26.195 --> 00:38:27.570 align:middle line:84% AUDIENCE: This is another thing-- 00:38:27.570 --> 00:38:32.110 align:middle line:84% I remember you telling us that every relationship in the model 00:38:32.110 --> 00:38:36.630 align:middle line:84% should have some controlling parameter. 00:38:36.630 --> 00:38:39.770 align:middle line:84% So in this example, if I were to do this formulation, 00:38:39.770 --> 00:38:42.230 align:middle line:84% the other issues aside, I think I 00:38:42.230 --> 00:38:46.090 align:middle line:84% would be trying to have some of sensitivity of withdrawal 00:38:46.090 --> 00:38:48.170 align:middle line:90% and confidence or something-- 00:38:48.170 --> 00:38:49.930 align:middle line:84% HAZHIR RAHMANDAD: So let's separate 00:38:49.930 --> 00:38:51.430 align:middle line:90% the two things from each other. 00:38:51.430 --> 00:38:54.930 align:middle line:84% Not every equation needs a controlling parameter. 00:38:54.930 --> 00:38:57.490 align:middle line:84% Some equations are just mathematical operations 00:38:57.490 --> 00:39:00.250 align:middle line:84% that bring things together, so that's not the case. 00:39:00.250 --> 00:39:05.450 align:middle line:84% Then there is the question of, OK, sensitivity to confidence 00:39:05.450 --> 00:39:06.890 align:middle line:90% or something like that. 00:39:06.890 --> 00:39:09.970 align:middle line:90% Would that be helpful? 00:39:09.970 --> 00:39:11.750 align:middle line:90% I could go either way. 00:39:11.750 --> 00:39:13.750 align:middle line:84% So there are two different ways to formulate. 00:39:13.750 --> 00:39:15.810 align:middle line:84% So Alexander's question is an important one 00:39:15.810 --> 00:39:18.770 align:middle line:84% that is, here, we have 1 minus confidence. 00:39:18.770 --> 00:39:21.570 align:middle line:84% So once confidence is defined, this equation 00:39:21.570 --> 00:39:24.890 align:middle line:84% is deterministic and is driving things. 00:39:24.890 --> 00:39:26.550 align:middle line:90% So I could do two things. 00:39:26.550 --> 00:39:28.610 align:middle line:84% I could add a parameter here that 00:39:28.610 --> 00:39:30.970 align:middle line:84% says the sensitivity of withdrawal 00:39:30.970 --> 00:39:34.290 align:middle line:84% to confidence-- so if you think of this one minus confidence 00:39:34.290 --> 00:39:36.330 align:middle line:84% as a switch that moves between those two 00:39:36.330 --> 00:39:40.090 align:middle line:84% extremes of maximum withdrawal rate and minimum withdrawal 00:39:40.090 --> 00:39:43.030 align:middle line:84% rate, it could be a linear thing, 00:39:43.030 --> 00:39:46.170 align:middle line:84% but it is still could be 1 minus confidence raised to some power, 00:39:46.170 --> 00:39:50.390 align:middle line:84% and that power can regulate how nonlinear that response is. 00:39:50.390 --> 00:39:54.130 align:middle line:84% Or I can build that nonlinearity or that response, 00:39:54.130 --> 00:39:58.670 align:middle line:84% whatever I call it, inside the confidence equation itself. 00:39:58.670 --> 00:40:01.010 align:middle line:84% That is, in the equation for confidence, 00:40:01.010 --> 00:40:03.710 align:middle line:84% I could make it to change nonlinearly 00:40:03.710 --> 00:40:06.830 align:middle line:84% rather than just being the ratio of the two things 00:40:06.830 --> 00:40:09.390 align:middle line:90% to be nonlinear. 00:40:09.390 --> 00:40:13.310 align:middle line:84% I think both of them are feasible, meaningful ways 00:40:13.310 --> 00:40:14.310 align:middle line:90% of doing things. 00:40:14.310 --> 00:40:17.890 align:middle line:84% In this equation, I would probably do the latter. 00:40:17.890 --> 00:40:22.190 align:middle line:84% That is, I would build that inside the confidence equation 00:40:22.190 --> 00:40:25.930 align:middle line:84% so that when I look at that confidence variable, 00:40:25.930 --> 00:40:31.990 align:middle line:84% it is already informing me about how strong this mechanism is 00:40:31.990 --> 00:40:35.170 align:middle line:84% kicking in because, otherwise, I'm calling it confidence. 00:40:35.170 --> 00:40:40.430 align:middle line:84% But it is some half-baked variable that is not really 00:40:40.430 --> 00:40:42.810 align:middle line:84% operating in my model, and therefore, it's 00:40:42.810 --> 00:40:45.130 align:middle line:84% not very informative to double-click on that 00:40:45.130 --> 00:40:46.890 align:middle line:90% and look at its graphs. 00:40:46.890 --> 00:40:49.330 align:middle line:84% So that would be my solution, which 00:40:49.330 --> 00:40:54.650 align:middle line:84% means I would make the confidence equation have that-- 00:40:54.650 --> 00:40:56.810 align:middle line:84% if you want to have sensitivity raised 00:40:56.810 --> 00:40:59.250 align:middle line:84% to the power of some sensitivity, take care of it 00:40:59.250 --> 00:40:59.870 align:middle line:90% there. 00:40:59.870 --> 00:41:03.030 align:middle line:84% And then when you come here, you just use that concept. 00:41:03.030 --> 00:41:06.290 align:middle line:84% Then you can look at the confidence variable directly. 00:41:06.290 --> 00:41:08.930 align:middle line:84% AUDIENCE: So your suggestion is to have, I guess, 00:41:08.930 --> 00:41:10.930 align:middle line:90% exactly one of the two. 00:41:10.930 --> 00:41:13.330 align:middle line:84% HAZHIR RAHMANDAD: Yes, but not both of them. 00:41:13.330 --> 00:41:15.610 align:middle line:90% So why not both of them? 00:41:15.610 --> 00:41:18.610 align:middle line:84% Because in this case, there is no-- 00:41:18.610 --> 00:41:21.110 align:middle line:84% the intermediate construct that you're generating, 00:41:21.110 --> 00:41:23.690 align:middle line:84% so let's say, we made this confidence 00:41:23.690 --> 00:41:24.938 align:middle line:90% and it had its own parameter. 00:41:24.938 --> 00:41:27.230 align:middle line:84% And then in the next step, we had a separate parameter. 00:41:27.230 --> 00:41:30.090 align:middle line:90% So we had two parameters. 00:41:30.090 --> 00:41:32.290 align:middle line:84% There are serial parameters that are just 00:41:32.290 --> 00:41:33.790 align:middle line:90% compounding on each other. 00:41:33.790 --> 00:41:36.370 align:middle line:84% We are not taking anything else from this confidence 00:41:36.370 --> 00:41:38.710 align:middle line:84% to go in another direction that has an impact. 00:41:38.710 --> 00:41:40.630 align:middle line:90% We don't have observables on it. 00:41:40.630 --> 00:41:43.170 align:middle line:84% So you basically have redundant parameters, 00:41:43.170 --> 00:41:45.870 align:middle line:84% and redundant parameters will cause havoc 00:41:45.870 --> 00:41:48.430 align:middle line:84% later on when you want to estimate the model, when you 00:41:48.430 --> 00:41:49.690 align:middle line:90% want to understand the model. 00:41:49.690 --> 00:41:52.252 align:middle line:90% So it doesn't help. 00:41:52.252 --> 00:41:53.710 align:middle line:84% AUDIENCE: I'm just wondering if you 00:41:53.710 --> 00:41:58.282 align:middle line:84% can clarify what this liability construct means 00:41:58.282 --> 00:41:59.490 align:middle line:90% [INAUDIBLE] supposed to mean. 00:41:59.490 --> 00:42:00.948 align:middle line:84% HAZHIR RAHMANDAD: So it is supposed 00:42:00.948 --> 00:42:03.830 align:middle line:84% to mean how much Ponzi owes people 00:42:03.830 --> 00:42:08.390 align:middle line:84% based on how people think they are owed, or based 00:42:08.390 --> 00:42:10.870 align:middle line:84% on the contacts because they are writing contacts 00:42:10.870 --> 00:42:14.550 align:middle line:90% to pay these people back. 00:42:14.550 --> 00:42:17.553 align:middle line:84% AUDIENCE: So it's how much people think they are owed? 00:42:17.553 --> 00:42:18.470 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:42:18.470 --> 00:42:21.510 align:middle line:84% Well, how much people are owed, let's say that way. 00:42:21.510 --> 00:42:23.090 align:middle line:90% Let's keep it that way. 00:42:23.090 --> 00:42:27.973 align:middle line:84% Why are you confused with the distinction between those two? 00:42:27.973 --> 00:42:29.890 align:middle line:84% AUDIENCE: Because when you make an investment, 00:42:29.890 --> 00:42:31.350 align:middle line:90% you're assuming some risk. 00:42:31.350 --> 00:42:34.990 align:middle line:90% So why should I-- 00:42:34.990 --> 00:42:37.890 align:middle line:84% HAZHIR RAHMANDAD: So yes, risk-- let's separate it. 00:42:37.890 --> 00:42:42.210 align:middle line:84% So risk is about investments that don't 00:42:42.210 --> 00:42:44.190 align:middle line:90% have promised rates of return. 00:42:44.190 --> 00:42:46.310 align:middle line:84% This has a fixed promise rate of return. 00:42:46.310 --> 00:42:49.810 align:middle line:84% Now, risk in the sense that it is part of the business-- that 00:42:49.810 --> 00:42:51.490 align:middle line:90% is, if it doesn't pay. 00:42:51.490 --> 00:42:52.670 align:middle line:90% I'm not cheated. 00:42:52.670 --> 00:42:56.030 align:middle line:84% I invested in the stocks, and the stocks go up and come down. 00:42:56.030 --> 00:42:58.130 align:middle line:84% And therefore, even if it is average 00:42:58.130 --> 00:43:01.290 align:middle line:84% 8% per year over the last two decades, 00:43:01.290 --> 00:43:06.130 align:middle line:84% I may be unlucky and get minus 20%, and I can't complain. 00:43:06.130 --> 00:43:08.190 align:middle line:84% This is not that type of investment. 00:43:08.190 --> 00:43:13.730 align:middle line:84% So it was an investment that says 45 days, 50% return, 00:43:13.730 --> 00:43:15.770 align:middle line:90% we will guarantee that. 00:43:15.770 --> 00:43:18.850 align:middle line:84% AUDIENCE: And then, so with that, 00:43:18.850 --> 00:43:24.410 align:middle line:84% how is this capturing that dynamic? 00:43:24.410 --> 00:43:25.970 align:middle line:84% HAZHIR RAHMANDAD: So the way this 00:43:25.970 --> 00:43:28.430 align:middle line:90% is capturing it is a bit tricky. 00:43:28.430 --> 00:43:30.850 align:middle line:84% So what is the problem with this formulation 00:43:30.850 --> 00:43:32.510 align:middle line:90% in terms of Ponzi's stories? 00:43:32.510 --> 00:43:34.890 align:middle line:84% It is a nice kind of formulation, 00:43:34.890 --> 00:43:36.370 align:middle line:90% keeping things very simple. 00:43:36.370 --> 00:43:39.910 align:middle line:84% But what is the shortcoming in connecting it 00:43:39.910 --> 00:43:42.790 align:middle line:90% with Ponzi's story? 00:43:42.790 --> 00:43:44.373 align:middle line:84% AUDIENCE: [INAUDIBLE] maturity period. 00:43:44.373 --> 00:43:45.998 align:middle line:84% HAZHIR RAHMANDAD: Basically, it doesn't 00:43:45.998 --> 00:43:47.050 align:middle line:90% have the maturity period. 00:43:47.050 --> 00:43:50.070 align:middle line:84% So what does that mean in this case? 00:43:50.070 --> 00:43:52.670 align:middle line:84% AUDIENCE: You have to be ready today to-- 00:43:52.670 --> 00:43:55.690 align:middle line:84% HAZHIR RAHMANDAD: It means as soon as you're matured, 00:43:55.690 --> 00:43:58.790 align:middle line:90% what will happen in this model? 00:43:58.790 --> 00:44:01.870 align:middle line:84% It is reinvested back into Ponzi. 00:44:01.870 --> 00:44:04.590 align:middle line:84% Now that reinvestment in the real world 00:44:04.590 --> 00:44:06.210 align:middle line:90% didn't happen automatically. 00:44:06.210 --> 00:44:09.510 align:middle line:84% Ponzi was not telling you, oh, if you didn't come and get 00:44:09.510 --> 00:44:15.190 align:middle line:84% your money at day 45, I will reinvest all of your investment, 00:44:15.190 --> 00:44:18.070 align:middle line:84% and it will grow exponentially forever. 00:44:18.070 --> 00:44:21.670 align:middle line:84% He was saying, no, you have to come get your money, 00:44:21.670 --> 00:44:23.750 align:middle line:90% then come back and reinvest. 00:44:23.750 --> 00:44:25.930 align:middle line:84% If you want to do that, you're welcome. 00:44:25.930 --> 00:44:27.950 align:middle line:84% But that creates this kind of group 00:44:27.950 --> 00:44:30.990 align:middle line:84% of people who have matured their investments 00:44:30.990 --> 00:44:34.050 align:middle line:84% but have not yet decided whether to reinvest or not. 00:44:34.050 --> 00:44:37.370 align:middle line:84% And that's why the formulation that Ross and Albon and a couple 00:44:37.370 --> 00:44:41.250 align:middle line:84% others had makes this a little bit more explicit and, as such, 00:44:41.250 --> 00:44:45.850 align:middle line:84% adds some additional value for the context of Ponzi's story. 00:44:45.850 --> 00:44:47.950 align:middle line:84% Is the distinction clear in this case? 00:44:47.950 --> 00:44:52.130 align:middle line:84% That's pretty important in the actual story 00:44:52.130 --> 00:44:54.770 align:middle line:84% because, then, you can actually create situations 00:44:54.770 --> 00:44:59.330 align:middle line:84% where the bottleneck is the payment processing system, 00:44:59.330 --> 00:45:02.670 align:middle line:84% and that may or may not help you. 00:45:02.670 --> 00:45:04.370 align:middle line:84% I mean, sometimes, it can even help you 00:45:04.370 --> 00:45:07.350 align:middle line:84% because I'm paying everybody with my fastest speed. 00:45:07.350 --> 00:45:10.870 align:middle line:84% It's just that I just have one processor who's paying people, 00:45:10.870 --> 00:45:13.530 align:middle line:84% so I'm not failing to pay people. 00:45:13.530 --> 00:45:15.370 align:middle line:90% It's just a slow process. 00:45:15.370 --> 00:45:17.330 align:middle line:90% Yes, wait here. 00:45:17.330 --> 00:45:20.910 align:middle line:84% There is a three day line to get your money back, 00:45:20.910 --> 00:45:23.750 align:middle line:84% and there is another three day line to invest it back. 00:45:23.750 --> 00:45:25.730 align:middle line:90% And you can do both of those. 00:45:25.730 --> 00:45:30.210 align:middle line:84% So capturing all of that complexity 00:45:30.210 --> 00:45:34.580 align:middle line:84% requires a lot more structure, but we 00:45:34.580 --> 00:45:37.620 align:middle line:84% want to be clear what is missing when you are going 00:45:37.620 --> 00:45:39.240 align:middle line:90% with this simple formulation. 00:45:39.240 --> 00:45:43.480 align:middle line:84% But otherwise, this is a pretty nice, decent formulation. 00:45:43.480 --> 00:45:45.960 align:middle line:84% So as soon as you settle the liability, 00:45:45.960 --> 00:45:50.060 align:middle line:84% basically, you are paid or you withdraw the money, 00:45:50.060 --> 00:45:52.500 align:middle line:90% that money goes out of cash. 00:45:52.500 --> 00:45:56.960 align:middle line:84% Note that cash availability is a constraint on that. 00:45:56.960 --> 00:45:59.620 align:middle line:84% So this is kind of a maximum delivery rate 00:45:59.620 --> 00:46:01.660 align:middle line:90% based on availability of cash. 00:46:01.660 --> 00:46:04.380 align:middle line:84% So if you are not settling liabilities 00:46:04.380 --> 00:46:09.100 align:middle line:84% here because delivery is constrained by cash, 00:46:09.100 --> 00:46:16.500 align:middle line:84% now things start to look bad for Ponzi in this case. 00:46:16.500 --> 00:46:20.600 align:middle line:84% Now I'm not seeing how that is reflected. 00:46:20.600 --> 00:46:22.500 align:middle line:84% That is, your measure of confidence 00:46:22.500 --> 00:46:27.380 align:middle line:84% here is only getting feedback from this ratio of cash 00:46:27.380 --> 00:46:29.380 align:middle line:90% to liability. 00:46:29.380 --> 00:46:32.720 align:middle line:84% The day that Ponzi is not paying people 00:46:32.720 --> 00:46:34.880 align:middle line:84% because he doesn't have cash, that 00:46:34.880 --> 00:46:37.160 align:middle line:84% is a very different day from the day 00:46:37.160 --> 00:46:43.120 align:middle line:84% before when he was paying people whatever they were asking for. 00:46:43.120 --> 00:46:44.880 align:middle line:84% Whereas in this model, confidence 00:46:44.880 --> 00:46:48.160 align:middle line:84% is only this kind of gradual decline 00:46:48.160 --> 00:46:52.720 align:middle line:84% based on the ratio of cash to liability. 00:46:52.720 --> 00:46:55.880 align:middle line:84% AUDIENCE: One thing that happens though is, because we 00:46:55.880 --> 00:46:57.420 align:middle line:90% will pay that liability out. 00:46:57.420 --> 00:47:00.600 align:middle line:84% So if he's short on cash, whatever cash there is 00:47:00.600 --> 00:47:02.860 align:middle line:90% will go out in that one day. 00:47:02.860 --> 00:47:04.180 align:middle line:90% So cash drops to 0. 00:47:04.180 --> 00:47:05.420 align:middle line:90% Confidence drops to 0. 00:47:05.420 --> 00:47:07.663 align:middle line:84% It's not exactly as it should be, but it [INAUDIBLE]. 00:47:07.663 --> 00:47:09.080 align:middle line:84% HAZHIR RAHMANDAD: So you're right. 00:47:09.080 --> 00:47:11.080 align:middle line:84% In that sense-- and you could also 00:47:11.080 --> 00:47:14.640 align:middle line:84% capture it using some additional nonlinearity in the definition 00:47:14.640 --> 00:47:18.360 align:middle line:84% of confidence that you have a cliff-like behavior that 00:47:18.360 --> 00:47:23.080 align:middle line:84% as long as cash to liability is above 0.1 or 0.2, 00:47:23.080 --> 00:47:26.220 align:middle line:84% nothing is happening because nobody is really seeing it. 00:47:26.220 --> 00:47:30.580 align:middle line:84% So raising it to a small power, like raising that ratio to power 00:47:30.580 --> 00:47:34.100 align:middle line:84% of 0.3 or 0.2, will give you that behavior 00:47:34.100 --> 00:47:39.340 align:middle line:84% that you have a cliff like end, but otherwise, things are fine. 00:47:39.340 --> 00:47:41.800 align:middle line:90% And that would do a decent job. 00:47:41.800 --> 00:47:45.580 align:middle line:84% So this is kind of good to think about it, 00:47:45.580 --> 00:47:51.980 align:middle line:84% that how does this confidence formulation address this failure 00:47:51.980 --> 00:47:52.520 align:middle line:90% mode. 00:47:52.520 --> 00:47:55.100 align:middle line:90% 00:47:55.100 --> 00:48:02.060 align:middle line:84% So I'm OK with it, but with the caveat that then you 00:48:02.060 --> 00:48:04.660 align:middle line:84% need to make sure this delivery time is small enough 00:48:04.660 --> 00:48:09.240 align:middle line:90% that feedback is not lost. 00:48:09.240 --> 00:48:11.940 align:middle line:90% 00:48:11.940 --> 00:48:13.640 align:middle line:84% AUDIENCE: One more formulation question. 00:48:13.640 --> 00:48:14.020 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:48:14.020 --> 00:48:16.395 align:middle line:84% AUDIENCE: [INAUDIBLE] do compounding interest [INAUDIBLE] 00:48:16.395 --> 00:48:18.700 align:middle line:90% cash? 00:48:18.700 --> 00:48:20.380 align:middle line:90% [INTERPOSING VOICES] 00:48:20.380 --> 00:48:21.940 align:middle line:90% AUDIENCE: Oh, this is the-- 00:48:21.940 --> 00:48:24.380 align:middle line:84% HAZHIR RAHMANDAD: Yes, that's just that if cash-- yes, 00:48:24.380 --> 00:48:27.020 align:middle line:90% so that's not really doing much. 00:48:27.020 --> 00:48:30.260 align:middle line:84% And then he has his own investments. 00:48:30.260 --> 00:48:34.000 align:middle line:84% So this is nice to have what the actual investment of Ponzi 00:48:34.000 --> 00:48:34.620 align:middle line:90% might be. 00:48:34.620 --> 00:48:38.860 align:middle line:84% So if there was a legitimate business, like Social Security, 00:48:38.860 --> 00:48:41.480 align:middle line:84% you could have that investment going into it. 00:48:41.480 --> 00:48:44.600 align:middle line:90% That's fine. 00:48:44.600 --> 00:48:49.320 align:middle line:84% And then because they have formulated it with liabilities, 00:48:49.320 --> 00:48:53.720 align:middle line:84% once you're getting funds out, you're getting funds out, 00:48:53.720 --> 00:48:55.500 align:middle line:84% and you're getting investors out. 00:48:55.500 --> 00:48:56.460 align:middle line:90% And that's fine. 00:48:56.460 --> 00:48:59.880 align:middle line:84% There's nothing strange happening there. 00:48:59.880 --> 00:49:03.600 align:middle line:84% And then these people, after a while, may decide to return. 00:49:03.600 --> 00:49:07.160 align:middle line:84% So this part of the formulation of people returning 00:49:07.160 --> 00:49:11.360 align:middle line:84% without any concern for confidence or anything else 00:49:11.360 --> 00:49:17.840 align:middle line:84% is a little bit kind of not a great alternative. 00:49:17.840 --> 00:49:19.800 align:middle line:84% So the way I would think of it is 00:49:19.800 --> 00:49:24.880 align:middle line:84% that people would return only if the confidence level is high, 00:49:24.880 --> 00:49:27.720 align:middle line:84% and if you have that confidence already defined, 00:49:27.720 --> 00:49:30.500 align:middle line:84% you can use the same construct for informing 00:49:30.500 --> 00:49:36.860 align:middle line:84% whether people return to the pool of potential investors. 00:49:36.860 --> 00:49:40.500 align:middle line:84% There is also nothing here about the rate of return 00:49:40.500 --> 00:49:44.960 align:middle line:90% impacting the choices to join. 00:49:44.960 --> 00:49:47.100 align:middle line:84% So the recruitment factor that you have here 00:49:47.100 --> 00:49:49.940 align:middle line:84% in your Bass diffusion type of a model 00:49:49.940 --> 00:49:53.220 align:middle line:84% is kind of just a free parameter, whereas in practice, 00:49:53.220 --> 00:49:57.500 align:middle line:84% it should be tightly coupled to the promised interest rate 00:49:57.500 --> 00:49:59.540 align:middle line:90% and to the confidence. 00:49:59.540 --> 00:50:02.700 align:middle line:84% So both of those are important inputs 00:50:02.700 --> 00:50:06.480 align:middle line:90% into the recruitment factor. 00:50:06.480 --> 00:50:08.687 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:50:08.687 --> 00:50:11.020 align:middle line:84% HAZHIR RAHMANDAD: Oh, you have feedback from confidence. 00:50:11.020 --> 00:50:13.400 align:middle line:84% AUDIENCE: But you're right, not from the interest rate. 00:50:13.400 --> 00:50:15.220 align:middle line:84% HAZHIR RAHMANDAD: Yes, but not from the interest rate. 00:50:15.220 --> 00:50:17.012 align:middle line:84% AUDIENCE: Reality should be some of measure 00:50:17.012 --> 00:50:20.860 align:middle line:84% of the fund's interest rate and the investment interest 00:50:20.860 --> 00:50:24.382 align:middle line:84% rates [INAUDIBLE] comparison [INAUDIBLE]. 00:50:24.382 --> 00:50:25.340 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:50:25.340 --> 00:50:26.120 align:middle line:84% AUDIENCE: You can't go [INAUDIBLE]. 00:50:26.120 --> 00:50:27.537 align:middle line:84% AUDIENCE: So just to clarify, when 00:50:27.537 --> 00:50:29.360 align:middle line:84% you're saying the promised interest rate, 00:50:29.360 --> 00:50:32.740 align:middle line:84% people are comparing it to the reference rate, 00:50:32.740 --> 00:50:35.760 align:middle line:84% so if it's higher than reference. 00:50:35.760 --> 00:50:37.280 align:middle line:90% HAZHIR RAHMANDAD: Yes, exactly. 00:50:37.280 --> 00:50:39.640 align:middle line:84% AUDIENCE: --like market administrators. 00:50:39.640 --> 00:50:41.200 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so the way 00:50:41.200 --> 00:50:46.360 align:middle line:84% I would probably formulate it, I would think of the confidence-- 00:50:46.360 --> 00:50:52.340 align:middle line:84% I would even name it as this is the risk of losing my money. 00:50:52.340 --> 00:50:59.480 align:middle line:84% So if that risk is 0, then I believe the promised interest 00:50:59.480 --> 00:51:00.160 align:middle line:90% rate. 00:51:00.160 --> 00:51:03.440 align:middle line:84% And if that risk is 1, they might 00:51:03.440 --> 00:51:08.120 align:middle line:84% then my expected return rate is minus 100% 00:51:08.120 --> 00:51:11.920 align:middle line:90% or kind of equivalent to that. 00:51:11.920 --> 00:51:17.120 align:middle line:84% And then I will formulate that risk of losing my money. 00:51:17.120 --> 00:51:20.560 align:middle line:84% I try to formulate it very robustly 00:51:20.560 --> 00:51:27.940 align:middle line:84% and then calculate the expected return rate using that, perhaps 00:51:27.940 --> 00:51:33.020 align:middle line:84% with some additional sensitivity that, OK, people are risk averse 00:51:33.020 --> 00:51:35.920 align:middle line:84% so that they don't just look at the expected return, 00:51:35.920 --> 00:51:38.640 align:middle line:84% but there is kind of a risk-adjusted expected return. 00:51:38.640 --> 00:51:45.300 align:middle line:84% So you can add volatility cost to it as well. 00:51:45.300 --> 00:51:48.460 align:middle line:84% Then that becomes kind of the key driver. 00:51:48.460 --> 00:51:51.340 align:middle line:84% And that's what I meant by when you're talking about confidence 00:51:51.340 --> 00:51:54.980 align:middle line:84% in this model or trust or reputation, 00:51:54.980 --> 00:52:00.780 align:middle line:84% building a very operational version of it really helps. 00:52:00.780 --> 00:52:03.660 align:middle line:84% So in this case, that operational version 00:52:03.660 --> 00:52:07.060 align:middle line:84% would be something like, what is the probability 00:52:07.060 --> 00:52:09.040 align:middle line:90% that I'll lose my money? 00:52:09.040 --> 00:52:10.680 align:middle line:90% It will be between 0 and 1. 00:52:10.680 --> 00:52:14.060 align:middle line:84% You can then use it in calculation of expected return 00:52:14.060 --> 00:52:16.080 align:middle line:84% into risk-adjusted expected return. 00:52:16.080 --> 00:52:18.540 align:middle line:84% And then those risk-adjusted expected returns 00:52:18.540 --> 00:52:24.400 align:middle line:84% can make up for attractiveness of this scheme compared 00:52:24.400 --> 00:52:26.200 align:middle line:90% to the alternative schemes. 00:52:26.200 --> 00:52:29.520 align:middle line:84% And then the Bass diffusion model-- remember, 00:52:29.520 --> 00:52:31.700 align:middle line:84% what's the idea of Bass diffusion model? 00:52:31.700 --> 00:52:34.440 align:middle line:84% It is about diffusion of information. 00:52:34.440 --> 00:52:40.160 align:middle line:84% So it is about people knowing about this risk-adjusted return 00:52:40.160 --> 00:52:40.660 align:middle line:90% rate. 00:52:40.660 --> 00:52:47.640 align:middle line:84% If the risk-adjusted return rate is below the market return rate, 00:52:47.640 --> 00:52:50.400 align:middle line:90% then nobody will adopt it. 00:52:50.400 --> 00:52:53.540 align:middle line:90% People will become aware of it. 00:52:53.540 --> 00:52:59.240 align:middle line:84% So the Bass diffusion model, what it does makes people aware, 00:52:59.240 --> 00:53:01.360 align:middle line:84% but then their decision whether to invest 00:53:01.360 --> 00:53:04.400 align:middle line:84% or not could actually come from the true-- 00:53:04.400 --> 00:53:11.160 align:middle line:84% or the market perceived risk-adjusted return. 00:53:11.160 --> 00:53:13.680 align:middle line:84% AUDIENCE: So how would you do this? 00:53:13.680 --> 00:53:16.460 align:middle line:84% How would you do this risk-adjusted expected return? 00:53:16.460 --> 00:53:18.700 align:middle line:84% So you have the expected return and that makes sense. 00:53:18.700 --> 00:53:20.520 align:middle line:84% You just multiply the probability. 00:53:20.520 --> 00:53:24.322 align:middle line:90% You just take it to some power-- 00:53:24.322 --> 00:53:25.780 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so I guess, 00:53:25.780 --> 00:53:27.320 align:middle line:84% in the kind of finance literature, 00:53:27.320 --> 00:53:28.980 align:middle line:84% they just have a volatility factor 00:53:28.980 --> 00:53:33.820 align:middle line:90% that says it is your risk-- 00:53:33.820 --> 00:53:36.380 align:middle line:90% so there is a linear-- 00:53:36.380 --> 00:53:39.420 align:middle line:84% so minus some alpha multiplied by a standard deviation 00:53:39.420 --> 00:53:43.820 align:middle line:84% of the return that you expect becomes your kind 00:53:43.820 --> 00:53:45.240 align:middle line:90% of risk-adjusted return. 00:53:45.240 --> 00:53:50.940 align:middle line:84% So it is the mean minus some beta 00:53:50.940 --> 00:53:57.660 align:middle line:84% by standard deviation of the return rate for that asset 00:53:57.660 --> 00:53:59.060 align:middle line:90% class. 00:53:59.060 --> 00:54:01.240 align:middle line:84% So you can use something similar. 00:54:01.240 --> 00:54:02.820 align:middle line:84% But here, you are not calculating 00:54:02.820 --> 00:54:05.220 align:middle line:90% the standard deviation. 00:54:05.220 --> 00:54:08.740 align:middle line:84% So you're calculating the risk that your money will be lost. 00:54:08.740 --> 00:54:11.900 align:middle line:84% You need to then go from there to something 00:54:11.900 --> 00:54:16.500 align:middle line:84% like a standard deviation of the volatility or kind of a measure 00:54:16.500 --> 00:54:19.000 align:middle line:90% of volatility in return. 00:54:19.000 --> 00:54:21.860 align:middle line:84% I haven't gone through making those calculations. 00:54:21.860 --> 00:54:22.360 align:middle line:90% You could-- 00:54:22.360 --> 00:54:25.400 align:middle line:84% AUDIENCE: Is volatility really what matters here, or is it 00:54:25.400 --> 00:54:28.680 align:middle line:84% rather that there's a nonlinear response to losses 00:54:28.680 --> 00:54:32.560 align:middle line:84% that losing $1 is much worse than gaining [INAUDIBLE]. 00:54:32.560 --> 00:54:35.500 align:middle line:84% HAZHIR RAHMANDAD: So there are really two different things. 00:54:35.500 --> 00:54:41.200 align:middle line:84% So the underlying reason why people are sensitive to risk 00:54:41.200 --> 00:54:45.160 align:middle line:84% is the same psychological story that losing $1 00:54:45.160 --> 00:54:50.300 align:middle line:84% is worse than gaining $1 or more utility loss than gaining $1. 00:54:50.300 --> 00:54:52.720 align:middle line:84% That's why people are sensitive to volatility. 00:54:52.720 --> 00:54:56.020 align:middle line:84% So the underlying mechanism is the same. 00:54:56.020 --> 00:54:59.600 align:middle line:84% But how you translate this probability of loss 00:54:59.600 --> 00:55:03.440 align:middle line:84% to an equivalent volatility is not obvious 00:55:03.440 --> 00:55:11.160 align:middle line:84% because it's a question about the distribution 00:55:11.160 --> 00:55:16.620 align:middle line:84% of the interests or the kind of return that you would expect. 00:55:16.620 --> 00:55:20.180 align:middle line:84% I would not go through building a whole machinery 00:55:20.180 --> 00:55:24.020 align:middle line:84% for that distribution because there are a bunch of assumptions 00:55:24.020 --> 00:55:25.980 align:middle line:84% that go into it, but ultimately, it is just 00:55:25.980 --> 00:55:27.740 align:middle line:90% something like a parameter. 00:55:27.740 --> 00:55:29.460 align:middle line:84% So I would just have a parameter that 00:55:29.460 --> 00:55:38.780 align:middle line:84% translates this probability into its impact on my expected 00:55:38.780 --> 00:55:40.820 align:middle line:90% return. 00:55:40.820 --> 00:55:45.780 align:middle line:84% So you could think about promised versus kind 00:55:45.780 --> 00:55:52.100 align:middle line:84% of full loss, which is minus 100% or per sum, that 45 days, 00:55:52.100 --> 00:55:53.740 align:middle line:90% as the range. 00:55:53.740 --> 00:55:56.320 align:middle line:84% And then you are scaling between the two. 00:55:56.320 --> 00:55:59.480 align:middle line:84% So that probability is a number between 0 and 1. 00:55:59.480 --> 00:56:03.260 align:middle line:84% So raise it to a power and do this-- 00:56:03.260 --> 00:56:04.280 align:middle line:90% switch between the two. 00:56:04.280 --> 00:56:05.480 align:middle line:90% That should do OK. 00:56:05.480 --> 00:56:09.620 align:middle line:84% I think that would be a decent first cut. 00:56:09.620 --> 00:56:12.540 align:middle line:84% AUDIENCE: Question-- it wasn't an easy decision for me 00:56:12.540 --> 00:56:16.160 align:middle line:84% to can go with confidence or trust or any measure of that 00:56:16.160 --> 00:56:18.200 align:middle line:90% [INAUDIBLE]. 00:56:18.200 --> 00:56:20.480 align:middle line:84% Do we need to start with that or [INAUDIBLE]? 00:56:20.480 --> 00:56:23.020 align:middle line:84% HAZHIR RAHMANDAD: So it's a very good question. 00:56:23.020 --> 00:56:25.600 align:middle line:84% And here, you have stocks in the sense 00:56:25.600 --> 00:56:29.780 align:middle line:84% that you are using the liability and cash, which are both stocks. 00:56:29.780 --> 00:56:32.360 align:middle line:84% So the inertia in the payments is showing up 00:56:32.360 --> 00:56:33.745 align:middle line:90% in these two stocks. 00:56:33.745 --> 00:56:35.120 align:middle line:84% So that was why I didn't actually 00:56:35.120 --> 00:56:39.560 align:middle line:84% bring up this as a problem that you don't have inertia. 00:56:39.560 --> 00:56:41.360 align:middle line:84% If you were getting it, for example, 00:56:41.360 --> 00:56:46.600 align:middle line:84% from this flow rate of actual payment versus desired payment, 00:56:46.600 --> 00:56:51.440 align:middle line:84% I would have signaled that as another issue to think about. 00:56:51.440 --> 00:56:56.520 align:middle line:84% But more generally, there is a question of spread of news 00:56:56.520 --> 00:57:00.200 align:middle line:84% about whatever the signal is and that is not 00:57:00.200 --> 00:57:01.380 align:middle line:90% captured in this model. 00:57:01.380 --> 00:57:07.680 align:middle line:84% You are assuming cash is known today, and not only that, 00:57:07.680 --> 00:57:10.880 align:middle line:84% people are responding to it right away. 00:57:10.880 --> 00:57:12.520 align:middle line:90% Not a great assumption. 00:57:12.520 --> 00:57:16.740 align:middle line:84% So an explicit delay process for perception, 00:57:16.740 --> 00:57:21.580 align:middle line:84% spread of the information becomes relevant as well. 00:57:21.580 --> 00:57:22.460 align:middle line:90% Yeah? 00:57:22.460 --> 00:57:24.900 align:middle line:84% AUDIENCE: So I know I'm talking about this [INAUDIBLE], 00:57:24.900 --> 00:57:31.100 align:middle line:84% but even if expected return is low-- 00:57:31.100 --> 00:57:34.060 align:middle line:84% I'm just thinking about this-- so long as that recruitment 00:57:34.060 --> 00:57:36.740 align:middle line:84% factor or whatever this infectivity is positive, 00:57:36.740 --> 00:57:39.900 align:middle line:84% then everyone will eventually join, just 00:57:39.900 --> 00:57:41.883 align:middle line:84% over a longer period of time, right? 00:57:41.883 --> 00:57:42.800 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:57:42.800 --> 00:57:44.258 align:middle line:84% AUDIENCE: So long as it's positive. 00:57:44.258 --> 00:57:47.180 align:middle line:90% And so that seems a little odd. 00:57:47.180 --> 00:57:49.420 align:middle line:84% HAZHIR RAHMANDAD: So why is it odd? 00:57:49.420 --> 00:57:51.740 align:middle line:84% So if this is the best investment 00:57:51.740 --> 00:57:54.500 align:middle line:84% available in a marketplace, why is it odd 00:57:54.500 --> 00:57:56.998 align:middle line:90% that everybody would try it? 00:57:56.998 --> 00:57:58.040 align:middle line:90% AUDIENCE: Well, I guess-- 00:57:58.040 --> 00:58:01.020 align:middle line:90% 00:58:01.020 --> 00:58:01.960 align:middle line:90% sorry. 00:58:01.960 --> 00:58:03.580 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:58:03.580 --> 00:58:07.820 align:middle line:84% AUDIENCE: I guess I was thinking that in the case that it's not-- 00:58:07.820 --> 00:58:14.223 align:middle line:84% I was thinking about of it being some ratio to the-- 00:58:14.223 --> 00:58:15.640 align:middle line:84% yeah, I guess I was thinking of it 00:58:15.640 --> 00:58:19.800 align:middle line:84% as being as it being some ratio to some reference to a term 00:58:19.800 --> 00:58:21.712 align:middle line:84% and that if the ratio is small, so it 00:58:21.712 --> 00:58:22.920 align:middle line:90% is worse than the reference-- 00:58:22.920 --> 00:58:24.795 align:middle line:84% HAZHIR RAHMANDAD: Oh, as soon as it is worse, 00:58:24.795 --> 00:58:26.880 align:middle line:84% it shouldn't then create-- and that 00:58:26.880 --> 00:58:31.080 align:middle line:84% was the point about this effect on your recruitment factor. 00:58:31.080 --> 00:58:34.000 align:middle line:84% Again, with the caveat that the Bass diffusion is 00:58:34.000 --> 00:58:36.640 align:middle line:84% kind of conflating two different things-- the diffusion 00:58:36.640 --> 00:58:40.040 align:middle line:84% of information about this thing that exists 00:58:40.040 --> 00:58:43.540 align:middle line:84% and the decision to actually become an investor. 00:58:43.540 --> 00:58:45.520 align:middle line:84% These two are separate from each other. 00:58:45.520 --> 00:58:50.520 align:middle line:84% In the current version, they are combined into a single action 00:58:50.520 --> 00:58:54.700 align:middle line:84% that is recruiting of investors whereas, in the real world, 00:58:54.700 --> 00:58:58.820 align:middle line:84% it is when a lot of people are investing with Ponzi, 00:58:58.820 --> 00:59:01.700 align:middle line:84% a lot of people will learn about this investment opportunity, 00:59:01.700 --> 00:59:04.120 align:middle line:84% and then they have a separate gate for deciding 00:59:04.120 --> 00:59:05.900 align:middle line:90% whether to invest in it or not. 00:59:05.900 --> 00:59:08.330 align:middle line:84% And that separate gate is informed 00:59:08.330 --> 00:59:11.170 align:middle line:84% by-- so I would probably, if I wanted to capture this 00:59:11.170 --> 00:59:13.690 align:middle line:84% separately, I would have, rather than 00:59:13.690 --> 00:59:15.890 align:middle line:84% this going to the recruited funds, 00:59:15.890 --> 00:59:22.010 align:middle line:84% it goes to considering Ponzi for investment or something 00:59:22.010 --> 00:59:22.750 align:middle line:90% like that. 00:59:22.750 --> 00:59:23.410 align:middle line:90% AUDIENCE: [INAUDIBLE] exposed. 00:59:23.410 --> 00:59:24.743 align:middle line:90% HAZHIR RAHMANDAD: Exposed, yeah. 00:59:24.743 --> 00:59:29.530 align:middle line:84% So that's kind of similar to the exposed state in the SCIR. 00:59:29.530 --> 00:59:30.532 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:59:30.532 --> 00:59:31.490 align:middle line:90% HAZHIR RAHMANDAD: Sure. 00:59:31.490 --> 00:59:32.865 align:middle line:84% AUDIENCE: --trust and confidence. 00:59:32.865 --> 00:59:38.970 align:middle line:84% So if you believe [INAUDIBLE] when 00:59:38.970 --> 00:59:42.530 align:middle line:84% I wanted to show this [INAUDIBLE] 00:59:42.530 --> 00:59:46.312 align:middle line:90% and then suddenly, [INAUDIBLE]. 00:59:46.312 --> 00:59:47.270 align:middle line:90% HAZHIR RAHMANDAD: Good. 00:59:47.270 --> 00:59:50.890 align:middle line:84% So if you have a stock, the signal 00:59:50.890 --> 00:59:52.930 align:middle line:84% that is going into it, whether this 00:59:52.930 --> 00:59:54.610 align:middle line:84% is the current version of the confidence 00:59:54.610 --> 00:59:57.730 align:middle line:84% that this model has or some alternative would have 00:59:57.730 --> 01:00:03.170 align:middle line:84% a sudden shift, but then, yes, the input 01:00:03.170 --> 01:00:08.670 align:middle line:84% into that delay function would have a sudden shift because-- 01:00:08.670 --> 01:00:10.350 align:middle line:90% and you would like it to have. 01:00:10.350 --> 01:00:12.590 align:middle line:84% The sudden shift comes from the fact 01:00:12.590 --> 01:00:16.610 align:middle line:84% that you don't have money to pay people or some other way. 01:00:16.610 --> 01:00:21.690 align:middle line:84% So for example, you may have people investigating you. 01:00:21.690 --> 01:00:23.790 align:middle line:84% Journalists were writing about Ponzi 01:00:23.790 --> 01:00:26.690 align:middle line:84% and investigating what is this guy doing. 01:00:26.690 --> 01:00:29.630 align:middle line:84% And that was actually the trigger mostly. 01:00:29.630 --> 01:00:34.590 align:middle line:84% So a couple of articles that came in Boston Globe and other-- 01:00:34.590 --> 01:00:36.130 align:middle line:84% I'm not sure if it was Boston Globe, 01:00:36.130 --> 01:00:40.310 align:middle line:84% but in a couple of news outlets were 01:00:40.310 --> 01:00:42.810 align:middle line:90% the triggers to runs on Ponzi. 01:00:42.810 --> 01:00:46.530 align:middle line:84% One of them, he managed to control the other one. 01:00:46.530 --> 01:00:49.590 align:middle line:84% He ultimately couldn't with some delay. 01:00:49.590 --> 01:00:55.750 align:middle line:84% So in that sense, there is the information 01:00:55.750 --> 01:01:00.230 align:middle line:84% coming in that is changing the trustworthiness 01:01:00.230 --> 01:01:03.070 align:middle line:84% of this investment very quickly, either because he's not 01:01:03.070 --> 01:01:06.490 align:middle line:84% paying people or because somebody is investigating them. 01:01:06.490 --> 01:01:09.690 align:middle line:84% Then there is the spread of that information in the population. 01:01:09.690 --> 01:01:16.350 align:middle line:84% And a simple delay has a kind of a delay in it, 01:01:16.350 --> 01:01:19.530 align:middle line:84% so people wouldn't know about it overnight. 01:01:19.530 --> 01:01:23.450 align:middle line:84% But in these cases, the real world of perception 01:01:23.450 --> 01:01:24.830 align:middle line:90% is very asymmetric. 01:01:24.830 --> 01:01:27.370 align:middle line:84% The adjustment time for that delay, 01:01:27.370 --> 01:01:31.470 align:middle line:84% if the confidence is increasing, people hear about it 01:01:31.470 --> 01:01:34.770 align:middle line:84% but more slowly because it's like, yeah, I actually 01:01:34.770 --> 01:01:37.750 align:middle line:84% haven't invested in Ponzi, and I got my money back. 01:01:37.750 --> 01:01:39.570 align:middle line:90% That's an interesting kind of-- 01:01:39.570 --> 01:01:41.450 align:middle line:84% I'm not sure if I will go and talk 01:01:41.450 --> 01:01:43.490 align:middle line:84% about it with a lot of people because now that's 01:01:43.490 --> 01:01:44.750 align:middle line:90% a good investment for me. 01:01:44.750 --> 01:01:48.750 align:middle line:84% I don't want others to saturate that investment opportunity. 01:01:48.750 --> 01:01:51.050 align:middle line:84% I'm more likely to just keep it to myself. 01:01:51.050 --> 01:01:53.930 align:middle line:84% But as soon as somebody is not paid, 01:01:53.930 --> 01:01:56.890 align:middle line:84% everybody starts shouting, oh, my cousin 01:01:56.890 --> 01:01:58.110 align:middle line:90% has invested with Ponzi. 01:01:58.110 --> 01:02:00.785 align:middle line:84% Let me call them and tell them or just go and bring them 01:02:00.785 --> 01:02:03.410 align:middle line:84% to the line because, otherwise, they wouldn't make their money. 01:02:03.410 --> 01:02:04.750 align:middle line:90% This thing is collapsing. 01:02:04.750 --> 01:02:10.350 align:middle line:84% So that asymmetry you can capture in the delay function 01:02:10.350 --> 01:02:11.970 align:middle line:90% for perception. 01:02:11.970 --> 01:02:16.270 align:middle line:84% So you would have a delay time that is very small when 01:02:16.270 --> 01:02:18.070 align:middle line:90% things are going down. 01:02:18.070 --> 01:02:23.150 align:middle line:84% But when things are going up, it would be a longer delay time. 01:02:23.150 --> 01:02:26.710 align:middle line:84% So that would be a little bit more advanced formulation 01:02:26.710 --> 01:02:27.930 align:middle line:90% but pretty standard. 01:02:27.930 --> 01:02:33.310 align:middle line:84% So is what I'm saying clear because-- 01:02:33.310 --> 01:02:34.250 align:middle line:90% yeah? 01:02:34.250 --> 01:02:35.750 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:02:35.750 --> 01:02:36.790 align:middle line:90% HAZHIR RAHMANDAD: Sure. 01:02:36.790 --> 01:02:43.150 align:middle line:84% So the switch would be basically the flow for the delay 01:02:43.150 --> 01:02:47.750 align:middle line:84% is desired minus current level of a stock divided by a time 01:02:47.750 --> 01:02:48.570 align:middle line:90% constant. 01:02:48.570 --> 01:02:51.850 align:middle line:84% So now, rather than dividing it by just the time constant, 01:02:51.850 --> 01:02:54.450 align:middle line:90% you divide it by if then else. 01:02:54.450 --> 01:02:55.590 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:02:55.590 --> 01:02:58.210 align:middle line:84% HAZHIR RAHMANDAD: Yes, desired is bigger than the stock T1. 01:02:58.210 --> 01:02:59.130 align:middle line:90% Otherwise, T2. 01:02:59.130 --> 01:03:01.770 align:middle line:90% That's all. 01:03:01.770 --> 01:03:04.530 align:middle line:90% So that was a good point. 01:03:04.530 --> 01:03:07.670 align:middle line:84% And I think that asymmetric delay may work well. 01:03:07.670 --> 01:03:11.030 align:middle line:84% So we kind of beat this model enough. 01:03:11.030 --> 01:03:14.510 align:middle line:84% Let's go to some random other one. 01:03:14.510 --> 01:03:15.570 align:middle line:90% So I don't know-- 01:03:15.570 --> 01:03:16.550 align:middle line:90% whose is this one. 01:03:16.550 --> 01:03:21.770 align:middle line:84% So Alban's, so let's take a look at Alban's model. 01:03:21.770 --> 01:03:28.890 align:middle line:84% So here, we have potential investors 01:03:28.890 --> 01:03:33.890 align:middle line:84% who invest who are waiting to be paid who are not 01:03:33.890 --> 01:03:36.650 align:middle line:90% interested in this scheme. 01:03:36.650 --> 01:03:39.850 align:middle line:90% The rate of becoming-- 01:03:39.850 --> 01:03:44.290 align:middle line:84% so with a payback time of, in this case, three months. 01:03:44.290 --> 01:03:45.910 align:middle line:90% Was it three months or 45 days? 01:03:45.910 --> 01:03:46.810 align:middle line:90% I don't remember. 01:03:46.810 --> 01:03:47.930 align:middle line:90% Was it three months? 01:03:47.930 --> 01:03:48.728 align:middle line:90% AUDIENCE: 45 days. 01:03:48.728 --> 01:03:49.770 align:middle line:90% AUDIENCE: It was 45 days. 01:03:49.770 --> 01:03:52.870 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:03:52.870 --> 01:03:58.690 align:middle line:84% HAZHIR RAHMANDAD: Yes, 45 days, 50%. 01:03:58.690 --> 01:04:02.110 align:middle line:84% So this is good because you get the investors going 01:04:02.110 --> 01:04:05.430 align:middle line:84% to this stock, and then they decide it's operationally 01:04:05.430 --> 01:04:08.030 align:middle line:84% a little bit cleaner to follow and kind of also 01:04:08.030 --> 01:04:09.370 align:middle line:90% avoids the problem with that. 01:04:09.370 --> 01:04:16.550 align:middle line:84% But of course, it adds one level of one additional stock. 01:04:16.550 --> 01:04:20.670 align:middle line:84% The Bass diffusion model idea is, again, pretty standard 01:04:20.670 --> 01:04:24.670 align:middle line:84% here, except that the adoption fraction also has some effective 01:04:24.670 --> 01:04:29.710 align:middle line:84% expected return rate, and expected return rate 01:04:29.710 --> 01:04:33.790 align:middle line:84% is coming from claimed interest rate of the scheme 01:04:33.790 --> 01:04:35.250 align:middle line:90% and confidence in the scheme. 01:04:35.250 --> 01:04:39.610 align:middle line:84% So this is very close to what we talked about right now. 01:04:39.610 --> 01:04:42.930 align:middle line:84% And we could take a look at how it is formulated. 01:04:42.930 --> 01:04:44.590 align:middle line:84% It is claimed interest rate multiplied 01:04:44.590 --> 01:04:46.310 align:middle line:90% by confidence in the scheme. 01:04:46.310 --> 01:04:48.950 align:middle line:90% 01:04:48.950 --> 01:04:51.130 align:middle line:90% It's largely unit-consistent. 01:04:51.130 --> 01:04:52.070 align:middle line:90% That's good. 01:04:52.070 --> 01:04:54.670 align:middle line:84% And then the confidence scheme is coming 01:04:54.670 --> 01:04:56.830 align:middle line:90% from that fulfillment ratio. 01:04:56.830 --> 01:04:59.810 align:middle line:84% So you may remember, we talked about one way 01:04:59.810 --> 01:05:03.370 align:middle line:84% to capture it is looking at how much he's 01:05:03.370 --> 01:05:06.810 align:middle line:84% paying people versus what people were expecting to be paid. 01:05:06.810 --> 01:05:10.210 align:middle line:84% And as soon as that ratio starts to fail, 01:05:10.210 --> 01:05:12.970 align:middle line:84% then you have a very strong signal. 01:05:12.970 --> 01:05:20.570 align:middle line:84% So that fulfillment ratio is a number between 0 and 1 01:05:20.570 --> 01:05:26.490 align:middle line:84% that he raises to a power for this sensitivity of confidence. 01:05:26.490 --> 01:05:30.530 align:middle line:84% And what should this sensitivity of confidence 01:05:30.530 --> 01:05:31.990 align:middle line:90% to fulfillment ratio be? 01:05:31.990 --> 01:05:34.690 align:middle line:90% Should it be below 1 or above 1? 01:05:34.690 --> 01:05:40.090 align:middle line:84% So that fulfillment ratio is a number between 0 and 1 01:05:40.090 --> 01:05:42.410 align:middle line:84% that says what fraction of what people 01:05:42.410 --> 01:05:45.130 align:middle line:90% are asking for you are paying. 01:05:45.130 --> 01:05:47.050 align:middle line:84% Would you put the sensitivity of confidence 01:05:47.050 --> 01:05:50.910 align:middle line:84% to fulfillment rate below 1 or above 1? 01:05:50.910 --> 01:05:52.930 align:middle line:90% That's the question. 01:05:52.930 --> 01:05:54.970 align:middle line:90% So think about it for a second. 01:05:54.970 --> 01:05:57.790 align:middle line:90% 01:05:57.790 --> 01:05:58.470 align:middle line:90% And why? 01:05:58.470 --> 01:06:11.270 align:middle line:90% 01:06:11.270 --> 01:06:12.670 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:06:12.670 --> 01:06:13.690 align:middle line:84% HAZHIR RAHMANDAD: So you would say below. 01:06:13.690 --> 01:06:14.190 align:middle line:90% Why? 01:06:14.190 --> 01:06:17.350 align:middle line:90% 01:06:17.350 --> 01:06:20.950 align:middle line:84% AUDIENCE: Well, not really because-- 01:06:20.950 --> 01:06:23.670 align:middle line:84% HAZHIR RAHMANDAD: So if I'm paying only 50% 01:06:23.670 --> 01:06:30.190 align:middle line:84% of what people are asking for, if I go with a below 1 number, 01:06:30.190 --> 01:06:36.470 align:middle line:84% then the indicated confidence will be 0.9. 01:06:36.470 --> 01:06:38.570 align:middle line:84% If you actually want it to be close-- 01:06:38.570 --> 01:06:42.150 align:middle line:84% if I pay even 90% of what people are owed, 01:06:42.150 --> 01:06:44.910 align:middle line:84% that's usually signal enough that this thing is going 01:06:44.910 --> 01:06:47.210 align:middle line:90% to be bankrupt in 24 hours. 01:06:47.210 --> 01:06:51.470 align:middle line:84% Everybody will be attacking the doors of Ponzi. 01:06:51.470 --> 01:06:54.530 align:middle line:84% So that means the confidence or indicated confidence 01:06:54.530 --> 01:07:01.310 align:middle line:84% should now go down to 0.01 or something, 01:07:01.310 --> 01:07:02.650 align:middle line:90% some very small number. 01:07:02.650 --> 01:07:05.930 align:middle line:90% So that requires a much-- 01:07:05.930 --> 01:07:10.150 align:middle line:90% I mean, above 1 number. 01:07:10.150 --> 01:07:12.830 align:middle line:90% So that's to think about this. 01:07:12.830 --> 01:07:18.610 align:middle line:84% And then, to his credit, Alban has the asymmetric adjustment 01:07:18.610 --> 01:07:19.310 align:middle line:90% here as well. 01:07:19.310 --> 01:07:22.350 align:middle line:84% So basically, he's accounting for that difference, 01:07:22.350 --> 01:07:23.350 align:middle line:90% which is very nice. 01:07:23.350 --> 01:07:29.382 align:middle line:84% It's exactly the formulation we just talked about [INAUDIBLE]. 01:07:29.382 --> 01:07:30.630 align:middle line:90% So that's good. 01:07:30.630 --> 01:07:37.570 align:middle line:84% And then this confidence, the parts 01:07:37.570 --> 01:07:44.890 align:middle line:84% that are feeding into adoption, it's an interesting part 01:07:44.890 --> 01:07:48.930 align:middle line:84% because this needs to go to 0, essentially, 01:07:48.930 --> 01:07:52.290 align:middle line:84% as soon as confidence starts to go down. 01:07:52.290 --> 01:08:03.970 align:middle line:90% 01:08:03.970 --> 01:08:09.310 align:middle line:84% So then Alban also has the effect 01:08:09.310 --> 01:08:16.550 align:middle line:84% of expected interest rate on fraction returning, which 01:08:16.550 --> 01:08:18.490 align:middle line:90% is good. 01:08:18.490 --> 01:08:21.950 align:middle line:84% I like to use the same effect here 01:08:21.950 --> 01:08:23.550 align:middle line:84% because, conceptually, it is coming 01:08:23.550 --> 01:08:26.609 align:middle line:84% from the same underlying cost-benefit analysis, 01:08:26.609 --> 01:08:28.910 align:middle line:84% so creating a separate channel for it 01:08:28.910 --> 01:08:31.990 align:middle line:84% would not be adding much value, and it introduces 01:08:31.990 --> 01:08:35.029 align:middle line:90% more free parameters. 01:08:35.029 --> 01:08:36.490 align:middle line:90% So this is fine. 01:08:36.490 --> 01:08:40.950 align:middle line:90% 01:08:40.950 --> 01:08:43.630 align:middle line:90% Let's see. 01:08:43.630 --> 01:08:44.790 align:middle line:90% Yes? 01:08:44.790 --> 01:08:46.670 align:middle line:84% AUDIENCE: So I know a few of the submissions 01:08:46.670 --> 01:08:51.010 align:middle line:84% have this idea of investors who are active investors who 01:08:51.010 --> 01:08:51.850 align:middle line:90% are waiting. 01:08:51.850 --> 01:08:55.410 align:middle line:84% But it seems like the only residence time in the w 01:08:55.410 --> 01:09:00.569 align:middle line:84% here is the minimum processing time. 01:09:00.569 --> 01:09:04.149 align:middle line:84% Couldn't you just have combined the two stocks? 01:09:04.149 --> 01:09:08.850 align:middle line:90% 01:09:08.850 --> 01:09:11.970 align:middle line:84% I guess I'm just asking what the purpose of it is. 01:09:11.970 --> 01:09:14.689 align:middle line:84% HAZHIR RAHMANDAD: So the purpose of this stock? 01:09:14.689 --> 01:09:16.897 align:middle line:90% AUDIENCE: Yeah. 01:09:16.897 --> 01:09:18.689 align:middle line:84% HAZHIR RAHMANDAD: Yes, you could combine it 01:09:18.689 --> 01:09:22.330 align:middle line:84% because it is a short period of time. 01:09:22.330 --> 01:09:26.710 align:middle line:84% And that short period of time is coming from-- 01:09:26.710 --> 01:09:28.210 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:09:28.210 --> 01:09:31.010 align:middle line:84% HAZHIR RAHMANDAD: Minimum money processing time. 01:09:31.010 --> 01:09:36.130 align:middle line:84% Well, part of it is coming from that. 01:09:36.130 --> 01:09:37.069 align:middle line:90% Yes, that's true. 01:09:37.069 --> 01:09:38.550 align:middle line:90% That's the main driver. 01:09:38.550 --> 01:09:44.689 align:middle line:84% So the time constant in that stock is fairly short 01:09:44.689 --> 01:09:46.870 align:middle line:84% and, therefore, there shouldn't be many people 01:09:46.870 --> 01:09:48.250 align:middle line:90% left in that stock. 01:09:48.250 --> 01:09:51.630 align:middle line:90% 01:09:51.630 --> 01:09:53.710 align:middle line:84% And then you go back to the formulation 01:09:53.710 --> 01:09:56.890 align:middle line:84% we saw with Ali's model, which I think is fine. 01:09:56.890 --> 01:10:00.250 align:middle line:84% I don't think there is any problem with using that. 01:10:00.250 --> 01:10:02.830 align:middle line:84% The only thing is that this allows 01:10:02.830 --> 01:10:06.350 align:middle line:84% you to track people a little bit more concretely 01:10:06.350 --> 01:10:11.250 align:middle line:84% in this intermediate state, that they want to be paid, 01:10:11.250 --> 01:10:16.050 align:middle line:84% but they are not accruing additional liability. 01:10:16.050 --> 01:10:18.590 align:middle line:90% So that's the core issue. 01:10:18.590 --> 01:10:25.390 align:middle line:84% So that way, he can basically say, OK, I will pay. 01:10:25.390 --> 01:10:27.710 align:middle line:84% As soon as somebody gives me money, 01:10:27.710 --> 01:10:32.430 align:middle line:84% I'll add 50% to it or 100% to it depending on what time. 01:10:32.430 --> 01:10:37.170 align:middle line:84% So he's using one third per month. 01:10:37.170 --> 01:10:40.190 align:middle line:90% 01:10:40.190 --> 01:10:41.570 align:middle line:90% Why is it per month? 01:10:41.570 --> 01:10:44.270 align:middle line:90% So this is actually interesting. 01:10:44.270 --> 01:10:46.730 align:middle line:84% I am not following what is happening. 01:10:46.730 --> 01:10:48.287 align:middle line:90% AUDIENCE: Alban, [INAUDIBLE]. 01:10:48.287 --> 01:10:49.870 align:middle line:84% HAZHIR RAHMANDAD: Oh, Alban, go ahead. 01:10:49.870 --> 01:10:53.770 align:middle line:90% 01:10:53.770 --> 01:10:57.050 align:middle line:84% AUDIENCE: Oh, I was just trying to say that [INAUDIBLE] 01:10:57.050 --> 01:11:00.170 align:middle line:84% to start because the word of mouth 01:11:00.170 --> 01:11:02.730 align:middle line:84% is only coming from an active investor, 01:11:02.730 --> 01:11:04.670 align:middle line:84% once you are waiting in the line, 01:11:04.670 --> 01:11:07.430 align:middle line:84% you're probably waiting for get paid. 01:11:07.430 --> 01:11:10.718 align:middle line:84% And if the fulfillment ratio is not 1, 01:11:10.718 --> 01:11:13.010 align:middle line:84% then you are waiting in line to get there, you probably 01:11:13.010 --> 01:11:15.530 align:middle line:90% don't [INAUDIBLE]. 01:11:15.530 --> 01:11:18.530 align:middle line:84% HAZHIR RAHMANDAD: So that's another reason 01:11:18.530 --> 01:11:20.150 align:middle line:90% that might be a good reason. 01:11:20.150 --> 01:11:22.910 align:middle line:84% But now there is an interesting piece here. 01:11:22.910 --> 01:11:27.610 align:middle line:84% If I understand it correctly, Alban, 01:11:27.610 --> 01:11:31.970 align:middle line:84% when you have debt in the scheme, 01:11:31.970 --> 01:11:38.210 align:middle line:84% that debt continues to grow until you are paid 01:11:38.210 --> 01:11:41.120 align:middle line:90% and you get out of-- 01:11:41.120 --> 01:11:44.020 align:middle line:90% you're cashed out, correct? 01:11:44.020 --> 01:11:44.980 align:middle line:90% AUDIENCE: Yes. 01:11:44.980 --> 01:11:47.480 align:middle line:84% HAZHIR RAHMANDAD: So at least in Ponzi's story, 01:11:47.480 --> 01:11:48.560 align:middle line:90% that's not how it works. 01:11:48.560 --> 01:11:52.060 align:middle line:84% Basically, as soon as the term has finished, 01:11:52.060 --> 01:11:54.740 align:middle line:90% you are not accruing interest. 01:11:54.740 --> 01:11:58.740 align:middle line:84% So the formulation for that inflow-- 01:11:58.740 --> 01:12:01.340 align:middle line:84% so that was why I was a bit confused 01:12:01.340 --> 01:12:04.960 align:middle line:90% was it can be even simpler. 01:12:04.960 --> 01:12:09.140 align:middle line:84% You don't need the debt in the scheme multiplied 01:12:09.140 --> 01:12:11.040 align:middle line:90% by claimed interest rate. 01:12:11.040 --> 01:12:12.940 align:middle line:84% You just need a claimed interest rate that 01:12:12.940 --> 01:12:18.060 align:middle line:90% is a fraction of the cash in. 01:12:18.060 --> 01:12:21.700 align:middle line:84% So it would be 1 plus that fraction. 01:12:21.700 --> 01:12:26.420 align:middle line:84% So if it is 50% over 45 days, it would 01:12:26.420 --> 01:12:29.140 align:middle line:90% be 1.5 multiplied by cashed in. 01:12:29.140 --> 01:12:31.900 align:middle line:84% And then that becomes how much he owes people 01:12:31.900 --> 01:12:34.600 align:middle line:90% as soon as they are going in. 01:12:34.600 --> 01:12:38.180 align:middle line:84% You don't accumulate this forever. 01:12:38.180 --> 01:12:41.820 align:middle line:84% That would do a better job of accounting here 01:12:41.820 --> 01:12:45.440 align:middle line:84% than the current version because here, people who are investors 01:12:45.440 --> 01:12:49.720 align:middle line:84% there waiting to be paid continue to accrue liability 01:12:49.720 --> 01:12:54.500 align:middle line:84% or Ponzi continues to accrue liability. 01:12:54.500 --> 01:12:58.120 align:middle line:90% So that's a minor-- 01:12:58.120 --> 01:13:00.403 align:middle line:84% AUDIENCE: Yeah, I misunderstood the [? contract. ?] 01:13:00.403 --> 01:13:01.820 align:middle line:84% HAZHIR RAHMANDAD: No, that's fine. 01:13:01.820 --> 01:13:04.920 align:middle line:90% That's otherwise pretty good. 01:13:04.920 --> 01:13:05.740 align:middle line:90% Let's see. 01:13:05.740 --> 01:13:09.400 align:middle line:84% Then there is the max cash out that 01:13:09.400 --> 01:13:15.740 align:middle line:84% should control the actual cash out, which does. 01:13:15.740 --> 01:13:22.040 align:middle line:84% And then this creates the debt fulfillment ratio, which 01:13:22.040 --> 01:13:35.280 align:middle line:90% impacts actual getting paid. 01:13:35.280 --> 01:13:39.700 align:middle line:84% And then that impacts people who leave. 01:13:39.700 --> 01:13:44.900 align:middle line:84% And what fraction return depends on effect of expected interest 01:13:44.900 --> 01:13:45.540 align:middle line:90% rate. 01:13:45.540 --> 01:13:48.120 align:middle line:90% Now I think this is all good. 01:13:48.120 --> 01:13:52.600 align:middle line:84% There is a subtle thing here, pretty subtle, 01:13:52.600 --> 01:13:56.580 align:middle line:84% but it might be interesting to think through it. 01:13:56.580 --> 01:14:03.540 align:middle line:84% So let's assume that fulfillment ratio overnight 01:14:03.540 --> 01:14:06.140 align:middle line:90% falls from 1 to 0. 01:14:06.140 --> 01:14:09.500 align:middle line:84% Basically, this is the night that Ponzi goes bust. 01:14:09.500 --> 01:14:14.400 align:middle line:84% So the confidence in the scheme starts to go down very rapidly. 01:14:14.400 --> 01:14:18.180 align:middle line:84% But it actually starts at a high level. 01:14:18.180 --> 01:14:22.100 align:middle line:84% So the fraction returning to Ponzi 01:14:22.100 --> 01:14:24.600 align:middle line:84% will actually be 1 at the very beginning of it, 01:14:24.600 --> 01:14:26.440 align:middle line:90% or a large number. 01:14:26.440 --> 01:14:30.700 align:middle line:84% Most of them will return to put their money back. 01:14:30.700 --> 01:14:33.660 align:middle line:84% But at that very point in time, these 01:14:33.660 --> 01:14:36.820 align:middle line:84% are people who are not being paid. 01:14:36.820 --> 01:14:40.840 align:middle line:84% That is, the actual getting paid is much smaller. 01:14:40.840 --> 01:14:43.720 align:middle line:84% So for a period, because of the delay 01:14:43.720 --> 01:14:46.200 align:middle line:84% in confidence in the scheme, you have 01:14:46.200 --> 01:14:49.520 align:middle line:84% people who are not paid but still are going 01:14:49.520 --> 01:14:53.080 align:middle line:90% back and reinvesting in Ponzi. 01:14:53.080 --> 01:14:58.920 align:middle line:84% And that's just not how the things would actually work. 01:14:58.920 --> 01:15:02.360 align:middle line:84% So I probably would have this fraction 01:15:02.360 --> 01:15:07.200 align:middle line:84% returning to A to be bounded by the debt fulfillment ratio 01:15:07.200 --> 01:15:07.700 align:middle line:90% as well. 01:15:07.700 --> 01:15:10.920 align:middle line:84% That is, it shouldn't go above that or something like that. 01:15:10.920 --> 01:15:12.440 align:middle line:90% Is that clear? 01:15:12.440 --> 01:15:14.180 align:middle line:90% Yeah, go ahead. 01:15:14.180 --> 01:15:16.960 align:middle line:84% AUDIENCE: Well, so I know we've kind of been talking 01:15:16.960 --> 01:15:21.420 align:middle line:84% a lot about the confidence idea, but in my head, 01:15:21.420 --> 01:15:23.760 align:middle line:84% system confidence is always going 01:15:23.760 --> 01:15:30.720 align:middle line:84% to be either 1 or 0 basically because that's basically 01:15:30.720 --> 01:15:32.880 align:middle line:84% what the debt [INAUDIBLE] rate is going to be. 01:15:32.880 --> 01:15:36.380 align:middle line:84% Either people are getting paid or one person didn't and now 01:15:36.380 --> 01:15:39.060 align:middle line:84% it's all canceled, and Ponzi probably won't even 01:15:39.060 --> 01:15:41.083 align:middle line:84% talk to new investors because he knows, 01:15:41.083 --> 01:15:43.000 align:middle line:84% eventually, somebody's going to come from him, 01:15:43.000 --> 01:15:44.620 align:middle line:84% so he's going to get out of there. 01:15:44.620 --> 01:15:49.300 align:middle line:84% So it feels like the confidence matters less on the system 01:15:49.300 --> 01:15:53.060 align:middle line:84% confidence and more just on your exposure to-- an individual's 01:15:53.060 --> 01:15:57.303 align:middle line:84% exposure to the idea that this can work and has worked. 01:15:57.303 --> 01:15:59.220 align:middle line:84% HAZHIR RAHMANDAD: So that's a good observation 01:15:59.220 --> 01:16:00.160 align:middle line:90% on the downside. 01:16:00.160 --> 01:16:05.260 align:middle line:84% That is, as soon as there is no payment to even a single person, 01:16:05.260 --> 01:16:07.740 align:middle line:84% things will unravel very quickly. 01:16:07.740 --> 01:16:11.140 align:middle line:84% But on the upside that is people building confidence 01:16:11.140 --> 01:16:13.480 align:middle line:84% into it, the reason at the very beginning, 01:16:13.480 --> 01:16:16.460 align:middle line:84% these schemes don't go to the roof is 01:16:16.460 --> 01:16:18.080 align:middle line:90% that most people are skeptical. 01:16:18.080 --> 01:16:20.500 align:middle line:84% That is, their initial assessment 01:16:20.500 --> 01:16:22.400 align:middle line:90% is that it's probably a scheme. 01:16:22.400 --> 01:16:24.620 align:middle line:90% We haven't seen the evidence. 01:16:24.620 --> 01:16:26.600 align:middle line:84% Maybe it takes a couple of years. 01:16:26.600 --> 01:16:27.440 align:middle line:90% But we are not-- 01:16:27.440 --> 01:16:28.800 align:middle line:90% I'm not going to invest in it. 01:16:28.800 --> 01:16:32.900 align:middle line:84% So that building of confidence, it starts from a small number. 01:16:32.900 --> 01:16:37.320 align:middle line:84% That is, their priors is that 90% this is just a scam. 01:16:37.320 --> 01:16:42.420 align:middle line:84% But after six months, I'm seeing my friends getting paid back. 01:16:42.420 --> 01:16:45.080 align:middle line:84% I would say, well, maybe it is not 90%. 01:16:45.080 --> 01:16:48.680 align:middle line:84% Now, it is 60% in my assessment, and I haven't 01:16:48.680 --> 01:16:50.620 align:middle line:90% seen any negative signal. 01:16:50.620 --> 01:16:57.100 align:middle line:84% As soon as I see a negative signal, hell breaks loose. 01:16:57.100 --> 01:16:57.900 align:middle line:90% Yeah? 01:16:57.900 --> 01:17:01.400 align:middle line:84% AUDIENCE: [INAUDIBLE] also have average investment [INAUDIBLE]? 01:17:01.400 --> 01:17:04.000 align:middle line:90% 01:17:04.000 --> 01:17:07.560 align:middle line:84% HAZHIR RAHMANDAD: We could, but then we 01:17:07.560 --> 01:17:10.800 align:middle line:84% are kind of adding a mechanism that is already 01:17:10.800 --> 01:17:15.760 align:middle line:84% can be captured in the number of investors. 01:17:15.760 --> 01:17:20.060 align:middle line:84% So in a way, I think what Ali and Hesam did, 01:17:20.060 --> 01:17:23.120 align:middle line:84% which was how much money can be invested, 01:17:23.120 --> 01:17:24.860 align:middle line:84% takes care of that to some extent, 01:17:24.860 --> 01:17:28.002 align:middle line:84% although it has its own kind of storytelling problems, 01:17:28.002 --> 01:17:29.460 align:middle line:84% that money doesn't talk with money, 01:17:29.460 --> 01:17:32.180 align:middle line:84% it is people who talk with each other. 01:17:32.180 --> 01:17:36.500 align:middle line:84% But I'm OK with keeping it simpler this way 01:17:36.500 --> 01:17:39.432 align:middle line:84% rather than making the amount of investment endogenous, 01:17:39.432 --> 01:17:41.640 align:middle line:84% even though, in practice, that was part of the story. 01:17:41.640 --> 01:17:44.860 align:middle line:84% That is, people would go, yeah, I just put a dollar here and see 01:17:44.860 --> 01:17:46.320 align:middle line:90% what happens. 01:17:46.320 --> 01:17:47.820 align:middle line:84% But next time, if it worked, I would 01:17:47.820 --> 01:17:52.740 align:middle line:84% put $10 or whatever was the scale of the investment. 01:17:52.740 --> 01:17:55.000 align:middle line:90% AUDIENCE: The idea [INAUDIBLE]. 01:17:55.000 --> 01:17:56.460 align:middle line:90% HAZHIR RAHMANDAD: Go ahead. 01:17:56.460 --> 01:17:58.180 align:middle line:84% AUDIENCE: On the idea of the [INAUDIBLE] 01:17:58.180 --> 01:18:02.260 align:middle line:84% I still feel like that's not necessarily a system confidence 01:18:02.260 --> 01:18:02.760 align:middle line:90% thing. 01:18:02.760 --> 01:18:04.980 align:middle line:84% I am becoming more confident because I 01:18:04.980 --> 01:18:07.940 align:middle line:84% have been exposed to more and more of my friends 01:18:07.940 --> 01:18:10.200 align:middle line:90% who have been successful. 01:18:10.200 --> 01:18:13.960 align:middle line:84% So that isn't that going to be, on the individual level, 01:18:13.960 --> 01:18:20.100 align:middle line:84% dependent on percentage exposure of my friends who have done it? 01:18:20.100 --> 01:18:26.100 align:middle line:84% HAZHIR RAHMANDAD: So partly yes, but partly 01:18:26.100 --> 01:18:28.660 align:middle line:84% depends on information diffusion mechanism 01:18:28.660 --> 01:18:31.540 align:middle line:84% you hypothesize is operating in that environment. 01:18:31.540 --> 01:18:33.180 align:middle line:90% So is it only my friends? 01:18:33.180 --> 01:18:36.720 align:middle line:84% Do I see news items about Ponzi and this scheme 01:18:36.720 --> 01:18:39.160 align:middle line:90% that might be actually working? 01:18:39.160 --> 01:18:42.980 align:middle line:84% Do I hear from people talking about it in the corner streets? 01:18:42.980 --> 01:18:47.800 align:middle line:84% So the more you expand that, the more generic 01:18:47.800 --> 01:18:50.920 align:middle line:84% for the whole population, you can talk about. 01:18:50.920 --> 01:18:53.530 align:middle line:84% Now the Bass diffusion model is essentially doing that. 01:18:53.530 --> 01:18:55.280 align:middle line:84% That is, it is saying people talk about it 01:18:55.280 --> 01:18:58.492 align:middle line:84% with their friends, and if they have experienced it, 01:18:58.492 --> 01:18:59.700 align:middle line:90% they will talk about it more. 01:18:59.700 --> 01:19:03.800 align:middle line:84% So you could basically think of this Bass diffusion model 01:19:03.800 --> 01:19:07.280 align:middle line:84% to be doing that for you with the caveat that I mentioned, 01:19:07.280 --> 01:19:10.320 align:middle line:84% that Bass diffusion model takes people to the state of I 01:19:10.320 --> 01:19:12.280 align:middle line:90% am now considering. 01:19:12.280 --> 01:19:15.600 align:middle line:84% And then there is a process of conversion 01:19:15.600 --> 01:19:18.080 align:middle line:84% that may take some time and depends 01:19:18.080 --> 01:19:20.840 align:middle line:84% on whether that expected rate of return 01:19:20.840 --> 01:19:24.460 align:middle line:84% is high enough at that point in time, based on their perception. 01:19:24.460 --> 01:19:27.420 align:middle line:90% 01:19:27.420 --> 01:19:31.380 align:middle line:84% So I think this is a pretty good model, Alban. 01:19:31.380 --> 01:19:34.660 align:middle line:84% I haven't checked every equation. 01:19:34.660 --> 01:19:36.460 align:middle line:84% So let's actually do a simulation here 01:19:36.460 --> 01:19:41.480 align:middle line:84% to just see what's the baseline behavior in the model. 01:19:41.480 --> 01:19:46.000 align:middle line:90% So we have investors. 01:19:46.000 --> 01:19:52.180 align:middle line:90% 01:19:52.180 --> 01:19:54.000 align:middle line:84% So more and more people are investing. 01:19:54.000 --> 01:19:55.480 align:middle line:90% But at some point, it stops. 01:19:55.480 --> 01:19:58.420 align:middle line:84% And the reason it stops is that the confidence 01:19:58.420 --> 01:20:04.000 align:middle line:84% crashes because it has a very short delay. 01:20:04.000 --> 01:20:08.000 align:middle line:84% So you see that the confidence goes up slowly as we discussed 01:20:08.000 --> 01:20:09.400 align:middle line:90% and then crashes very quickly. 01:20:09.400 --> 01:20:15.300 align:middle line:84% This asymmetry delay does the job nicely here. 01:20:15.300 --> 01:20:22.660 align:middle line:84% And then the cash in this scheme, it is crashing. 01:20:22.660 --> 01:20:27.520 align:middle line:84% It's an interesting double dip here. 01:20:27.520 --> 01:20:32.320 align:middle line:84% So what is happening that is creating that double dip? 01:20:32.320 --> 01:20:41.020 align:middle line:84% So part of it is cash out being slowed down, I think. 01:20:41.020 --> 01:20:44.940 align:middle line:84% And then part of it is cash in being shut down. 01:20:44.940 --> 01:20:54.680 align:middle line:84% So if we look at what is driving it, so cashing 01:20:54.680 --> 01:20:58.740 align:middle line:84% slows down for a little bit and then crashes. 01:20:58.740 --> 01:21:02.080 align:middle line:90% 01:21:02.080 --> 01:21:06.880 align:middle line:84% Cash out starts to go down because of the constraint 01:21:06.880 --> 01:21:09.700 align:middle line:90% on how fast you pay. 01:21:09.700 --> 01:21:22.040 align:middle line:90% 01:21:22.040 --> 01:21:23.360 align:middle line:90% So max cash out-- 01:21:23.360 --> 01:21:25.840 align:middle line:90% 13 million. 01:21:25.840 --> 01:21:28.980 align:middle line:84% Yes, this is exactly when the max cash out 01:21:28.980 --> 01:21:33.180 align:middle line:84% starts to become the binding constraint. 01:21:33.180 --> 01:21:40.900 align:middle line:84% So for a few periods, max cash out keeps the stock of cash 01:21:40.900 --> 01:21:43.200 align:middle line:90% to go down even faster. 01:21:43.200 --> 01:21:44.720 align:middle line:90% But then there is no inflow. 01:21:44.720 --> 01:21:51.280 align:middle line:90% And then it goes to 0. 01:21:51.280 --> 01:21:54.180 align:middle line:90% That all makes sense. 01:21:54.180 --> 01:21:59.560 align:middle line:84% And then you have investors that are waiting to be paid. 01:21:59.560 --> 01:22:03.100 align:middle line:90% 01:22:03.100 --> 01:22:09.140 align:middle line:84% So when he can't pay, basically, people wait there to be paid. 01:22:09.140 --> 01:22:13.020 align:middle line:84% And that actually creates an interesting reinforcing loop 01:22:13.020 --> 01:22:17.780 align:middle line:84% because then you have desired to be getting paid 01:22:17.780 --> 01:22:22.100 align:middle line:84% and, therefore, you have bigger desired cash out. 01:22:22.100 --> 01:22:26.720 align:middle line:84% I mean that strengthens the rapid adjustment 01:22:26.720 --> 01:22:28.440 align:middle line:84% at that point in time because you can 01:22:28.440 --> 01:22:31.160 align:middle line:90% settle your accounts basically. 01:22:31.160 --> 01:22:34.720 align:middle line:84% I think the behavior makes sense in this case. 01:22:34.720 --> 01:22:37.120 align:middle line:84% One thing that would have been nice to have 01:22:37.120 --> 01:22:40.500 align:middle line:90% here is to have two things. 01:22:40.500 --> 01:22:45.040 align:middle line:84% One is to have actual return of the investment, 01:22:45.040 --> 01:22:47.440 align:middle line:84% if Ponzi was actually making money or investing 01:22:47.440 --> 01:22:50.640 align:middle line:84% this in some meaningful investment that 01:22:50.640 --> 01:22:52.480 align:middle line:90% had a rate of return here. 01:22:52.480 --> 01:22:56.440 align:middle line:84% And then comparison of expected rate 01:22:56.440 --> 01:23:03.160 align:middle line:84% of return of the scheme versus some outside option for people 01:23:03.160 --> 01:23:06.520 align:middle line:84% for their investments so that they decide whether to-- 01:23:06.520 --> 01:23:08.460 align:middle line:84% so this adoption fraction comes from that. 01:23:08.460 --> 01:23:12.480 align:middle line:84% It is kind of built into this max effect and sensitivity 01:23:12.480 --> 01:23:13.420 align:middle line:90% factors. 01:23:13.420 --> 01:23:16.560 align:middle line:84% But having an explicit external investment option 01:23:16.560 --> 01:23:18.020 align:middle line:90% would make it nicer. 01:23:18.020 --> 01:23:19.380 align:middle line:90% But this is pretty good. 01:23:19.380 --> 01:23:23.460 align:middle line:90% 01:23:23.460 --> 01:23:28.620 align:middle line:84% So maybe we should take a break, 10-minutes. 01:23:28.620 --> 01:23:31.260 align:middle line:84% We can come back and look at a few more models 01:23:31.260 --> 01:23:36.460 align:middle line:84% and then go to the next few weeks assignment. 01:23:36.460 --> 01:23:41.960 align:middle line:84% So maybe for this part, let's get volunteers. 01:23:41.960 --> 01:23:45.780 align:middle line:84% Who wants us to look at their model? 01:23:45.780 --> 01:23:46.620 align:middle line:90% Cathy? 01:23:46.620 --> 01:23:47.240 align:middle line:90% Sure. 01:23:47.240 --> 01:23:50.980 align:middle line:90% 01:23:50.980 --> 01:23:51.920 align:middle line:90% Let's see. 01:23:51.920 --> 01:23:54.510 align:middle line:90% This is Cathy. 01:23:54.510 --> 01:23:55.260 align:middle line:90% AUDIENCE: I think? 01:23:55.260 --> 01:23:55.580 align:middle line:90% Yeah. 01:23:55.580 --> 01:23:57.380 align:middle line:84% So I don't have liabilities, and then I 01:23:57.380 --> 01:24:00.020 align:middle line:84% think I heard you say-- so I'm driving 01:24:00.020 --> 01:24:04.442 align:middle line:84% the kind of indicated payout to current payout from the flows. 01:24:04.442 --> 01:24:05.900 align:middle line:84% HAZHIR RAHMANDAD: So let's actually 01:24:05.900 --> 01:24:09.100 align:middle line:84% look at that because let's see whether it works 01:24:09.100 --> 01:24:10.480 align:middle line:90% or what are the challenges. 01:24:10.480 --> 01:24:13.780 align:middle line:84% So basically, you have cash on hand. 01:24:13.780 --> 01:24:17.300 align:middle line:84% And it is coming from investment and average investment 01:24:17.300 --> 01:24:21.150 align:middle line:90% amount and something else. 01:24:21.150 --> 01:24:23.250 align:middle line:84% It's investment or reinvesting also. 01:24:23.250 --> 01:24:24.910 align:middle line:90% That's fine. 01:24:24.910 --> 01:24:32.710 align:middle line:84% AUDIENCE: Oh, and I also found a bug at 908 in my investors stock 01:24:32.710 --> 01:24:33.650 align:middle line:90% formulation. 01:24:33.650 --> 01:24:36.130 align:middle line:84% Could you click into the equation for that really-- 01:24:36.130 --> 01:24:39.173 align:middle line:84% HAZHIR RAHMANDAD: So in the investor stock formulation. 01:24:39.173 --> 01:24:41.590 align:middle line:84% AUDIENCE: It should be minus reinvesting plus reinvesting. 01:24:41.590 --> 01:24:45.230 align:middle line:84% I think when it autopopulated it-- 01:24:45.230 --> 01:24:48.880 align:middle line:84% it should be both minus and plus. 01:24:48.880 --> 01:24:50.630 align:middle line:84% HAZHIR RAHMANDAD: Sorry, what do you mean? 01:24:50.630 --> 01:24:52.910 align:middle line:84% AUDIENCE: Like minus reinvest plus reinvest. 01:24:52.910 --> 01:24:54.868 align:middle line:84% AUDIENCE: It goes out and then it goes back in? 01:24:54.868 --> 01:24:55.555 align:middle line:90% AUDIENCE: Yeah. 01:24:55.555 --> 01:24:56.430 align:middle line:90% HAZHIR RAHMANDAD: Ah. 01:24:56.430 --> 01:24:59.190 align:middle line:90% 01:24:59.190 --> 01:25:02.400 align:middle line:84% So what it basically means is that it doesn't have any impact. 01:25:02.400 --> 01:25:03.150 align:middle line:90% AUDIENCE: Exactly. 01:25:03.150 --> 01:25:04.450 align:middle line:90% So I wanted to ask about that. 01:25:04.450 --> 01:25:09.470 align:middle line:84% I wanted this capturing thing to happen just 01:25:09.470 --> 01:25:11.330 align:middle line:90% for face validity reasons. 01:25:11.330 --> 01:25:15.470 align:middle line:84% And then [INAUDIBLE] overwrites it every time I 01:25:15.470 --> 01:25:16.530 align:middle line:90% open the formula. 01:25:16.530 --> 01:25:20.650 align:middle line:84% And so that indicates that it's not that good. 01:25:20.650 --> 01:25:22.330 align:middle line:84% And I think that the better way to do 01:25:22.330 --> 01:25:27.810 align:middle line:84% it is this two-flow maturing investor thing. 01:25:27.810 --> 01:25:30.610 align:middle line:84% HAZHIR RAHMANDAD: And basically, that's what you-- 01:25:30.610 --> 01:25:32.167 align:middle line:84% it forces you to do for good reasons 01:25:32.167 --> 01:25:34.250 align:middle line:84% because, otherwise, it's very confusing for people 01:25:34.250 --> 01:25:34.910 align:middle line:90% looking at it. 01:25:34.910 --> 01:25:38.050 align:middle line:84% And then it really doesn't have any impact on that stock. 01:25:38.050 --> 01:25:41.070 align:middle line:84% So basically, you would have an outflow and an inflow. 01:25:41.070 --> 01:25:43.990 align:middle line:84% And then the outflow informs the inflow directly. 01:25:43.990 --> 01:25:45.630 align:middle line:90% AUDIENCE: Exactly. 01:25:45.630 --> 01:25:50.070 align:middle line:84% So these are discrete packets of, like, you have your 45 days. 01:25:50.070 --> 01:25:52.437 align:middle line:90% 01:25:52.437 --> 01:25:54.270 align:middle line:84% I guess, the way I was thinking about it is. 01:25:54.270 --> 01:25:57.150 align:middle line:84% You just need not investors and investors. 01:25:57.150 --> 01:26:00.130 align:middle line:84% And they can just cycle between each other. 01:26:00.130 --> 01:26:02.570 align:middle line:84% The whole reinvesting thing is not at all-- 01:26:02.570 --> 01:26:06.510 align:middle line:84% the actual individual, whether they [INAUDIBLE] doesn't matter. 01:26:06.510 --> 01:26:07.730 align:middle line:90% It has no influence. 01:26:07.730 --> 01:26:09.563 align:middle line:84% HAZHIR RAHMANDAD: So you would put them back 01:26:09.563 --> 01:26:12.930 align:middle line:84% into the noninvestors or potential investors, 01:26:12.930 --> 01:26:15.010 align:middle line:84% and then they can come back and decide. 01:26:15.010 --> 01:26:15.690 align:middle line:90% That's right. 01:26:15.690 --> 01:26:16.610 align:middle line:90% You could do that. 01:26:16.610 --> 01:26:19.050 align:middle line:90% I don't think that is wrong. 01:26:19.050 --> 01:26:22.825 align:middle line:84% The only thing is that in different models, 01:26:22.825 --> 01:26:24.450 align:middle line:84% people have implemented it differently. 01:26:24.450 --> 01:26:28.590 align:middle line:84% But the investment decision is not just a decision to invest. 01:26:28.590 --> 01:26:31.190 align:middle line:84% In most of these models, it's also 01:26:31.190 --> 01:26:34.410 align:middle line:84% being informed about this investment opportunity. 01:26:34.410 --> 01:26:37.470 align:middle line:84% So people are using Bass diffusion model in most of these 01:26:37.470 --> 01:26:40.310 align:middle line:90% to drive that investment flow. 01:26:40.310 --> 01:26:43.190 align:middle line:84% So if you put them into potential investors, 01:26:43.190 --> 01:26:46.590 align:middle line:84% now there is a kind of additional process 01:26:46.590 --> 01:26:49.070 align:middle line:84% of being informed about this opportunity that 01:26:49.070 --> 01:26:51.670 align:middle line:84% doesn't apply to these people who are reinvesting. 01:26:51.670 --> 01:26:56.110 align:middle line:84% If we had it into those kind of an intermediate stage of people 01:26:56.110 --> 01:26:58.710 align:middle line:84% who know about this opportunity but have 01:26:58.710 --> 01:27:02.130 align:middle line:84% to decide right now whether to invest in it or not, 01:27:02.130 --> 01:27:04.230 align:middle line:90% then it would be a better fit. 01:27:04.230 --> 01:27:05.650 align:middle line:90% So you go into there and then. 01:27:05.650 --> 01:27:08.190 align:middle line:90% 01:27:08.190 --> 01:27:10.330 align:middle line:90% So that's that. 01:27:10.330 --> 01:27:12.570 align:middle line:84% So now, here, the inflow is clear. 01:27:12.570 --> 01:27:15.710 align:middle line:84% The outflow is the more interesting thing. 01:27:15.710 --> 01:27:19.810 align:middle line:84% So you have the minimum time to pay that puts the upper bound-- 01:27:19.810 --> 01:27:23.890 align:middle line:84% so it's a minimum of cash on hand divided minimum time to pay 01:27:23.890 --> 01:27:27.410 align:middle line:90% and indicated payout. 01:27:27.410 --> 01:27:31.290 align:middle line:84% I'm OK with this, but perhaps a good idea 01:27:31.290 --> 01:27:34.450 align:middle line:84% to separate that max feasible payment or something 01:27:34.450 --> 01:27:36.770 align:middle line:90% as a separate variable. 01:27:36.770 --> 01:27:42.250 align:middle line:84% It's mathematically equivalent but a little bit cleaner. 01:27:42.250 --> 01:27:48.850 align:middle line:84% And then the indicated payout is coming from how many people 01:27:48.850 --> 01:27:50.630 align:middle line:90% are cashing out. 01:27:50.630 --> 01:27:53.850 align:middle line:90% 01:27:53.850 --> 01:27:58.530 align:middle line:84% And then the amount owed at payout, which is just 01:27:58.530 --> 01:28:03.230 align:middle line:90% a promised fraction expanded. 01:28:03.230 --> 01:28:13.070 align:middle line:90% 01:28:13.070 --> 01:28:17.670 align:middle line:84% So right now, the payout is happening. 01:28:17.670 --> 01:28:19.570 align:middle line:90% That is investors are leaving. 01:28:19.570 --> 01:28:24.030 align:middle line:90% 01:28:24.030 --> 01:28:29.910 align:middle line:84% But if there is no money, they are not paid, correct? 01:28:29.910 --> 01:28:31.630 align:middle line:90% AUDIENCE: Yes. 01:28:31.630 --> 01:28:36.670 align:middle line:84% HAZHIR RAHMANDAD: So how do you account, accounting-wise, 01:28:36.670 --> 01:28:40.670 align:middle line:84% about how much money is lost in this scam? 01:28:40.670 --> 01:28:45.230 align:middle line:84% That is, when all is said and done, 01:28:45.230 --> 01:28:50.530 align:middle line:84% how do you calculate how much money was owed and never paid? 01:28:50.530 --> 01:28:53.650 align:middle line:84% AUDIENCE: So those are the scamages, the scam damages, 01:28:53.650 --> 01:28:58.510 align:middle line:84% so that's just the indicated payouts minus the payouts. 01:28:58.510 --> 01:29:00.110 align:middle line:90% HAZHIR RAHMANDAD: Got it. 01:29:00.110 --> 01:29:03.290 align:middle line:90% So yes, then this works. 01:29:03.290 --> 01:29:06.350 align:middle line:84% That is basically what you have here, 01:29:06.350 --> 01:29:09.150 align:middle line:84% this additional stock of scamages 01:29:09.150 --> 01:29:14.270 align:middle line:84% is doing what you could also do with the liabilities. 01:29:14.270 --> 01:29:20.210 align:middle line:84% But it is the gap between the cash and the liability that is-- 01:29:20.210 --> 01:29:22.890 align:middle line:90% not the cash and liabilities. 01:29:22.890 --> 01:29:26.330 align:middle line:84% What he had to pay and he didn't. 01:29:26.330 --> 01:29:30.170 align:middle line:84% AUDIENCE: I suppose I just didn't have a-- 01:29:30.170 --> 01:29:34.650 align:middle line:84% because investors can't observe liabilities, 01:29:34.650 --> 01:29:38.930 align:middle line:84% I like what Jake said about liabilities 01:29:38.930 --> 01:29:42.170 align:middle line:84% being a pressure on the scheme leader 01:29:42.170 --> 01:29:44.190 align:middle line:90% to go recruit more people. 01:29:44.190 --> 01:29:45.390 align:middle line:90% I didn't think about that. 01:29:45.390 --> 01:29:50.450 align:middle line:84% But other than that, I didn't have a good feedback 01:29:50.450 --> 01:29:55.362 align:middle line:84% story about what are liabilities doing outside of-- 01:29:55.362 --> 01:29:56.570 align:middle line:90% HAZHIR RAHMANDAD: Accounting. 01:29:56.570 --> 01:29:57.610 align:middle line:90% AUDIENCE: --accounting. 01:29:57.610 --> 01:29:59.910 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so I think that's fair. 01:29:59.910 --> 01:30:03.970 align:middle line:84% And liabilities are really-- their first-order effect 01:30:03.970 --> 01:30:05.790 align:middle line:84% in this model is actually accounting. 01:30:05.790 --> 01:30:09.430 align:middle line:84% So that's why once you have it in this way, 01:30:09.430 --> 01:30:10.970 align:middle line:90% it does that accounting job. 01:30:10.970 --> 01:30:13.030 align:middle line:84% Now the reason this is working partly 01:30:13.030 --> 01:30:17.970 align:middle line:84% is that you are getting everybody out at the 45 days. 01:30:17.970 --> 01:30:20.150 align:middle line:90% They are not any more investors. 01:30:20.150 --> 01:30:25.390 align:middle line:84% They are people who had invested and had to be paid at that time. 01:30:25.390 --> 01:30:29.130 align:middle line:84% And if they weren't paid, bad luck. 01:30:29.130 --> 01:30:34.250 align:middle line:84% They are not willing to invest or some other category. 01:30:34.250 --> 01:30:38.770 align:middle line:84% Now the reinvesting part is tricky here because it is not-- 01:30:38.770 --> 01:30:46.790 align:middle line:90% 01:30:46.790 --> 01:30:48.910 align:middle line:84% because you have the cash out, and cash out 01:30:48.910 --> 01:30:49.910 align:middle line:90% is coming from what? 01:30:49.910 --> 01:30:54.752 align:middle line:84% This is from the payout time and total investors. 01:30:54.752 --> 01:30:56.210 align:middle line:84% AUDIENCE: So investors are leaving. 01:30:56.210 --> 01:30:58.150 align:middle line:84% And then some fraction decide to reinvest. 01:30:58.150 --> 01:30:59.150 align:middle line:90% HAZHIR RAHMANDAD: I see. 01:30:59.150 --> 01:31:00.750 align:middle line:90% I see. 01:31:00.750 --> 01:31:03.630 align:middle line:84% AUDIENCE: And those who don't just cash out. 01:31:03.630 --> 01:31:08.730 align:middle line:84% And I assume the baseline fraction deciding to reinvest 01:31:08.730 --> 01:31:09.590 align:middle line:90% is 0.9. 01:31:09.590 --> 01:31:13.570 align:middle line:84% And then that decrements by losing trust. 01:31:13.570 --> 01:31:16.810 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so you have these people who 01:31:16.810 --> 01:31:19.710 align:middle line:84% are reinvesting in this way of thinking, 01:31:19.710 --> 01:31:22.330 align:middle line:84% assuming that this reinvesting basically doesn't do anything 01:31:22.330 --> 01:31:24.650 align:middle line:84% to the stock that is on the flow. 01:31:24.650 --> 01:31:26.495 align:middle line:90% That flow has no effect. 01:31:26.495 --> 01:31:28.370 align:middle line:84% AUDIENCE: I think the assumption is that they 01:31:28.370 --> 01:31:31.010 align:middle line:90% have to go see their money. 01:31:31.010 --> 01:31:35.450 align:middle line:90% They can't just say, I guess-- 01:31:35.450 --> 01:31:40.490 align:middle line:84% there has to be some proof that their return existed. 01:31:40.490 --> 01:31:41.750 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:31:41.750 --> 01:31:50.210 align:middle line:84% And the way they do it in this case is-- 01:31:50.210 --> 01:31:54.090 align:middle line:84% so you are getting the indicated payout from cash out. 01:31:54.090 --> 01:31:56.857 align:middle line:84% So this is only people who decide not to reinvest. 01:31:56.857 --> 01:31:59.190 align:middle line:84% AUDIENCE: No, it's also coming from reinvesting as well. 01:31:59.190 --> 01:31:59.590 align:middle line:90% HAZHIR RAHMANDAD: Oh, OK. 01:31:59.590 --> 01:32:01.410 align:middle line:90% It is coming from reinvesting. 01:32:01.410 --> 01:32:02.210 align:middle line:90% Got it. 01:32:02.210 --> 01:32:07.710 align:middle line:90% 01:32:07.710 --> 01:32:11.510 align:middle line:84% And you need that because you get to reinvesting 01:32:11.510 --> 01:32:15.670 align:middle line:90% to also impact investments. 01:32:15.670 --> 01:32:17.270 align:middle line:90% Yes. 01:32:17.270 --> 01:32:19.990 align:middle line:84% So this is actually the right way 01:32:19.990 --> 01:32:24.270 align:middle line:84% of doing it in the case of Ponzi because they 01:32:24.270 --> 01:32:27.490 align:middle line:84% had to go and get the money and then go back and invest it. 01:32:27.490 --> 01:32:29.750 align:middle line:90% So I think that's fine. 01:32:29.750 --> 01:32:31.710 align:middle line:84% In fact, all you need to do is to have 01:32:31.710 --> 01:32:34.450 align:middle line:84% this reinvesting without having it impact the investors. 01:32:34.450 --> 01:32:39.710 align:middle line:84% That's basically what is happening. 01:32:39.710 --> 01:32:43.070 align:middle line:84% I mean, you just don't need this flow variable 01:32:43.070 --> 01:32:44.250 align:middle line:90% to be a flow variable. 01:32:44.250 --> 01:32:46.250 align:middle line:84% It just is an auxiliary variable. 01:32:46.250 --> 01:32:48.408 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:32:48.408 --> 01:32:49.950 align:middle line:84% HAZHIR RAHMANDAD: And then your model 01:32:49.950 --> 01:32:51.410 align:middle line:90% will be fine on that front. 01:32:51.410 --> 01:32:55.430 align:middle line:90% 01:32:55.430 --> 01:32:59.910 align:middle line:84% Population growth-- it's an overkill for this model. 01:32:59.910 --> 01:33:02.770 align:middle line:84% AUDIENCE: Oh, I was wondering-- so the last question was 01:33:02.770 --> 01:33:06.450 align:middle line:84% how do you get it to be sustainable over time. 01:33:06.450 --> 01:33:07.630 align:middle line:90% And population growth-- 01:33:07.630 --> 01:33:07.950 align:middle line:90% HAZHIR RAHMANDAD: I see. 01:33:07.950 --> 01:33:08.170 align:middle line:90% I see. 01:33:08.170 --> 01:33:09.962 align:middle line:84% So you were thinking that population growth 01:33:09.962 --> 01:33:11.670 align:middle line:90% could be a driver of that. 01:33:11.670 --> 01:33:14.090 align:middle line:90% So that's interesting. 01:33:14.090 --> 01:33:17.130 align:middle line:84% The first-order answer is, well, you also 01:33:17.130 --> 01:33:19.510 align:middle line:84% need to have return on your cash. 01:33:19.510 --> 01:33:22.170 align:middle line:84% That is, you need to grow the pot of money. 01:33:22.170 --> 01:33:23.970 align:middle line:90% That's important. 01:33:23.970 --> 01:33:29.708 align:middle line:84% So that is currently missing but could be added. 01:33:29.708 --> 01:33:31.250 align:middle line:84% AUDIENCE: I suppose I was assuming it 01:33:31.250 --> 01:33:34.050 align:middle line:90% was purely a scam, [INAUDIBLE]. 01:33:34.050 --> 01:33:39.870 align:middle line:84% HAZHIR RAHMANDAD: Yes, then it is the slow growth. 01:33:39.870 --> 01:33:43.670 align:middle line:84% That's the only way is that within a finite time horizon, 01:33:43.670 --> 01:33:47.910 align:middle line:84% you might be able to sustain it if you are not too attractive. 01:33:47.910 --> 01:33:51.730 align:middle line:84% So perhaps Madoff was closer to this model 01:33:51.730 --> 01:33:53.990 align:middle line:84% because he sustained it for decades, 01:33:53.990 --> 01:33:57.290 align:middle line:84% if I remember correctly, more than 20 years. 01:33:57.290 --> 01:34:01.070 align:middle line:84% And that was basically, yeah, this 01:34:01.070 --> 01:34:03.770 align:middle line:84% is not an unbelievable rate of return. 01:34:03.770 --> 01:34:06.270 align:middle line:84% He was just kind of a little bit more stable than the market 01:34:06.270 --> 01:34:09.870 align:middle line:84% and a little bit better than the average investment opportunity 01:34:09.870 --> 01:34:10.747 align:middle line:90% in the market. 01:34:10.747 --> 01:34:12.830 align:middle line:84% AUDIENCE: And he never had to-- or he didn't often 01:34:12.830 --> 01:34:14.830 align:middle line:84% have to show someone their money. 01:34:14.830 --> 01:34:17.250 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so that's also part of it. 01:34:17.250 --> 01:34:21.950 align:middle line:84% But nobody is showing all the money in the account. 01:34:21.950 --> 01:34:25.590 align:middle line:84% Whoever wanted to be paid back, he would pay them back. 01:34:25.590 --> 01:34:28.110 align:middle line:84% So in that sense, he was paying things back. 01:34:28.110 --> 01:34:30.710 align:middle line:90% But then he would reinvest. 01:34:30.710 --> 01:34:33.590 align:middle line:84% So whether this-- so right now, you 01:34:33.590 --> 01:34:36.390 align:middle line:84% have reinvesting going both into the indicated payout 01:34:36.390 --> 01:34:38.830 align:middle line:90% and investment. 01:34:38.830 --> 01:34:41.950 align:middle line:84% You could say, for Madoff, he didn't 01:34:41.950 --> 01:34:43.450 align:middle line:90% use either of these channels. 01:34:43.450 --> 01:34:45.530 align:middle line:84% That is, it didn't go into the indicated payout, 01:34:45.530 --> 01:34:47.510 align:middle line:84% but it also didn't go into reinvestment. 01:34:47.510 --> 01:34:49.350 align:middle line:84% And there will be a bit of a difference 01:34:49.350 --> 01:34:55.390 align:middle line:84% because your max cash out becomes more quickly binding 01:34:55.390 --> 01:34:58.610 align:middle line:84% if you have both of them in the indicated payout. 01:34:58.610 --> 01:35:02.210 align:middle line:90% But not a big deal. 01:35:02.210 --> 01:35:04.650 align:middle line:84% AUDIENCE: [INAUDIBLE] could have actually gone 01:35:04.650 --> 01:35:07.250 align:middle line:84% on for a long time if there wasn't an exogenous shock to 01:35:07.250 --> 01:35:08.730 align:middle line:90% [INAUDIBLE]. 01:35:08.730 --> 01:35:11.510 align:middle line:84% HAZHIR RAHMANDAD: Yeah, basically. 01:35:11.510 --> 01:35:13.770 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:35:13.770 --> 01:35:15.810 align:middle line:90% HAZHIR RAHMANDAD: Yeah, exactly. 01:35:15.810 --> 01:35:16.970 align:middle line:90% It could have continued. 01:35:16.970 --> 01:35:19.790 align:middle line:84% AUDIENCE: He might have started as early as the 1970s 01:35:19.790 --> 01:35:20.290 align:middle line:90% [INAUDIBLE]. 01:35:20.290 --> 01:35:21.457 align:middle line:90% HAZHIR RAHMANDAD: Oh my god. 01:35:21.457 --> 01:35:23.570 align:middle line:90% OK. 01:35:23.570 --> 01:35:26.650 align:middle line:84% AUDIENCE: So you could wait a few minutes longer [INAUDIBLE]. 01:35:26.650 --> 01:35:28.990 align:middle line:84% But what's the point of the scamages? 01:35:28.990 --> 01:35:31.868 align:middle line:84% Is that just because it's just a [INAUDIBLE]? 01:35:31.868 --> 01:35:33.410 align:middle line:84% HAZHIR RAHMANDAD: Yeah, it is, but it 01:35:33.410 --> 01:35:35.160 align:middle line:84% is important for accounting because that's 01:35:35.160 --> 01:35:39.690 align:middle line:84% one of the key outcomes in this case. 01:35:39.690 --> 01:35:42.790 align:middle line:84% And then let's look at the trust equations. 01:35:42.790 --> 01:35:46.730 align:middle line:90% So trust is coming fraction. 01:35:46.730 --> 01:35:51.370 align:middle line:84% This indicated trust, and indicated trust is coming, 01:35:51.370 --> 01:35:53.670 align:middle line:84% effective fraction of obligations met. 01:35:53.670 --> 01:35:58.350 align:middle line:84% So this is kind of perceived fraction of obligations met. 01:35:58.350 --> 01:36:01.450 align:middle line:84% So you have this perception delay here. 01:36:01.450 --> 01:36:05.350 align:middle line:84% What's the idea of having this intermediate perception 01:36:05.350 --> 01:36:10.550 align:middle line:84% delay and then the trust, again, adjusting with some time 01:36:10.550 --> 01:36:11.710 align:middle line:90% constant? 01:36:11.710 --> 01:36:13.010 align:middle line:90% AUDIENCE: It could do without. 01:36:13.010 --> 01:36:19.410 align:middle line:84% I think the idea, though, is just that people don't get paid, 01:36:19.410 --> 01:36:23.430 align:middle line:84% and then it takes some time for them to tell people. 01:36:23.430 --> 01:36:25.710 align:middle line:84% HAZHIR RAHMANDAD: Yeah, but that is also 01:36:25.710 --> 01:36:29.470 align:middle line:84% inside the trust and investment slow adjustment 01:36:29.470 --> 01:36:33.190 align:middle line:84% that the reason that is adjusting as a stock with-- 01:36:33.190 --> 01:36:36.950 align:middle line:84% and nicely, you have also the asymmetric adjustment 01:36:36.950 --> 01:36:40.790 align:middle line:84% is basically that, that it takes time for people 01:36:40.790 --> 01:36:41.890 align:middle line:90% to learn about it. 01:36:41.890 --> 01:36:46.990 align:middle line:84% And so I wouldn't have a separate delay process here. 01:36:46.990 --> 01:36:49.490 align:middle line:90% It's kind of too much overlap. 01:36:49.490 --> 01:36:53.830 align:middle line:84% Now you have an S-shaped function. 01:36:53.830 --> 01:36:57.890 align:middle line:84% AUDIENCE: Yeah, so actually the function that's active right now 01:36:57.890 --> 01:37:04.170 align:middle line:84% is an exponential reactivity parameter-- 01:37:04.170 --> 01:37:04.775 align:middle line:90% the bottom. 01:37:04.775 --> 01:37:06.150 align:middle line:84% HAZHIR RAHMANDAD: This last part. 01:37:06.150 --> 01:37:09.090 align:middle line:84% So this is similar to what Alban had as well. 01:37:09.090 --> 01:37:10.130 align:middle line:90% So then that-- 01:37:10.130 --> 01:37:12.830 align:middle line:84% AUDIENCE: I want it just to fall very quickly. 01:37:12.830 --> 01:37:16.050 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so that reactivity parameter 01:37:16.050 --> 01:37:18.770 align:middle line:84% would be-- yeah, so you have a large value 01:37:18.770 --> 01:37:24.810 align:middle line:84% so that it goes quickly to 0 if you're not meeting obligations. 01:37:24.810 --> 01:37:25.330 align:middle line:90% Good. 01:37:25.330 --> 01:37:27.310 align:middle line:90% So that's working fine. 01:37:27.310 --> 01:37:31.730 align:middle line:84% I'm not looking at the logistic one. 01:37:31.730 --> 01:37:35.930 align:middle line:84% Yeah, this should work fine, I think. 01:37:35.930 --> 01:37:40.330 align:middle line:84% Well, we didn't look at-- so this trust, 01:37:40.330 --> 01:37:41.990 align:middle line:90% where does it impact things? 01:37:41.990 --> 01:37:44.850 align:middle line:90% One is on adoption fraction. 01:37:44.850 --> 01:37:48.650 align:middle line:84% So if trust goes down, you're bringing the adoption fraction 01:37:48.650 --> 01:37:52.090 align:middle line:90% down linearly with trust. 01:37:52.090 --> 01:37:57.060 align:middle line:84% So we have one nonlinearity for this reactivity parameter 01:37:57.060 --> 01:38:01.340 align:middle line:90% that then reflects in trust. 01:38:01.340 --> 01:38:03.860 align:middle line:90% Yeah, that's fine. 01:38:03.860 --> 01:38:06.740 align:middle line:84% AUDIENCE: So I think if I were to make an edit, 01:38:06.740 --> 01:38:10.420 align:middle line:84% I would also have it affect time to forget and just blow that 01:38:10.420 --> 01:38:13.785 align:middle line:84% to infinity or something-- or very high. 01:38:13.785 --> 01:38:15.160 align:middle line:84% HAZHIR RAHMANDAD: Time to forget. 01:38:15.160 --> 01:38:15.920 align:middle line:90% Forget what? 01:38:15.920 --> 01:38:18.365 align:middle line:84% AUDIENCE: So people become not willing to invest, 01:38:18.365 --> 01:38:19.240 align:middle line:90% but then eventually-- 01:38:19.240 --> 01:38:25.100 align:middle line:84% HAZHIR RAHMANDAD: Oh yes, so you don't have this decide not 01:38:25.100 --> 01:38:28.080 align:middle line:90% to invest is impacted by trust. 01:38:28.080 --> 01:38:33.640 align:middle line:84% But becoming willing to invest is not. 01:38:33.640 --> 01:38:37.700 align:middle line:84% And therefore, they would continue to become interested. 01:38:37.700 --> 01:38:40.860 align:middle line:84% AUDIENCE: Yeah, so I think that's-- 01:38:40.860 --> 01:38:42.558 align:middle line:84% AUDIENCE: Why do we even need that? 01:38:42.558 --> 01:38:44.100 align:middle line:84% HAZHIR RAHMANDAD: Why do I need what? 01:38:44.100 --> 01:38:46.820 align:middle line:90% AUDIENCE: Forgetting. 01:38:46.820 --> 01:38:50.180 align:middle line:84% The people who get scammed are susceptible to get 01:38:50.180 --> 01:38:51.520 align:middle line:90% scammed again. 01:38:51.520 --> 01:38:56.000 align:middle line:84% And I think it was another thing that I added thinking 01:38:56.000 --> 01:38:58.760 align:middle line:90% about how could this go on. 01:38:58.760 --> 01:39:00.900 align:middle line:84% HAZHIR RAHMANDAD: So it is not just time to forget. 01:39:00.900 --> 01:39:04.280 align:middle line:84% So we need to be a little bit careful about what exactly 01:39:04.280 --> 01:39:05.780 align:middle line:90% is happening conceptually. 01:39:05.780 --> 01:39:07.760 align:middle line:84% So potential investors are people 01:39:07.760 --> 01:39:10.840 align:middle line:84% who are willing to invest in Ponzi 01:39:10.840 --> 01:39:14.280 align:middle line:84% and then not willing to invest are people who 01:39:14.280 --> 01:39:16.200 align:middle line:90% are not interested in Ponzi. 01:39:16.200 --> 01:39:21.080 align:middle line:84% And let's for a minute forget about this deciding 01:39:21.080 --> 01:39:24.280 align:middle line:84% not to invest part, so just the inflow from not 01:39:24.280 --> 01:39:27.160 align:middle line:84% willing to invest to potential investors. 01:39:27.160 --> 01:39:32.520 align:middle line:84% That flow is capturing the idea that some people had no interest 01:39:32.520 --> 01:39:35.840 align:middle line:90% in Ponzi at the very beginning. 01:39:35.840 --> 01:39:40.440 align:middle line:84% And then, over time, they become interested 01:39:40.440 --> 01:39:43.340 align:middle line:84% and they're willing to consider it in some sense. 01:39:43.340 --> 01:39:48.120 align:middle line:90% 01:39:48.120 --> 01:39:50.620 align:middle line:84% But they don't know about it, correct? 01:39:50.620 --> 01:39:53.300 align:middle line:84% Because they haven't heard about it. 01:39:53.300 --> 01:39:55.500 align:middle line:90% AUDIENCE: I assumed-- 01:39:55.500 --> 01:39:57.980 align:middle line:84% HAZHIR RAHMANDAD: But because the potential investors-- 01:39:57.980 --> 01:40:00.480 align:middle line:84% AUDIENCE: --are coming out of investors as well, 01:40:00.480 --> 01:40:02.925 align:middle line:84% then they know about what happened. 01:40:02.925 --> 01:40:04.300 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so that's 01:40:04.300 --> 01:40:06.300 align:middle line:84% why I'm saying this is kind of conceptually 01:40:06.300 --> 01:40:09.040 align:middle line:84% a little bit unclear what is happening here. 01:40:09.040 --> 01:40:11.900 align:middle line:84% So the not willing to invest right 01:40:11.900 --> 01:40:15.380 align:middle line:84% now includes people who know about Ponzi 01:40:15.380 --> 01:40:17.700 align:middle line:84% but are not willing to invest, and people 01:40:17.700 --> 01:40:19.580 align:middle line:84% who don't know about Ponzi and are not 01:40:19.580 --> 01:40:23.460 align:middle line:84% willing to invest just because they are not 01:40:23.460 --> 01:40:27.700 align:middle line:84% into financial investment, for example. 01:40:27.700 --> 01:40:30.540 align:middle line:90% So which of the two? 01:40:30.540 --> 01:40:32.787 align:middle line:84% AUDIENCE: I think it's everybody knows about Ponzi. 01:40:32.787 --> 01:40:34.620 align:middle line:84% HAZHIR RAHMANDAD: So that's your assumption, 01:40:34.620 --> 01:40:36.360 align:middle line:84% that everybody knows about Ponzi. 01:40:36.360 --> 01:40:39.260 align:middle line:84% But then if everybody knows about Ponzi, why do you 01:40:39.260 --> 01:40:40.840 align:middle line:90% have Bass diffusion model? 01:40:40.840 --> 01:40:42.720 align:middle line:84% AUDIENCE: No, so that everybody-- 01:40:42.720 --> 01:40:45.780 align:middle line:90% 01:40:45.780 --> 01:40:48.200 align:middle line:84% sorry, everybody would be willing to invest 01:40:48.200 --> 01:40:49.340 align:middle line:90% if they knew about it. 01:40:49.340 --> 01:40:54.000 align:middle line:84% I think my initial people not willing to invest is 0. 01:40:54.000 --> 01:40:57.400 align:middle line:84% So everybody who's in that not willing to invest stock 01:40:57.400 --> 01:41:00.520 align:middle line:84% is either a potential investor or somebody who would 01:41:00.520 --> 01:41:01.898 align:middle line:90% or somebody who has. 01:41:01.898 --> 01:41:02.940 align:middle line:90% HAZHIR RAHMANDAD: Oh, OK. 01:41:02.940 --> 01:41:06.560 align:middle line:84% So these are people knowing about Ponzi 01:41:06.560 --> 01:41:07.980 align:middle line:90% but not willing to invest. 01:41:07.980 --> 01:41:12.000 align:middle line:90% So at the beginning this is 0. 01:41:12.000 --> 01:41:14.700 align:middle line:84% That makes it internally consistent. 01:41:14.700 --> 01:41:17.240 align:middle line:90% 01:41:17.240 --> 01:41:19.640 align:middle line:84% So this is different from assignment 01:41:19.640 --> 01:41:24.400 align:middle line:84% for people not interested in VCRs 01:41:24.400 --> 01:41:27.040 align:middle line:90% because the price was too high. 01:41:27.040 --> 01:41:29.360 align:middle line:90% It is different. 01:41:29.360 --> 01:41:30.840 align:middle line:90% OK, good. 01:41:30.840 --> 01:41:33.680 align:middle line:84% So in that case, then just making this time 01:41:33.680 --> 01:41:38.400 align:middle line:84% to forget dependent on trust and investment would, I think, 01:41:38.400 --> 01:41:47.100 align:middle line:84% take care of the people forgetting about this. 01:41:47.100 --> 01:41:47.600 align:middle line:90% Good. 01:41:47.600 --> 01:41:50.100 align:middle line:84% So if we run this, now if I run this right now, 01:41:50.100 --> 01:41:52.600 align:middle line:84% because of this reinvesting going into investors, 01:41:52.600 --> 01:41:54.240 align:middle line:90% things may not work well. 01:41:54.240 --> 01:41:56.900 align:middle line:84% AUDIENCE: I think it works if you do plus reinvesting minus 01:41:56.900 --> 01:41:58.672 align:middle line:90% [INAUDIBLE]. 01:41:58.672 --> 01:42:00.380 align:middle line:84% HAZHIR RAHMANDAD: Or doing this this way. 01:42:00.380 --> 01:42:07.430 align:middle line:90% 01:42:07.430 --> 01:42:10.360 align:middle line:84% Ah, because we have the other model open. 01:42:10.360 --> 01:42:14.420 align:middle line:90% 01:42:14.420 --> 01:42:24.360 align:middle line:84% So we get the collapse, as we expected. 01:42:24.360 --> 01:42:28.300 align:middle line:84% And the reason is that the fraction of obligation 01:42:28.300 --> 01:42:32.340 align:middle line:90% met collapses. 01:42:32.340 --> 01:42:36.940 align:middle line:90% So that fraction is one. 01:42:36.940 --> 01:42:42.080 align:middle line:84% And how come that fraction goes to 50%? 01:42:42.080 --> 01:42:45.840 align:middle line:84% Because in the very long term, you just 01:42:45.840 --> 01:42:50.600 align:middle line:84% can't pay 50% of what he's getting. 01:42:50.600 --> 01:42:51.200 align:middle line:90% I mean-- 01:42:51.200 --> 01:42:54.742 align:middle line:84% AUDIENCE: He can pay back what he receives. 01:42:54.742 --> 01:42:56.200 align:middle line:84% HAZHIR RAHMANDAD: And then fraction 01:42:56.200 --> 01:43:02.860 align:middle line:84% deciding to reinvest in the long term is not zero. 01:43:02.860 --> 01:43:07.000 align:middle line:84% It's kind of 6% reinvest, even though they are not 01:43:07.000 --> 01:43:07.940 align:middle line:90% making any money. 01:43:07.940 --> 01:43:12.450 align:middle line:84% So kind of long-term things are not that meaningful here 01:43:12.450 --> 01:43:14.200 align:middle line:84% because, basically, once you have crashed, 01:43:14.200 --> 01:43:16.120 align:middle line:90% you have crashed in these. 01:43:16.120 --> 01:43:20.320 align:middle line:84% But it is still informative about how the underlying 01:43:20.320 --> 01:43:21.860 align:middle line:90% formulations are working. 01:43:21.860 --> 01:43:24.780 align:middle line:84% So in that sense, it is not a bad idea to look at those. 01:43:24.780 --> 01:43:29.780 align:middle line:90% 01:43:29.780 --> 01:43:39.320 align:middle line:84% I think pretty much everything is in the meaningful space 01:43:39.320 --> 01:43:41.900 align:middle line:90% and is working decently. 01:43:41.900 --> 01:43:44.820 align:middle line:84% Now you have a relatively large total population 01:43:44.820 --> 01:43:51.460 align:middle line:84% that basically people come into the population, many of them 01:43:51.460 --> 01:43:53.520 align:middle line:84% just leave into not willing to invest. 01:43:53.520 --> 01:43:57.000 align:middle line:84% Some of them go in at the very long term, get burnt, 01:43:57.000 --> 01:43:59.080 align:middle line:84% and then that way, they come back. 01:43:59.080 --> 01:44:03.820 align:middle line:84% So that's not also unrealistic completely. 01:44:03.820 --> 01:44:08.520 align:middle line:84% And then Ponzi doesn't have much money all the time. 01:44:08.520 --> 01:44:11.280 align:middle line:90% It's kind of hand to mouth. 01:44:11.280 --> 01:44:12.280 align:middle line:90% OK, cool. 01:44:12.280 --> 01:44:13.977 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:44:13.977 --> 01:44:15.560 align:middle line:84% HAZHIR RAHMANDAD: Yes, Anne, go ahead. 01:44:15.560 --> 01:44:20.940 align:middle line:90% 01:44:20.940 --> 01:44:24.740 align:middle line:84% Somehow we are not hearing you, even though you are not mute. 01:44:24.740 --> 01:44:26.843 align:middle line:90% AUDIENCE: Maybe your microphone. 01:44:26.843 --> 01:44:27.760 align:middle line:90% AUDIENCE: Let me know. 01:44:27.760 --> 01:44:28.880 align:middle line:84% HAZHIR RAHMANDAD: Now it is good. 01:44:28.880 --> 01:44:29.500 align:middle line:90% Thank you. 01:44:29.500 --> 01:44:35.220 align:middle line:84% AUDIENCE: So I used your reason for reinvesting would be 01:44:35.220 --> 01:44:37.103 align:middle line:90% [INAUDIBLE]. 01:44:37.103 --> 01:44:38.020 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:44:38.020 --> 01:44:47.240 align:middle line:84% So the formulation that Cathy has here says people-- 01:44:47.240 --> 01:44:49.820 align:middle line:84% so basically, people who are reinvesting, 01:44:49.820 --> 01:44:53.440 align:middle line:84% they get out of the stock and instantaneously 01:44:53.440 --> 01:44:55.640 align:middle line:90% come back into the stock. 01:44:55.640 --> 01:45:00.280 align:middle line:84% So as such, the net effect on the stock of investors 01:45:00.280 --> 01:45:04.020 align:middle line:84% is 0 because you come out and then you come back in. 01:45:04.020 --> 01:45:06.340 align:middle line:84% So that's why it is not an actual flow 01:45:06.340 --> 01:45:08.920 align:middle line:84% in the mathematical sense, even though, conceptually, it 01:45:08.920 --> 01:45:10.940 align:middle line:90% is both an inflow and outflow. 01:45:10.940 --> 01:45:14.317 align:middle line:90% 01:45:14.317 --> 01:45:15.900 align:middle line:84% AUDIENCE: Oh, I have another question. 01:45:15.900 --> 01:45:16.858 align:middle line:90% HAZHIR RAHMANDAD: Sure. 01:45:16.858 --> 01:45:17.880 align:middle line:90% No, no, that's good. 01:45:17.880 --> 01:45:21.560 align:middle line:84% AUDIENCE: So I was thinking about the relationship 01:45:21.560 --> 01:45:24.500 align:middle line:90% between investors and cash. 01:45:24.500 --> 01:45:30.760 align:middle line:84% I think, in a lot of the models, when investors leave 01:45:30.760 --> 01:45:32.900 align:middle line:84% or there's one when investors leave, 01:45:32.900 --> 01:45:35.960 align:middle line:84% which is they're no longer contributing cash 01:45:35.960 --> 01:45:37.860 align:middle line:90% to the Ponzi scheme. 01:45:37.860 --> 01:45:41.780 align:middle line:84% But what about investors who vary 01:45:41.780 --> 01:45:45.380 align:middle line:84% the cash that they reinvest at different times 01:45:45.380 --> 01:45:47.500 align:middle line:90% depending on trust? 01:45:47.500 --> 01:45:52.340 align:middle line:84% So maybe early on were reinvesting all of the money 01:45:52.340 --> 01:45:56.220 align:middle line:84% that you made plus principal back into the scheme. 01:45:56.220 --> 01:45:59.620 align:middle line:84% But over time, you slowly reduced the amount of cash 01:45:59.620 --> 01:46:00.720 align:middle line:90% that you reinvested. 01:46:00.720 --> 01:46:03.420 align:middle line:84% How would we capture something like that? 01:46:03.420 --> 01:46:05.600 align:middle line:84% HAZHIR RAHMANDAD: Yes, so basically, 01:46:05.600 --> 01:46:08.040 align:middle line:84% in all of the formulations we have seen so far, 01:46:08.040 --> 01:46:10.060 align:middle line:84% although kind of Ali and Hasem have 01:46:10.060 --> 01:46:13.340 align:middle line:84% a little bit of a different version that kind of combines 01:46:13.340 --> 01:46:15.740 align:middle line:84% the two effects, but in most of the formulations 01:46:15.740 --> 01:46:18.300 align:middle line:84% we have an amount that each person-- average 01:46:18.300 --> 01:46:21.540 align:middle line:84% investment amount that's kind of a fixed parameter. 01:46:21.540 --> 01:46:26.280 align:middle line:84% Now you could have a couple alternative versions of it. 01:46:26.280 --> 01:46:27.860 align:middle line:84% One is that the average investment 01:46:27.860 --> 01:46:30.220 align:middle line:90% amount can change over time. 01:46:30.220 --> 01:46:32.740 align:middle line:84% Now if we do that, and that's something also, 01:46:32.740 --> 01:46:35.500 align:middle line:84% Cathy, for you to keep in mind, if you 01:46:35.500 --> 01:46:37.760 align:middle line:84% do that, then your formulation starts 01:46:37.760 --> 01:46:42.360 align:middle line:84% to fail because then the amount that is indicated payment 01:46:42.360 --> 01:46:45.260 align:middle line:84% is not based on the current average investment amount, 01:46:45.260 --> 01:46:47.140 align:middle line:84% but based on the delayed version of it. 01:46:47.140 --> 01:46:50.360 align:middle line:84% Then you would need either the liability or some hack 01:46:50.360 --> 01:46:54.800 align:middle line:84% to account for how those average investment amounts are changing. 01:46:54.800 --> 01:47:00.600 align:middle line:84% And then back to your question, Anne, 01:47:00.600 --> 01:47:02.760 align:middle line:84% there is also the reinvestment, what 01:47:02.760 --> 01:47:04.920 align:middle line:84% fraction of the money that you get back 01:47:04.920 --> 01:47:06.760 align:middle line:90% do you want to reinvest. 01:47:06.760 --> 01:47:10.000 align:middle line:84% Now that is less important in the sense 01:47:10.000 --> 01:47:14.120 align:middle line:84% that you already have a fraction deciding to reinvest. 01:47:14.120 --> 01:47:16.120 align:middle line:90% This is fraction of people. 01:47:16.120 --> 01:47:18.120 align:middle line:84% But for each person, you're assuming 01:47:18.120 --> 01:47:22.200 align:middle line:84% it is 0 or 1, that is either reinvest or reinvest. 01:47:22.200 --> 01:47:25.560 align:middle line:84% Now, if you had this intermediate range of I 01:47:25.560 --> 01:47:28.840 align:middle line:84% am reinvesting only 50% of what I got, 01:47:28.840 --> 01:47:33.160 align:middle line:84% it is OK to think of them as half a person who reinvested 01:47:33.160 --> 01:47:36.980 align:middle line:84% fully and half a person who didn't reinvest at all, 01:47:36.980 --> 01:47:41.020 align:middle line:84% and you get the same result. So in that sense, 01:47:41.020 --> 01:47:44.460 align:middle line:84% having a continuous fraction, deciding to reinvest, 01:47:44.460 --> 01:47:47.580 align:middle line:84% takes care of that issue by and large. 01:47:47.580 --> 01:47:50.480 align:middle line:84% That is, it gives you enough flexibility on that front. 01:47:50.480 --> 01:47:53.620 align:middle line:84% Where the difference is more salient 01:47:53.620 --> 01:47:55.860 align:middle line:84% is the average investment amount that 01:47:55.860 --> 01:47:59.060 align:middle line:84% may change over time as people build confidence or lose 01:47:59.060 --> 01:47:59.640 align:middle line:90% confidence. 01:47:59.640 --> 01:48:02.240 align:middle line:84% And it's more in the building confidence part. 01:48:02.240 --> 01:48:04.420 align:middle line:84% That is, at the beginning, people 01:48:04.420 --> 01:48:06.560 align:middle line:84% don't have confidence about these things, 01:48:06.560 --> 01:48:09.300 align:middle line:84% so they are willing to test it with the small amounts of money 01:48:09.300 --> 01:48:10.500 align:middle line:90% to see, maybe it works. 01:48:10.500 --> 01:48:14.200 align:middle line:84% Like Bitcoin-- I mean, when it started, 01:48:14.200 --> 01:48:15.820 align:middle line:84% people would just put a few dollars 01:48:15.820 --> 01:48:17.080 align:middle line:90% to see what this thing is. 01:48:17.080 --> 01:48:18.800 align:middle line:90% It's a matter of curiosity. 01:48:18.800 --> 01:48:20.740 align:middle line:84% But then if, six months later, they 01:48:20.740 --> 01:48:22.388 align:middle line:84% see that they made a lot of money, 01:48:22.388 --> 01:48:24.180 align:middle line:84% they are willing to put more money and then 01:48:24.180 --> 01:48:29.900 align:middle line:84% more money and more money, and now becomes $1 trillion market, 01:48:29.900 --> 01:48:32.920 align:middle line:84% even though it doesn't have any meaningful return. 01:48:32.920 --> 01:48:35.060 align:middle line:90% It's a different story. 01:48:35.060 --> 01:48:39.000 align:middle line:90% 01:48:39.000 --> 01:48:41.540 align:middle line:84% In that sense, if you wanted to capture that, 01:48:41.540 --> 01:48:44.140 align:middle line:84% I think there is definitely a way to do that. 01:48:44.140 --> 01:48:47.480 align:middle line:84% You can basically use the thrust to drive the average investment 01:48:47.480 --> 01:48:51.680 align:middle line:84% amount, and it cannot go beyond whatever is people's typical 01:48:51.680 --> 01:48:56.240 align:middle line:90% saving or ability to invest. 01:48:56.240 --> 01:48:59.060 align:middle line:84% To be honest, in these investment schemes-- now 01:48:59.060 --> 01:49:02.120 align:middle line:84% Ponzi is a bit of an old-school, physical 01:49:02.120 --> 01:49:08.240 align:middle line:84% get cash, go to the bank, get slips of paper back. 01:49:08.240 --> 01:49:11.680 align:middle line:84% But these days, you probably want 01:49:11.680 --> 01:49:14.180 align:middle line:84% to break the market into different sectors. 01:49:14.180 --> 01:49:18.160 align:middle line:84% So small investors are very different story 01:49:18.160 --> 01:49:21.040 align:middle line:84% than large investors, and there are these kind 01:49:21.040 --> 01:49:23.800 align:middle line:90% of mega whales of investors. 01:49:23.800 --> 01:49:28.480 align:middle line:84% And probably you separate the model for those categories 01:49:28.480 --> 01:49:30.740 align:middle line:84% because their sources of information, 01:49:30.740 --> 01:49:33.860 align:middle line:84% their depth of knowledge about what you do or don't do 01:49:33.860 --> 01:49:35.080 align:middle line:90% is different. 01:49:35.080 --> 01:49:40.180 align:middle line:84% If somebody is going to spend or invest $100 million with you, 01:49:40.180 --> 01:49:43.020 align:middle line:84% they'll definitely spend quite a bit of money 01:49:43.020 --> 01:49:44.880 align:middle line:84% figuring out whether you are a trustable. 01:49:44.880 --> 01:49:49.780 align:middle line:90% 01:49:49.780 --> 01:49:53.740 align:middle line:84% But that's beyond our problem definition for sure. 01:49:53.740 --> 01:49:54.560 align:middle line:90% Others? 01:49:54.560 --> 01:49:57.080 align:middle line:84% Anybody else wants us to look at their model? 01:49:57.080 --> 01:50:04.740 align:middle line:90% 01:50:04.740 --> 01:50:05.727 align:middle line:90% Everybody is shy? 01:50:05.727 --> 01:50:07.060 align:middle line:90% AUDIENCE: A couple of questions. 01:50:07.060 --> 01:50:07.420 align:middle line:90% HAZHIR RAHMANDAD: Sure. 01:50:07.420 --> 01:50:10.160 align:middle line:84% AUDIENCE: I was missing some big parts of the story, 01:50:10.160 --> 01:50:15.260 align:middle line:84% so I didn't have any notion of promises or liabilities. 01:50:15.260 --> 01:50:20.080 align:middle line:84% Instead, I had return rates, reported returns, 01:50:20.080 --> 01:50:26.640 align:middle line:84% so the investment manager returns money, 01:50:26.640 --> 01:50:29.370 align:middle line:84% and then the reports of those returns 01:50:29.370 --> 01:50:33.510 align:middle line:84% feed back to give you new investors. 01:50:33.510 --> 01:50:34.390 align:middle line:90% I guess-- 01:50:34.390 --> 01:50:37.610 align:middle line:84% HAZHIR RAHMANDAD: OK, let's look at what you're doing here. 01:50:37.610 --> 01:50:39.310 align:middle line:90% So this is your model. 01:50:39.310 --> 01:50:40.490 align:middle line:90% So you have new investors. 01:50:40.490 --> 01:50:42.390 align:middle line:84% These are people who basically have invested, 01:50:42.390 --> 01:50:44.530 align:middle line:84% and their investment has not matured. 01:50:44.530 --> 01:50:46.350 align:middle line:84% After a while, they become matured. 01:50:46.350 --> 01:50:49.470 align:middle line:84% When you are matured, you want to leave. 01:50:49.470 --> 01:50:52.450 align:middle line:84% I mean, lifetime is killing them. 01:50:52.450 --> 01:50:56.650 align:middle line:90% It's a bit hard, but you stay-- 01:50:56.650 --> 01:50:57.650 align:middle line:90% AUDIENCE: For some time. 01:50:57.650 --> 01:50:58.290 align:middle line:90% HAZHIR RAHMANDAD: For some time. 01:50:58.290 --> 01:51:00.190 align:middle line:84% But what's the idea of this some time? 01:51:00.190 --> 01:51:01.970 align:middle line:84% Five years you're staying in this stock. 01:51:01.970 --> 01:51:05.150 align:middle line:84% So what's the point of being in this stock for five years? 01:51:05.150 --> 01:51:08.670 align:middle line:84% AUDIENCE: Basically, at some point, 01:51:08.670 --> 01:51:11.750 align:middle line:90% you decide you want to get out. 01:51:11.750 --> 01:51:13.590 align:middle line:84% HAZHIR RAHMANDAD: No, but get out of what? 01:51:13.590 --> 01:51:15.090 align:middle line:90% This is a mature investor. 01:51:15.090 --> 01:51:17.930 align:middle line:84% If I understood you correctly, when we first mentioned it, 01:51:17.930 --> 01:51:21.175 align:middle line:84% you said these are people whose investment has already matured. 01:51:21.175 --> 01:51:23.050 align:middle line:84% That means they are not earning any interest. 01:51:23.050 --> 01:51:25.510 align:middle line:90% So why would I-- oh, you are. 01:51:25.510 --> 01:51:29.210 align:middle line:84% AUDIENCE: Yeah, so it takes a minute before they can start. 01:51:29.210 --> 01:51:33.122 align:middle line:90% I was [INAUDIBLE] on the story. 01:51:33.122 --> 01:51:34.830 align:middle line:84% For the first year, they're just waiting, 01:51:34.830 --> 01:51:40.630 align:middle line:84% and then, at maturity, they start accruing. 01:51:40.630 --> 01:51:43.130 align:middle line:84% HAZHIR RAHMANDAD: Ah, so the new investors 01:51:43.130 --> 01:51:45.450 align:middle line:90% are the ones who haven't yet-- 01:51:45.450 --> 01:51:47.450 align:middle line:84% AUDIENCE: They're not accruing any interest. 01:51:47.450 --> 01:51:48.908 align:middle line:84% HAZHIR RAHMANDAD: Accrued interest. 01:51:48.908 --> 01:51:51.430 align:middle line:90% So how are you capturing that? 01:51:51.430 --> 01:51:53.470 align:middle line:90% So funds are going into this. 01:51:53.470 --> 01:51:56.490 align:middle line:84% This is money that investors put. 01:51:56.490 --> 01:52:00.290 align:middle line:84% Maturing-- OK, this goes to the next step. 01:52:00.290 --> 01:52:05.050 align:middle line:90% Then I'm accruing interest. 01:52:05.050 --> 01:52:08.035 align:middle line:84% Where does that get accounted for? 01:52:08.035 --> 01:52:09.410 align:middle line:84% AUDIENCE: All that's happening is 01:52:09.410 --> 01:52:12.610 align:middle line:84% we're taking the total pot of money, [INAUDIBLE] 01:52:12.610 --> 01:52:16.770 align:middle line:84% new and old funds and spreading it over everyone 01:52:16.770 --> 01:52:18.610 align:middle line:90% in the old population. 01:52:18.610 --> 01:52:22.030 align:middle line:90% So I'm in the old population. 01:52:22.030 --> 01:52:25.170 align:middle line:84% I came in with some initial investment. 01:52:25.170 --> 01:52:27.910 align:middle line:84% And my returns are equal to whatever 01:52:27.910 --> 01:52:33.470 align:middle line:84% is currently in the total pot divided by whatever I invested. 01:52:33.470 --> 01:52:36.510 align:middle line:84% HAZHIR RAHMANDAD: Wait, that's not how your return is actually 01:52:36.510 --> 01:52:40.270 align:middle line:90% calculated. 01:52:40.270 --> 01:52:42.690 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:52:42.690 --> 01:52:43.830 align:middle line:90% 01:52:43.830 --> 01:52:46.230 align:middle line:84% HAZHIR RAHMANDAD: So what you are being paid 01:52:46.230 --> 01:52:49.530 align:middle line:84% is the average money that is associated with you. 01:52:49.530 --> 01:52:51.750 align:middle line:90% So you have an aging chain-- 01:52:51.750 --> 01:52:54.182 align:middle line:90% AUDIENCE: No, you're-- 01:52:54.182 --> 01:52:56.390 align:middle line:84% HAZHIR RAHMANDAD: I'm just looking at the formulation 01:52:56.390 --> 01:52:58.310 align:middle line:90% for fund depletion. 01:52:58.310 --> 01:53:03.310 align:middle line:84% It is investor exit multiplied by average old member balance. 01:53:03.310 --> 01:53:05.055 align:middle line:90% And average old member balance-- 01:53:05.055 --> 01:53:06.930 align:middle line:84% AUDIENCE: It's not going into the right spot. 01:53:06.930 --> 01:53:09.430 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so this part, the actual money being 01:53:09.430 --> 01:53:13.150 align:middle line:84% dispersed, is based on how much you invested 01:53:13.150 --> 01:53:15.250 align:middle line:90% and it accrues no interest. 01:53:15.250 --> 01:53:17.450 align:middle line:84% Then you have this other thingy here, 01:53:17.450 --> 01:53:20.830 align:middle line:84% which is reported old account balance, where 01:53:20.830 --> 01:53:23.810 align:middle line:84% you are calculating something different, which 01:53:23.810 --> 01:53:29.490 align:middle line:84% is total fund divided by mature investors. 01:53:29.490 --> 01:53:33.290 align:middle line:84% And that number will be larger than average old member balance. 01:53:33.290 --> 01:53:36.890 align:middle line:84% And then you are calling that reported balance. 01:53:36.890 --> 01:53:39.830 align:middle line:84% But you're not taking that out of the funds. 01:53:39.830 --> 01:53:42.050 align:middle line:90% So that's two errors-- 01:53:42.050 --> 01:53:45.330 align:middle line:90% 18 out of 20. 01:53:45.330 --> 01:53:46.590 align:middle line:90% AUDIENCE: That's not bad. 01:53:46.590 --> 01:53:48.890 align:middle line:90% No, it's worse than that. 01:53:48.890 --> 01:53:51.530 align:middle line:84% The main question I have is about the Bass diffusion part. 01:53:51.530 --> 01:53:54.530 align:middle line:90% I know this is wrong. 01:53:54.530 --> 01:54:00.650 align:middle line:84% So I did one more into the VCR model, where becoming interested 01:54:00.650 --> 01:54:04.490 align:middle line:84% is driven by the return relative to the reference. 01:54:04.490 --> 01:54:08.690 align:middle line:84% And then it's a normal information diffusion. 01:54:08.690 --> 01:54:11.450 align:middle line:84% But mostly everyone else seems good. 01:54:11.450 --> 01:54:15.270 align:middle line:84% The investment probability depends on the return. 01:54:15.270 --> 01:54:17.350 align:middle line:90% So my question is this-- 01:54:17.350 --> 01:54:19.370 align:middle line:84% HAZHIR RAHMANDAD: So this is actually 01:54:19.370 --> 01:54:22.290 align:middle line:90% an important difference. 01:54:22.290 --> 01:54:24.250 align:middle line:84% So this is the Bass diffusion model. 01:54:24.250 --> 01:54:28.170 align:middle line:84% Once you are in the potential investors, 01:54:28.170 --> 01:54:32.470 align:middle line:90% you will be investing basically. 01:54:32.470 --> 01:54:36.390 align:middle line:84% And that's kind of what you are formulating. 01:54:36.390 --> 01:54:42.630 align:middle line:84% So if, today, you have learned that Ponzi is a scam 01:54:42.630 --> 01:54:44.430 align:middle line:90% and is not trustable-- 01:54:44.430 --> 01:54:48.450 align:middle line:84% now you don't have that part very clearly accounted for here. 01:54:48.450 --> 01:54:50.430 align:middle line:90% But let's assume you had it-- 01:54:50.430 --> 01:54:54.970 align:middle line:84% still, these potential investors will be adopting with the same-- 01:54:54.970 --> 01:54:57.550 align:middle line:90% 01:54:57.550 --> 01:55:01.030 align:middle line:84% AUDIENCE: Unless they flow back into-- 01:55:01.030 --> 01:55:03.510 align:middle line:84% HAZHIR RAHMANDAD: How do they flow back 01:55:03.510 --> 01:55:05.210 align:middle line:90% based on the indicated billing? 01:55:05.210 --> 01:55:08.050 align:middle line:90% So that may work. 01:55:08.050 --> 01:55:13.750 align:middle line:84% So max indicated willing to invest minus actual willing 01:55:13.750 --> 01:55:18.190 align:middle line:84% to invest versus minus potential investor divided 01:55:18.190 --> 01:55:20.330 align:middle line:90% by time to become interested. 01:55:20.330 --> 01:55:24.430 align:middle line:84% I mean, you adopted this from the homework assignment, 01:55:24.430 --> 01:55:26.890 align:middle line:84% and this is kind of a [INAUDIBLE] formulation 01:55:26.890 --> 01:55:32.610 align:middle line:84% that we put in that assignment to make it simple enough that we 01:55:32.610 --> 01:55:34.602 align:middle line:90% can give it to students. 01:55:34.602 --> 01:55:36.810 align:middle line:84% But it's not the perfect one because, basically, it's 01:55:36.810 --> 01:55:40.190 align:middle line:84% saying the time to become interested is symmetrical. 01:55:40.190 --> 01:55:41.970 align:middle line:84% That is, the time to become interested 01:55:41.970 --> 01:55:43.070 align:middle line:90% and time to lose interest. 01:55:43.070 --> 01:55:51.770 align:middle line:84% Whereas in this case, if you are moving backwards, 01:55:51.770 --> 01:55:53.850 align:middle line:84% the chances are it is a much faster move 01:55:53.850 --> 01:55:56.550 align:middle line:90% backwards than the forward part. 01:55:56.550 --> 01:55:58.485 align:middle line:90% But putting that aside-- 01:55:58.485 --> 01:56:00.110 align:middle line:84% AUDIENCE: Just the choice of where to-- 01:56:00.110 --> 01:56:02.027 align:middle line:84% HAZHIR RAHMANDAD: Yes, but putting that aside, 01:56:02.027 --> 01:56:04.650 align:middle line:84% you still will have people-- so today, 01:56:04.650 --> 01:56:08.890 align:middle line:84% everybody knows this is a scam, but you have 100,000 people 01:56:08.890 --> 01:56:10.890 align:middle line:90% in potential investors. 01:56:10.890 --> 01:56:14.810 align:middle line:84% You will continue to turn them into new investors 01:56:14.810 --> 01:56:16.650 align:middle line:90% even though none of them should. 01:56:16.650 --> 01:56:18.770 align:middle line:90% So that is not-- 01:56:18.770 --> 01:56:24.170 align:middle line:84% so you do need the impact on the actual investor transition. 01:56:24.170 --> 01:56:27.230 align:middle line:90% 01:56:27.230 --> 01:56:30.210 align:middle line:84% And the other parts, you already know some of the challenges. 01:56:30.210 --> 01:56:31.670 align:middle line:84% AUDIENCE: It's not the right story. 01:56:31.670 --> 01:56:32.850 align:middle line:90% HAZHIR RAHMANDAD: OK, cool. 01:56:32.850 --> 01:56:37.550 align:middle line:90% 01:56:37.550 --> 01:56:40.130 align:middle line:90% Any other one? 01:56:40.130 --> 01:56:42.870 align:middle line:90% 01:56:42.870 --> 01:56:45.330 align:middle line:90% This is Cathy. 01:56:45.330 --> 01:56:48.150 align:middle line:90% 01:56:48.150 --> 01:56:50.910 align:middle line:84% AUDIENCE: Mine is different in that it just captures-- in 01:56:50.910 --> 01:56:53.770 align:middle line:84% that it doesn't capture a lot of what you're talking about, 01:56:53.770 --> 01:56:56.230 align:middle line:90% but it does have the pull. 01:56:56.230 --> 01:56:58.390 align:middle line:84% HAZHIR RAHMANDAD: Yeah, let's take a look. 01:56:58.390 --> 01:56:59.330 align:middle line:90% Let's take a look. 01:56:59.330 --> 01:57:01.910 align:middle line:90% So this is Jake's. 01:57:01.910 --> 01:57:06.990 align:middle line:84% So we have the different categories of investors, 01:57:06.990 --> 01:57:10.070 align:middle line:90% so scheme susceptible group. 01:57:10.070 --> 01:57:13.790 align:middle line:84% This goes grows with population growth rate. 01:57:13.790 --> 01:57:19.173 align:middle line:90% They may decide to join-- 01:57:19.173 --> 01:57:21.090 align:middle line:84% AUDIENCE: That's just going to be [INAUDIBLE]. 01:57:21.090 --> 01:57:23.950 align:middle line:84% HAZHIR RAHMANDAD: So you have a collapsed function. 01:57:23.950 --> 01:57:26.350 align:middle line:84% So as long as it has not collapsed, 01:57:26.350 --> 01:57:32.410 align:middle line:84% it is minimum of this kind of maximum rate and then desired 01:57:32.410 --> 01:57:33.530 align:middle line:90% people rate. 01:57:33.530 --> 01:57:36.410 align:middle line:84% So a couple of items here that comes to my mind 01:57:36.410 --> 01:57:41.110 align:middle line:84% just quickly-- so first, this expression here, 01:57:41.110 --> 01:57:44.570 align:middle line:84% even though it is kind of unit consistent and does 01:57:44.570 --> 01:57:48.690 align:middle line:84% the job for you, it is using time step inside formulations. 01:57:48.690 --> 01:57:52.330 align:middle line:84% And using time step inside formulations is not a good idea. 01:57:52.330 --> 01:57:55.330 align:middle line:84% And the reason it is not a Good idea is that it is conceptually 01:57:55.330 --> 01:57:56.830 align:middle line:90% doesn't exist in the real world. 01:57:56.830 --> 01:57:58.730 align:middle line:84% There is nothing called time step. 01:57:58.730 --> 01:58:04.370 align:middle line:84% It is fully a mathematical artifact needed 01:58:04.370 --> 01:58:09.610 align:middle line:90% for numerical integration. 01:58:09.610 --> 01:58:14.590 align:middle line:84% So you don't want to use those concepts inside things that have 01:58:14.590 --> 01:58:16.330 align:middle line:90% a meaning inside the model. 01:58:16.330 --> 01:58:20.710 align:middle line:84% In this case, the meaning is that the scheme-susceptible 01:58:20.710 --> 01:58:25.190 align:middle line:84% population cannot be depleted instantaneously. 01:58:25.190 --> 01:58:30.410 align:middle line:84% Or it can-- actually, with this one in [INAUDIBLE] it can, 01:58:30.410 --> 01:58:37.950 align:middle line:84% but you cannot exceed a maximum rate of depleting these people. 01:58:37.950 --> 01:58:42.950 align:middle line:84% So just have minimum time to deplete the scheme susceptible 01:58:42.950 --> 01:58:44.450 align:middle line:90% population as a parameter. 01:58:44.450 --> 01:58:45.610 align:middle line:90% Don't use time step. 01:58:45.610 --> 01:58:47.510 align:middle line:90% So that's standard. 01:58:47.510 --> 01:58:51.150 align:middle line:84% And then the other one is the collapse thingy. 01:58:51.150 --> 01:58:53.790 align:middle line:84% I'm a little bit worried what is happening 01:58:53.790 --> 01:58:55.230 align:middle line:90% inside the formulation for it. 01:58:55.230 --> 01:58:57.070 align:middle line:84% Until we go into it, I don't know. 01:58:57.070 --> 01:59:00.250 align:middle line:84% Just the term collapse sounds a very switchy thing, 01:59:00.250 --> 01:59:03.190 align:middle line:84% and I'm wondering whether you wanted it to be a very kind 01:59:03.190 --> 01:59:07.590 align:middle line:84% of 0-1 switch, or is it something that you want to work 01:59:07.590 --> 01:59:08.770 align:middle line:90% for you continuously? 01:59:08.770 --> 01:59:10.010 align:middle line:90% If it is continuous-- 01:59:10.010 --> 01:59:11.290 align:middle line:90% AUDIENCE: It's 0. 01:59:11.290 --> 01:59:14.970 align:middle line:84% HAZHIR RAHMANDAD: And then these are people. 01:59:14.970 --> 01:59:17.270 align:middle line:84% So ultimately, this is actually more interesting. 01:59:17.270 --> 01:59:19.970 align:middle line:84% Part is what is the desired people rate. 01:59:19.970 --> 01:59:22.250 align:middle line:84% And the desired people rate is coming 01:59:22.250 --> 01:59:28.690 align:middle line:84% from desired money and average investor contribution. 01:59:28.690 --> 01:59:36.090 align:middle line:84% So basically, you have something about desired money, 01:59:36.090 --> 01:59:38.150 align:middle line:90% which is a complex formulation. 01:59:38.150 --> 01:59:41.570 align:middle line:84% So it's current investors divided by promised return 01:59:41.570 --> 01:59:45.410 align:middle line:84% time multiplied by average investor contribution multiplied 01:59:45.410 --> 01:59:48.050 align:middle line:90% by promised return factor. 01:59:48.050 --> 01:59:54.770 align:middle line:84% So basically, you're saying if I need to pay people $1,000 based 01:59:54.770 --> 02:00:00.530 align:middle line:84% on their maturing rate, I need $1,000 of new investment. 02:00:00.530 --> 02:00:02.430 align:middle line:90% So that's my desired money. 02:00:02.430 --> 02:00:04.065 align:middle line:90% Is that the idea? 02:00:04.065 --> 02:00:04.690 align:middle line:90% AUDIENCE: Yeah. 02:00:04.690 --> 02:00:09.110 align:middle line:84% So Ponzi is going to recognize, I have to pay out twice, 02:00:09.110 --> 02:00:10.610 align:middle line:84% so I'm going to go get two people. 02:00:10.610 --> 02:00:13.990 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so that's 02:00:13.990 --> 02:00:17.110 align:middle line:84% an interesting story that is basically 02:00:17.110 --> 02:00:21.550 align:middle line:84% Ponzi's proactively trying to go and recruit investors, which 02:00:21.550 --> 02:00:22.670 align:middle line:90% perhaps happens. 02:00:22.670 --> 02:00:25.370 align:middle line:84% Now, I don't know the story of Ponzi, 02:00:25.370 --> 02:00:28.350 align:middle line:84% how much that played a role because probably 02:00:28.350 --> 02:00:32.790 align:middle line:84% the word of mouth type of things were much more important driver 02:00:32.790 --> 02:00:34.650 align:middle line:90% of investment acquisition. 02:00:34.650 --> 02:00:37.190 align:middle line:84% But in Madoff's story, perhaps this 02:00:37.190 --> 02:00:39.310 align:middle line:84% was important as well, I don't know, 02:00:39.310 --> 02:00:41.710 align:middle line:84% or some of the other schemes that 02:00:41.710 --> 02:00:45.750 align:middle line:84% are more slow burning, the active engagement 02:00:45.750 --> 02:00:55.630 align:middle line:84% and recruitment of investors may be important. 02:00:55.630 --> 02:00:59.790 align:middle line:84% AUDIENCE: My thought was maybe that even if there 02:00:59.790 --> 02:01:02.350 align:middle line:84% was a lot of demand to invest, Ponzi 02:01:02.350 --> 02:01:04.870 align:middle line:84% would recognize if everybody invests at once, that's 02:01:04.870 --> 02:01:07.625 align:middle line:90% going to be a problem for me. 02:01:07.625 --> 02:01:09.750 align:middle line:84% HAZHIR RAHMANDAD: Yeah, that's an interesting idea. 02:01:09.750 --> 02:01:15.570 align:middle line:84% So basically, you're saying Ponzi keeps the new investment 02:01:15.570 --> 02:01:17.930 align:middle line:84% at an optimal level of sorts that 02:01:17.930 --> 02:01:24.010 align:middle line:84% is close to what he needs to just pay back the maturing 02:01:24.010 --> 02:01:25.370 align:middle line:90% investors. 02:01:25.370 --> 02:01:26.650 align:middle line:90% So that way-- 02:01:26.650 --> 02:01:28.950 align:middle line:84% AUDIENCE: To prove that he can do it 02:01:28.950 --> 02:01:32.210 align:middle line:84% because he can go to anybody and call 50 people that they 02:01:32.210 --> 02:01:34.328 align:middle line:90% know and say this works. 02:01:34.328 --> 02:01:35.870 align:middle line:84% HAZHIR RAHMANDAD: That's interesting. 02:01:35.870 --> 02:01:39.170 align:middle line:90% So I like that. 02:01:39.170 --> 02:01:41.870 align:middle line:84% But the way I would capture that idea, 02:01:41.870 --> 02:01:44.390 align:middle line:84% if I wanted to incorporate that idea in the model, 02:01:44.390 --> 02:01:48.650 align:middle line:84% would be to have this act as a gate for getting 02:01:48.650 --> 02:01:52.770 align:middle line:84% new investors when they have been convinced 02:01:52.770 --> 02:01:54.590 align:middle line:90% of becoming a new investors. 02:01:54.590 --> 02:01:56.850 align:middle line:84% So I would have the Bass diffusion 02:01:56.850 --> 02:02:02.170 align:middle line:84% model to transform people from not interested to interested. 02:02:02.170 --> 02:02:06.550 align:middle line:84% And then, from that interested into actually getting 02:02:06.550 --> 02:02:10.270 align:middle line:84% their money into the scheme, it is gated by Ponzi 02:02:10.270 --> 02:02:12.590 align:middle line:84% accepting their money, essentially, 02:02:12.590 --> 02:02:16.870 align:middle line:84% and Ponzi can, at that point, put an upper bound on that. 02:02:16.870 --> 02:02:20.030 align:middle line:84% He cannot control the lower bound if there is nobody willing 02:02:20.030 --> 02:02:23.590 align:middle line:84% to invest because now he has lost his reputation-- 02:02:23.590 --> 02:02:26.245 align:middle line:90% he goes bust. 02:02:26.245 --> 02:02:27.370 align:middle line:90% That's an interesting idea. 02:02:27.370 --> 02:02:33.190 align:middle line:84% I think it does make sense for the kind of designing 02:02:33.190 --> 02:02:36.190 align:middle line:90% a good scam. 02:02:36.190 --> 02:02:43.950 align:middle line:84% Good that is working, not good for the human utility functions. 02:02:43.950 --> 02:02:46.590 align:middle line:90% 02:02:46.590 --> 02:02:51.190 align:middle line:84% Current investors-- and then they 02:02:51.190 --> 02:02:55.110 align:middle line:84% have the promised rate of return. 02:02:55.110 --> 02:03:00.850 align:middle line:84% They try to cash out, but sometimes, they don't succeed. 02:03:00.850 --> 02:03:02.590 align:middle line:84% And you have the time step going here 02:03:02.590 --> 02:03:05.060 align:middle line:90% to limit the money out as well. 02:03:05.060 --> 02:03:07.900 align:middle line:84% So that's a little bit of kludgy as well. 02:03:07.900 --> 02:03:09.240 align:middle line:90% So you want that. 02:03:09.240 --> 02:03:11.200 align:middle line:90% And then the ratio of-- 02:03:11.200 --> 02:03:13.897 align:middle line:84% AUDIENCE: I think, originally, they were all promised return 02:03:13.897 --> 02:03:16.480 align:middle line:84% time rather than time stuff, but at some point, I switched one 02:03:16.480 --> 02:03:18.800 align:middle line:90% and then I got it. 02:03:18.800 --> 02:03:20.880 align:middle line:84% HAZHIR RAHMANDAD: And then if you are not 02:03:20.880 --> 02:03:23.280 align:middle line:84% paying what people are asking for, this 02:03:23.280 --> 02:03:25.420 align:middle line:90% is what will happen here? 02:03:25.420 --> 02:03:28.560 align:middle line:90% Anything happens in your model? 02:03:28.560 --> 02:03:32.800 align:middle line:84% AUDIENCE: So the second that you have-- 02:03:32.800 --> 02:03:34.640 align:middle line:84% the switch for collapse variable is 02:03:34.640 --> 02:03:38.020 align:middle line:84% going to be the one that you want to look at, 02:03:38.020 --> 02:03:39.560 align:middle line:90% which is above-- 02:03:39.560 --> 02:03:41.550 align:middle line:90% switch for collapse, yeah. 02:03:41.550 --> 02:03:43.800 align:middle line:84% Collapse and switch collapse are the exact same thing. 02:03:43.800 --> 02:03:48.560 align:middle line:84% Earlier, I iteratively built it [INAUDIBLE] there. 02:03:48.560 --> 02:03:50.680 align:middle line:90% So the second bit-- 02:03:50.680 --> 02:03:53.080 align:middle line:84% HAZHIR RAHMANDAD: So basically, you either 02:03:53.080 --> 02:03:55.720 align:middle line:84% don't have the money coverage that is 1 02:03:55.720 --> 02:03:58.440 align:middle line:84% or you have some unpaid population, 02:03:58.440 --> 02:04:01.900 align:middle line:84% you kind of kill everything in the operation. 02:04:01.900 --> 02:04:04.420 align:middle line:84% You have the collapse, which in this case 02:04:04.420 --> 02:04:06.880 align:middle line:84% means nobody is accepting investor equity. 02:04:06.880 --> 02:04:11.600 align:middle line:84% I mean, Ponzi is trying, but nobody is paying him. 02:04:11.600 --> 02:04:14.460 align:middle line:90% 02:04:14.460 --> 02:04:17.820 align:middle line:84% AUDIENCE: So the second you don't pay one person, suddenly, 02:04:17.820 --> 02:04:19.005 align:middle line:90% it's over. 02:04:19.005 --> 02:04:19.880 align:middle line:90% HAZHIR RAHMANDAD: OK. 02:04:19.880 --> 02:04:28.460 align:middle line:84% So I think this is kind of working for you because it grows 02:04:28.460 --> 02:04:33.300 align:middle line:84% exponentially as long as Ponzi is 02:04:33.300 --> 02:04:37.320 align:middle line:84% able to bring people in, but then, at some point, 02:04:37.320 --> 02:04:38.240 align:middle line:90% it collapses. 02:04:38.240 --> 02:04:41.200 align:middle line:84% So it's an interesting story here. 02:04:41.200 --> 02:04:43.920 align:middle line:84% So let's look at what is happening here. 02:04:43.920 --> 02:04:46.420 align:middle line:84% So there is the exponential growth phase. 02:04:46.420 --> 02:04:48.760 align:middle line:84% Then there is a kind of a slowdown phase. 02:04:48.760 --> 02:04:51.642 align:middle line:90% So what is driving slowdown? 02:04:51.642 --> 02:04:53.100 align:middle line:84% AUDIENCE: The slowdown phase starts 02:04:53.100 --> 02:04:58.620 align:middle line:84% when the game-susceptible population just 02:04:58.620 --> 02:05:01.520 align:middle line:84% is equal to the-- it becomes equal to the growth 02:05:01.520 --> 02:05:04.280 align:middle line:84% in population rather than having some excess. 02:05:04.280 --> 02:05:06.460 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:05:06.460 --> 02:05:10.040 align:middle line:84% So for a while, population growth 02:05:10.040 --> 02:05:15.280 align:middle line:90% becomes the bounding factor. 02:05:15.280 --> 02:05:18.220 align:middle line:84% AUDIENCE: And then you run out of cash that you would saved up. 02:05:18.220 --> 02:05:20.700 align:middle line:84% HAZHIR RAHMANDAD: I see, so you had saved up. 02:05:20.700 --> 02:05:24.540 align:middle line:90% But how did you save up? 02:05:24.540 --> 02:05:29.800 align:middle line:84% Because you were recruiting just enough to pay back these people. 02:05:29.800 --> 02:05:32.000 align:middle line:90% How is it that you save money? 02:05:32.000 --> 02:05:35.040 align:middle line:84% AUDIENCE: I think it's because your reinvestors who 02:05:35.040 --> 02:05:37.040 align:middle line:90% are convinced, oh, this-- 02:05:37.040 --> 02:05:38.520 align:middle line:84% basically everyone who invests is 02:05:38.520 --> 02:05:40.960 align:middle line:84% going to reinvest in this case, so you always 02:05:40.960 --> 02:05:43.200 align:middle line:84% have their cash in the system apart 02:05:43.200 --> 02:05:46.580 align:middle line:84% from the time that it takes them to actually-- 02:05:46.580 --> 02:05:49.480 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so you have the reinvestment 02:05:49.480 --> 02:05:51.460 align:middle line:90% process also here. 02:05:51.460 --> 02:05:54.140 align:middle line:84% And that allows you to accumulate money. 02:05:54.140 --> 02:05:56.660 align:middle line:90% 02:05:56.660 --> 02:05:58.940 align:middle line:84% So you're bringing in new investors 02:05:58.940 --> 02:06:00.980 align:middle line:84% even though you actually don't necessarily 02:06:00.980 --> 02:06:05.390 align:middle line:84% need all of those new investors at the beginning of the time. 02:06:05.390 --> 02:06:06.140 align:middle line:90% AUDIENCE: Correct. 02:06:06.140 --> 02:06:08.100 align:middle line:90% HAZHIR RAHMANDAD: Got it. 02:06:08.100 --> 02:06:09.640 align:middle line:90% It's interesting. 02:06:09.640 --> 02:06:14.440 align:middle line:84% It has kind of these challenges we talked about, 02:06:14.440 --> 02:06:16.475 align:middle line:84% but it has an interesting feature 02:06:16.475 --> 02:06:18.100 align:middle line:84% that other models didn't have, and that 02:06:18.100 --> 02:06:21.940 align:middle line:84% is kind of the pool from Ponzi side 02:06:21.940 --> 02:06:24.740 align:middle line:84% for getting money or kind of putting a gate on how 02:06:24.740 --> 02:06:27.740 align:middle line:90% much money he is trying to get. 02:06:27.740 --> 02:06:29.440 align:middle line:90% Cool. 02:06:29.440 --> 02:06:32.700 align:middle line:90% So I think this was pretty good. 02:06:32.700 --> 02:06:34.340 align:middle line:84% Across the models, there were several 02:06:34.340 --> 02:06:38.140 align:middle line:84% that had most of the components in a good shape. 02:06:38.140 --> 02:06:40.200 align:middle line:84% I think we could go through more, 02:06:40.200 --> 02:06:45.580 align:middle line:84% but I want to get to the other parts of the conversation 02:06:45.580 --> 02:06:54.340 align:middle line:84% because next week and the week after, we don't have class. 02:06:54.340 --> 02:06:57.000 align:middle line:84% It's Sloan innovation period, and then it 02:06:57.000 --> 02:06:59.680 align:middle line:90% is spring break at MIT. 02:06:59.680 --> 02:07:07.440 align:middle line:84% So we would be meeting up April 4, something like that. 02:07:07.440 --> 02:07:10.400 align:middle line:90% So that's a bit of a time. 02:07:10.400 --> 02:07:21.960 align:middle line:84% So for that longer time, we have the next session-- 02:07:21.960 --> 02:07:24.640 align:middle line:84% for next session, we have the market growth model. 02:07:24.640 --> 02:07:30.840 align:middle line:84% Now this is basically adopted from Jay Forrester's 02:07:30.840 --> 02:07:33.920 align:middle line:90% famous market growth paper. 02:07:33.920 --> 02:07:36.760 align:middle line:84% Don't look at that model so that you build it 02:07:36.760 --> 02:07:38.060 align:middle line:90% from scratch on your own. 02:07:38.060 --> 02:07:41.240 align:middle line:84% And it is not replicating exactly what the market growth 02:07:41.240 --> 02:07:41.900 align:middle line:90% model does. 02:07:41.900 --> 02:07:46.600 align:middle line:84% It has a couple other additional pieces to it. 02:07:46.600 --> 02:07:48.720 align:middle line:84% This is also like Ponzi, a little bit kind 02:07:48.720 --> 02:07:50.060 align:middle line:90% of broader boundary. 02:07:50.060 --> 02:07:52.920 align:middle line:84% You might formulate things a bit differently. 02:07:52.920 --> 02:07:56.060 align:middle line:84% So it's about a company that is selling 02:07:56.060 --> 02:08:01.260 align:middle line:84% a durable product in a limited market, but a large market. 02:08:01.260 --> 02:08:03.820 align:middle line:84% It is in a monopolistic setting, so you don't need 02:08:03.820 --> 02:08:07.220 align:middle line:90% to worry about competition. 02:08:07.220 --> 02:08:10.340 align:middle line:84% And you're kind of looking at the market growth 02:08:10.340 --> 02:08:13.620 align:middle line:84% from inception all the way to maturity. 02:08:13.620 --> 02:08:16.300 align:middle line:84% And this is a product that is complex 02:08:16.300 --> 02:08:20.880 align:middle line:84% and life-long kind of durable products. 02:08:20.880 --> 02:08:24.360 align:middle line:84% So they sell it through direct sales force. 02:08:24.360 --> 02:08:27.360 align:middle line:84% This is not a Bass diffusion type of a word of mouth. 02:08:27.360 --> 02:08:32.100 align:middle line:84% People hear about it and come and order a million dollar item. 02:08:32.100 --> 02:08:38.260 align:middle line:84% It's kind of a much more structured go and sell it type. 02:08:38.260 --> 02:08:42.620 align:middle line:84% And the firm's heuristic is to allocate 02:08:42.620 --> 02:08:46.180 align:middle line:84% a fraction of its revenue to Salesforce for selling things. 02:08:46.180 --> 02:08:53.260 align:middle line:90% And also, if they can't-- 02:08:53.260 --> 02:08:56.740 align:middle line:84% if they don't have product, they can't sell. 02:08:56.740 --> 02:09:01.560 align:middle line:84% Basically, their delivery delay increases. 02:09:01.560 --> 02:09:03.140 align:middle line:90% They make it to order. 02:09:03.140 --> 02:09:04.657 align:middle line:90% That is, there is a backlog. 02:09:04.657 --> 02:09:06.740 align:middle line:84% When they get orders, they will make the products. 02:09:06.740 --> 02:09:10.160 align:middle line:84% It's not that they have an inventory of the product. 02:09:10.160 --> 02:09:13.100 align:middle line:84% And if they can't deliver on time, 02:09:13.100 --> 02:09:14.780 align:middle line:90% they promise a delivery delay. 02:09:14.780 --> 02:09:17.240 align:middle line:84% If they can't deliver on time, customers 02:09:17.240 --> 02:09:19.180 align:middle line:84% become less interested to buy from them. 02:09:19.180 --> 02:09:22.000 align:middle line:84% So the success rate of their sales force 02:09:22.000 --> 02:09:25.080 align:middle line:84% in selling the product goes down if they are not 02:09:25.080 --> 02:09:28.400 align:middle line:90% delivering on time. 02:09:28.400 --> 02:09:32.080 align:middle line:84% Their manufacturing operations have-- 02:09:32.080 --> 02:09:35.140 align:middle line:90% 02:09:35.140 --> 02:09:38.360 align:middle line:84% it takes time to build the facilities. 02:09:38.360 --> 02:09:42.400 align:middle line:84% And the signal they look at to decide to expand manufacturing 02:09:42.400 --> 02:09:45.020 align:middle line:90% capacity is the delivery delay. 02:09:45.020 --> 02:09:54.040 align:middle line:84% So they use that to expand their manufacturing facilities, 02:09:54.040 --> 02:09:58.740 align:middle line:84% and those facilities stay around for a while. 02:09:58.740 --> 02:10:03.020 align:middle line:84% But they also depreciate, ultimately. 02:10:03.020 --> 02:10:07.040 align:middle line:84% You want to build a model of the dynamics in this setting, 02:10:07.040 --> 02:10:11.460 align:middle line:84% kind of the historical case that you are trying to explain 02:10:11.460 --> 02:10:14.420 align:middle line:84% is this is a very good market in the sense 02:10:14.420 --> 02:10:17.760 align:middle line:84% that these guys have a monopolistic setup, 02:10:17.760 --> 02:10:23.480 align:middle line:84% they have the market, and they have a good product in general, 02:10:23.480 --> 02:10:26.120 align:middle line:84% but they have seen kind of ups and downs in their growth. 02:10:26.120 --> 02:10:29.120 align:middle line:84% They have been growing, but have been seeing ups and downs in it. 02:10:29.120 --> 02:10:31.860 align:middle line:84% So that's the reference mode of sorts. 02:10:31.860 --> 02:10:37.200 align:middle line:84% But you also want to understand what is driving it 02:10:37.200 --> 02:10:40.980 align:middle line:84% and what are the alternative policies that may help 02:10:40.980 --> 02:10:44.180 align:middle line:90% them avoid the ups and downs. 02:10:44.180 --> 02:10:49.060 align:middle line:84% So that's the big picture of the case. 02:10:49.060 --> 02:10:54.480 align:middle line:84% Now, this is, again, a model that I'm 02:10:54.480 --> 02:10:57.400 align:middle line:84% explaining the components of it-- in a way, 02:10:57.400 --> 02:11:00.240 align:middle line:84% I'm telling you the mechanisms to model. 02:11:00.240 --> 02:11:02.960 align:middle line:84% You didn't need to go and do the research to decide 02:11:02.960 --> 02:11:04.060 align:middle line:90% what are the mechanisms. 02:11:04.060 --> 02:11:07.440 align:middle line:84% So as such, it is a simplified modeling task compared 02:11:07.440 --> 02:11:11.280 align:middle line:84% to most real-world problems, but it has more moving components 02:11:11.280 --> 02:11:14.680 align:middle line:90% than some of the previous work. 02:11:14.680 --> 02:11:20.640 align:middle line:84% So we could think about what are the questions that 02:11:20.640 --> 02:11:23.620 align:middle line:84% come to your mind, thinking about this formulation right now 02:11:23.620 --> 02:11:27.720 align:middle line:84% or this problem definition right now. 02:11:27.720 --> 02:11:30.660 align:middle line:84% What are some of the things you say, 02:11:30.660 --> 02:11:33.600 align:middle line:84% OK, I don't know how to think about it or how to model it. 02:11:33.600 --> 02:11:37.920 align:middle line:84% We could have maybe five or seven minutes of conversation 02:11:37.920 --> 02:11:43.320 align:middle line:84% around questions, and then we can switch to your problem 02:11:43.320 --> 02:11:47.440 align:middle line:84% definitions for your personal problems, which some of you 02:11:47.440 --> 02:11:48.640 align:middle line:90% have already shared. 02:11:48.640 --> 02:11:54.660 align:middle line:90% 02:11:54.660 --> 02:12:00.940 align:middle line:84% AUDIENCE: Maybe the depreciation of factories [INAUDIBLE]. 02:12:00.940 --> 02:12:02.100 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 02:12:02.100 --> 02:12:06.940 align:middle line:84% So it's a very important part of the model 02:12:06.940 --> 02:12:09.680 align:middle line:84% to build the production facilities as well. 02:12:09.680 --> 02:12:12.340 align:middle line:84% And there is kind of two or three pieces to it 02:12:12.340 --> 02:12:13.300 align:middle line:90% to do it well. 02:12:13.300 --> 02:12:15.920 align:middle line:84% One is it takes time to build things. 02:12:15.920 --> 02:12:19.500 align:middle line:84% So you have to separate work in progress factories that 02:12:19.500 --> 02:12:21.620 align:middle line:84% are kind of under construction versus factories 02:12:21.620 --> 02:12:23.388 align:middle line:90% that are constructed. 02:12:23.388 --> 02:12:25.180 align:middle line:84% Then there is the depreciation of factories 02:12:25.180 --> 02:12:26.940 align:middle line:90% that are already constructed. 02:12:26.940 --> 02:12:32.860 align:middle line:84% That depreciation, perhaps a simple delay function works, 02:12:32.860 --> 02:12:35.880 align:middle line:84% but a simple delay function with higher order delays. 02:12:35.880 --> 02:12:39.860 align:middle line:84% If you have a first order delay, it's kind of weird 02:12:39.860 --> 02:12:42.620 align:middle line:84% because production facilities don't 02:12:42.620 --> 02:12:45.400 align:middle line:84% start depreciating the day they are built, 02:12:45.400 --> 02:12:48.920 align:middle line:84% so accounting for that would be important. 02:12:48.920 --> 02:12:53.380 align:middle line:84% Then going back to your question about I have a factory. 02:12:53.380 --> 02:12:58.200 align:middle line:84% Does it mean it is producing at its full capacity or not? 02:12:58.200 --> 02:13:02.017 align:middle line:84% The answer is it doesn't need to be producing at full capacity. 02:13:02.017 --> 02:13:03.600 align:middle line:84% If you don't have demand, it shouldn't 02:13:03.600 --> 02:13:07.480 align:middle line:84% be because then you would be in a different business 02:13:07.480 --> 02:13:09.260 align:middle line:90% model with inventory. 02:13:09.260 --> 02:13:13.120 align:middle line:84% And even there, you wouldn't produce 02:13:13.120 --> 02:13:16.040 align:middle line:90% when there is no customer. 02:13:16.040 --> 02:13:19.900 align:middle line:84% So accounting for that capacity utilization-- 02:13:19.900 --> 02:13:21.920 align:middle line:84% so there is a capacity utilization feedback 02:13:21.920 --> 02:13:23.980 align:middle line:90% that you need to keep in mind. 02:13:23.980 --> 02:13:25.563 align:middle line:84% AUDIENCE: [INAUDIBLE] if we're running 02:13:25.563 --> 02:13:28.040 align:middle line:90% at full capacity [INAUDIBLE]. 02:13:28.040 --> 02:13:32.360 align:middle line:84% HAZHIR RAHMANDAD: That's an interesting observation. 02:13:32.360 --> 02:13:33.700 align:middle line:90% Don't worry about that. 02:13:33.700 --> 02:13:36.760 align:middle line:90% 02:13:36.760 --> 02:13:40.380 align:middle line:84% In practice, it is not a very clear-cut case. 02:13:40.380 --> 02:13:45.140 align:middle line:84% So for simpler equipment, whether it is running or not 02:13:45.140 --> 02:13:47.820 align:middle line:84% does make a difference in the depreciation time, 02:13:47.820 --> 02:13:49.860 align:middle line:84% but not running something actually 02:13:49.860 --> 02:13:53.500 align:middle line:84% can lead to depreciation as well. 02:13:53.500 --> 02:13:55.500 align:middle line:84% If you leave your car in the garage, 02:13:55.500 --> 02:13:59.420 align:middle line:84% it actually depreciates as fast as if not faster. 02:13:59.420 --> 02:14:03.280 align:middle line:84% A lot of the parts may rot in place and rust in place. 02:14:03.280 --> 02:14:06.625 align:middle line:90% So that's the argument. 02:14:06.625 --> 02:14:08.000 align:middle line:84% AUDIENCE: Same thing with planes. 02:14:08.000 --> 02:14:09.333 align:middle line:90% HAZHIR RAHMANDAD: Good question. 02:14:09.333 --> 02:14:14.145 align:middle line:84% Other thoughts, questions in how you think about this model? 02:14:14.145 --> 02:14:16.020 align:middle line:84% You have a little bit more time, but you also 02:14:16.020 --> 02:14:20.940 align:middle line:84% have your personal projects to define. 02:14:20.940 --> 02:14:22.580 align:middle line:90% AUDIENCE: [? Oscillation? ?] 02:14:22.580 --> 02:14:25.320 align:middle line:84% HAZHIR RAHMANDAD: You don't have to expect that, 02:14:25.320 --> 02:14:31.380 align:middle line:84% but you would try to see whether you can get oscillations 02:14:31.380 --> 02:14:32.780 align:middle line:90% from it. 02:14:32.780 --> 02:14:37.140 align:middle line:84% And what are the conditions under which oscillations happen? 02:14:37.140 --> 02:14:40.340 align:middle line:84% And on the bonus side, this one kind 02:14:40.340 --> 02:14:44.760 align:middle line:84% of in the original model and the version that is your baseline, 02:14:44.760 --> 02:14:49.120 align:middle line:84% the fraction of revenue that goes to the sales force 02:14:49.120 --> 02:14:51.880 align:middle line:90% is a fixed number. 02:14:51.880 --> 02:14:55.680 align:middle line:84% | can endogenize that based on marginal productivity 02:14:55.680 --> 02:14:59.040 align:middle line:84% of the sales force or how useful is 02:14:59.040 --> 02:15:00.820 align:middle line:84% to have sales force at any point in time. 02:15:00.820 --> 02:15:03.920 align:middle line:84% So that adds a separate feedback mechanism that is interesting 02:15:03.920 --> 02:15:06.100 align:middle line:84% and may change some of the dynamics. 02:15:06.100 --> 02:15:08.540 align:middle line:84% I actually haven't built that version myself, 02:15:08.540 --> 02:15:11.880 align:middle line:84% so I'm curious to see how you do it. 02:15:11.880 --> 02:15:13.945 align:middle line:84% I mean, if you had time, that's a good expansion. 02:15:13.945 --> 02:15:15.320 align:middle line:84% AUDIENCE: Endogenize [INAUDIBLE]? 02:15:15.320 --> 02:15:17.280 align:middle line:84% HAZHIR RAHMANDAD: Yeah, endogenous. 02:15:17.280 --> 02:15:20.540 align:middle line:84% Endogenize is something about your sales 02:15:20.540 --> 02:15:23.840 align:middle line:90% force size or budget or-- 02:15:23.840 --> 02:15:25.540 align:middle line:90% sales force size is endogenous. 02:15:25.540 --> 02:15:30.360 align:middle line:84% Sales force budget as a fraction of total revenue is not. 02:15:30.360 --> 02:15:33.640 align:middle line:90% 02:15:33.640 --> 02:15:34.640 align:middle line:90% Good. 02:15:34.640 --> 02:15:36.000 align:middle line:90% Go ahead. 02:15:36.000 --> 02:15:38.160 align:middle line:84% AUDIENCE: So when you manufacturing operation 02:15:38.160 --> 02:15:40.140 align:middle line:84% with the backlog, that means that they only 02:15:40.140 --> 02:15:42.017 align:middle line:90% produce what customers order. 02:15:42.017 --> 02:15:43.100 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 02:15:43.100 --> 02:15:46.900 align:middle line:84% So when customers order, it goes into a backlog. 02:15:46.900 --> 02:15:50.580 align:middle line:90% That drives desired delivery. 02:15:50.580 --> 02:15:54.120 align:middle line:84% That desired delivery is fulfilled based on production 02:15:54.120 --> 02:15:57.220 align:middle line:84% but is bounded by your production capacity. 02:15:57.220 --> 02:16:01.960 align:middle line:84% And if you have plenty of capacity, 02:16:01.960 --> 02:16:05.020 align:middle line:84% you will produce all that is desired, 02:16:05.020 --> 02:16:08.940 align:middle line:84% and you will have excess capacity that is not used. 02:16:08.940 --> 02:16:11.940 align:middle line:84% If you are bounded by capacity, you 02:16:11.940 --> 02:16:15.680 align:middle line:84% are delivering as much as you can, 02:16:15.680 --> 02:16:18.800 align:middle line:84% but you are not fulfilling the customer's demand. 02:16:18.800 --> 02:16:23.060 align:middle line:90% So that's the balancing act. 02:16:23.060 --> 02:16:25.460 align:middle line:84% AUDIENCE: [INAUDIBLE] don't have any measure 02:16:25.460 --> 02:16:27.918 align:middle line:90% of quality of the product? 02:16:27.918 --> 02:16:29.460 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so right now, 02:16:29.460 --> 02:16:31.860 align:middle line:84% we are assuming the quality of product is either 02:16:31.860 --> 02:16:33.780 align:middle line:90% exogenous or fixed or whatever. 02:16:33.780 --> 02:16:35.500 align:middle line:90% It's not part of the-- 02:16:35.500 --> 02:16:37.292 align:middle line:90% AUDIENCE: [INAUDIBLE] 02:16:37.292 --> 02:16:39.750 align:middle line:84% HAZHIR RAHMANDAD: Yes, for now, assume price is also fixed. 02:16:39.750 --> 02:16:42.841 align:middle line:84% AUDIENCE: --impacting the customers is this [INAUDIBLE]. 02:16:42.841 --> 02:16:44.549 align:middle line:84% HAZHIR RAHMANDAD: Only the delivery delay 02:16:44.549 --> 02:16:48.590 align:middle line:84% that is changing the customer's utility in this case. 02:16:48.590 --> 02:16:51.709 align:middle line:90% AUDIENCE: [INAUDIBLE] 02:16:51.709 --> 02:16:54.430 align:middle line:84% HAZHIR RAHMANDAD: Delivery delay as a proxy for price? 02:16:54.430 --> 02:16:56.190 align:middle line:84% AUDIENCE: Because it decreases demand. 02:16:56.190 --> 02:16:58.209 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so it is a feedback. 02:16:58.209 --> 02:17:01.389 align:middle line:84% It is not price feedback because price has 02:17:01.389 --> 02:17:03.730 align:middle line:90% its own impact on your budget. 02:17:03.730 --> 02:17:06.889 align:middle line:84% So price is completely ignorable. 02:17:06.889 --> 02:17:10.530 align:middle line:84% You need it in the machinery of your machine, your model. 02:17:10.530 --> 02:17:13.750 align:middle line:84% And you need a very simple accounting sector 02:17:13.750 --> 02:17:18.129 align:middle line:84% to think about, OK, costs and benefits and net gains 02:17:18.129 --> 02:17:20.910 align:middle line:90% and so on. 02:17:20.910 --> 02:17:23.629 align:middle line:84% AUDIENCE: So delivery delay signals the firm 02:17:23.629 --> 02:17:25.670 align:middle line:84% to expand their production capacity. 02:17:25.670 --> 02:17:27.045 align:middle line:84% HAZHIR RAHMANDAD: That's correct. 02:17:27.045 --> 02:17:30.150 align:middle line:84% AUDIENCE: That means there's always interested customers. 02:17:30.150 --> 02:17:32.510 align:middle line:84% HAZHIR RAHMANDAD: Yes, so this is-- 02:17:32.510 --> 02:17:35.450 align:middle line:84% now the size of the market is limited. 02:17:35.450 --> 02:17:37.650 align:middle line:84% So it's not an infinite size market. 02:17:37.650 --> 02:17:39.430 align:middle line:90% And it is a durable good. 02:17:39.430 --> 02:17:43.290 align:middle line:84% So once you buy it, you don't need it for a while. 02:17:43.290 --> 02:17:47.209 align:middle line:84% So the maximum demand is constrained. 02:17:47.209 --> 02:17:53.610 align:middle line:84% But that maximum demand is materializing. 02:17:53.610 --> 02:17:56.490 align:middle line:84% What fraction of it you can materialize 02:17:56.490 --> 02:18:01.170 align:middle line:84% depends on your sales force partly. 02:18:01.170 --> 02:18:07.209 align:middle line:84% So your sales force is going and getting these people. 02:18:07.209 --> 02:18:08.809 align:middle line:84% AUDIENCE: But does the demand change 02:18:08.809 --> 02:18:11.632 align:middle line:84% because it's monopolistic, so there's no competition? 02:18:11.632 --> 02:18:13.090 align:middle line:84% HAZHIR RAHMANDAD: So it does change 02:18:13.090 --> 02:18:18.850 align:middle line:84% because of the durable nature of the product. 02:18:18.850 --> 02:18:21.870 align:middle line:90% So that's the constraint. 02:18:21.870 --> 02:18:24.790 align:middle line:84% There is also, of course, your sales force effectiveness. 02:18:24.790 --> 02:18:27.330 align:middle line:84% So if your sales force-- you don't have anybody to sell, 02:18:27.330 --> 02:18:28.590 align:middle line:90% you wouldn't sell anything. 02:18:28.590 --> 02:18:31.709 align:middle line:90% 02:18:31.709 --> 02:18:33.209 align:middle line:84% AUDIENCE: So the delivery date delay 02:18:33.209 --> 02:18:37.687 align:middle line:84% doesn't at all impact the customers [INAUDIBLE]. 02:18:37.687 --> 02:18:38.770 align:middle line:90% HAZHIR RAHMANDAD: They do. 02:18:38.770 --> 02:18:39.910 align:middle line:90% It does. 02:18:39.910 --> 02:18:43.690 align:middle line:84% It changes the effectiveness of your sales force. 02:18:43.690 --> 02:18:45.570 align:middle line:90% So that's how it affects it. 02:18:45.570 --> 02:18:50.430 align:middle line:90% 02:18:50.430 --> 02:18:53.170 align:middle line:84% The writeup has these details in it. 02:18:53.170 --> 02:18:58.110 align:middle line:84% So this is a shorter version than what is in the writeup. 02:18:58.110 --> 02:19:01.350 align:middle line:84% For the last 10-15 minutes, I wanted to go back 02:19:01.350 --> 02:19:05.469 align:middle line:84% to the personal projects, and basically, 02:19:05.469 --> 02:19:08.510 align:middle line:84% my plan is to read through what you have submitted or will be 02:19:08.510 --> 02:19:13.030 align:middle line:84% submitting in the next day or two so that I can give you some 02:19:13.030 --> 02:19:17.684 align:middle line:84% feedback and you can adjust it, rework it, 02:19:17.684 --> 02:19:19.476 align:middle line:84% get to the level that you feel comfortable, 02:19:19.476 --> 02:19:21.670 align:middle line:90% you know how to move forward. 02:19:21.670 --> 02:19:26.450 align:middle line:84% Now, so far, as you have seen, we have defined the problems. 02:19:26.450 --> 02:19:30.430 align:middle line:84% If you remember in the memo note that I had and also briefly 02:19:30.430 --> 02:19:32.250 align:middle line:84% in the first session we discussed, 02:19:32.250 --> 02:19:34.610 align:middle line:84% there are different ways to define a problem. 02:19:34.610 --> 02:19:36.770 align:middle line:84% You may start from a reference mode 02:19:36.770 --> 02:19:39.530 align:middle line:84% that you are trying to explain and understand. 02:19:39.530 --> 02:19:42.290 align:middle line:84% You may start from a set of mechanisms 02:19:42.290 --> 02:19:43.750 align:middle line:90% that you are trying to model. 02:19:43.750 --> 02:19:47.270 align:middle line:84% You may start from policy levers that you want to then find. 02:19:47.270 --> 02:19:49.530 align:middle line:84% What are the mechanisms, what that 02:19:49.530 --> 02:19:53.210 align:middle line:84% need to be captured to measure the reference [INAUDIBLE]. 02:19:53.210 --> 02:19:55.548 align:middle line:84% In this class, so far, in all of our assignments, 02:19:55.548 --> 02:19:57.090 align:middle line:84% we have gone with the second approach 02:19:57.090 --> 02:20:00.050 align:middle line:84% of giving you the mechanisms and asking you to build 02:20:00.050 --> 02:20:02.050 align:middle line:90% models of those mechanisms. 02:20:02.050 --> 02:20:04.630 align:middle line:84% In some ways, this is the simpler way of doing things. 02:20:04.630 --> 02:20:10.730 align:middle line:84% That is, basically, I have already removed a lot of things 02:20:10.730 --> 02:20:12.030 align:middle line:90% that you could consider. 02:20:12.030 --> 02:20:14.650 align:middle line:84% I've kind of given you, these are the mechanisms 02:20:14.650 --> 02:20:15.670 align:middle line:90% you want to have. 02:20:15.670 --> 02:20:17.650 align:middle line:84% Ignore everything else so that we 02:20:17.650 --> 02:20:21.330 align:middle line:84% can have more focused conversation about formulations 02:20:21.330 --> 02:20:23.370 align:middle line:90% and so on. 02:20:23.370 --> 02:20:29.050 align:middle line:84% It may not be easy for you to get to this type of a problem 02:20:29.050 --> 02:20:32.390 align:middle line:84% definition because whatever you're interested in, 02:20:32.390 --> 02:20:35.790 align:middle line:84% you don't know what is it that you need to focus on. 02:20:35.790 --> 02:20:40.730 align:middle line:84% So as you think about it, first of all, 02:20:40.730 --> 02:20:46.670 align:middle line:84% do your best in defining what is important or interesting 02:20:46.670 --> 02:20:50.670 align:middle line:84% to model in terms of mechanisms to capture the problem that 02:20:50.670 --> 02:20:53.270 align:middle line:84% might be more motivated by a reference mode 02:20:53.270 --> 02:20:58.950 align:middle line:84% or by some policy questions by some pain point. 02:20:58.950 --> 02:21:02.810 align:middle line:84% And then I'll try to help you with that process. 02:21:02.810 --> 02:21:04.630 align:middle line:84% So whatever you have written down 02:21:04.630 --> 02:21:08.790 align:middle line:84% or are writing down for this first draft, I'll look at it 02:21:08.790 --> 02:21:11.750 align:middle line:84% and try to turn it into something 02:21:11.750 --> 02:21:15.990 align:middle line:84% that is a bit more closer to mechanisms 02:21:15.990 --> 02:21:18.670 align:middle line:84% so that you don't need to go through the process 02:21:18.670 --> 02:21:23.670 align:middle line:84% of clarifying a problem and the feedback mechanisms that 02:21:23.670 --> 02:21:25.630 align:middle line:84% will need to be in the model versus those that 02:21:25.630 --> 02:21:28.310 align:middle line:90% are not to be in the model. 02:21:28.310 --> 02:21:30.650 align:middle line:90% But that is not an easy task. 02:21:30.650 --> 02:21:32.610 align:middle line:84% I'm just highlighting it because that's, 02:21:32.610 --> 02:21:36.970 align:middle line:84% in some ways, the more vaguely defined, harder part 02:21:36.970 --> 02:21:40.130 align:middle line:84% of modeling, going from a broad problem definition 02:21:40.130 --> 02:21:41.970 align:middle line:84% into what are the mechanisms that need 02:21:41.970 --> 02:21:44.410 align:middle line:90% to go into a simulation model. 02:21:44.410 --> 02:21:47.350 align:middle line:90% So I want to be helpful on that. 02:21:47.350 --> 02:21:51.130 align:middle line:84% But maybe for the few minutes that we have, if any of you 02:21:51.130 --> 02:21:54.870 align:middle line:84% want to say, OK, I felt confused because I was thinking about it 02:21:54.870 --> 02:21:58.870 align:middle line:84% and I had no clue how to do it, or this is the problem space, 02:21:58.870 --> 02:22:00.380 align:middle line:84% but I don't know what to focus on, 02:22:00.380 --> 02:22:02.130 align:middle line:84% we can have a little bit of a conversation 02:22:02.130 --> 02:22:05.230 align:middle line:84% on a couple of cases, I think, with this limited time we have. 02:22:05.230 --> 02:22:09.330 align:middle line:84% That's what I wanted to talk about before we close. 02:22:09.330 --> 02:22:15.410 align:middle line:84% AUDIENCE: So just to clarify, talking about going from problem 02:22:15.410 --> 02:22:17.730 align:middle line:90% of interest to mechanism? 02:22:17.730 --> 02:22:21.610 align:middle line:90% HAZHIR RAHMANDAD: Yes, exactly. 02:22:21.610 --> 02:22:24.030 align:middle line:90% I mean, whatever you had-- 02:22:24.030 --> 02:22:26.550 align:middle line:84% I haven't read through the ones that were submitted, 02:22:26.550 --> 02:22:28.850 align:middle line:84% so I don't know what is in there, 02:22:28.850 --> 02:22:31.630 align:middle line:84% but if anybody wants to bring it up as a case 02:22:31.630 --> 02:22:34.210 align:middle line:84% because they felt confused or didn't know, 02:22:34.210 --> 02:22:36.470 align:middle line:84% I'm happy to have that conversation. 02:22:36.470 --> 02:22:37.630 align:middle line:90% Go for it. 02:22:37.630 --> 02:22:40.150 align:middle line:84% AUDIENCE: What I was thinking of doing was talking about 02:22:40.150 --> 02:22:44.150 align:middle line:84% how does the fashion resale industry affect brand 02:22:44.150 --> 02:22:46.430 align:middle line:90% recognition for luxury brands. 02:22:46.430 --> 02:22:51.810 align:middle line:84% So it kind of reminded me of the car case for GM. 02:22:51.810 --> 02:22:54.390 align:middle line:84% It was the used cars, but the difference 02:22:54.390 --> 02:22:57.010 align:middle line:84% is there's no leasing program in luxury. 02:22:57.010 --> 02:23:00.310 align:middle line:84% So my idea was you have luxury brands that 02:23:00.310 --> 02:23:02.790 align:middle line:84% want to gain, to some extent, brand recognition 02:23:02.790 --> 02:23:05.650 align:middle line:84% within their clientele, but for luxury brands, 02:23:05.650 --> 02:23:08.390 align:middle line:84% they don't want the wrong clientele using it because it 02:23:08.390 --> 02:23:11.310 align:middle line:90% ruins their brand image. 02:23:11.310 --> 02:23:15.310 align:middle line:84% So there is a level of, well, they want the-- 02:23:15.310 --> 02:23:17.290 align:middle line:84% you could argue, like in Supreme's case, 02:23:17.290 --> 02:23:20.710 align:middle line:84% the resale market really helped build up like the clout 02:23:20.710 --> 02:23:22.950 align:middle line:90% and how attractive it was. 02:23:22.950 --> 02:23:26.570 align:middle line:84% But then you can also see high luxury brands 02:23:26.570 --> 02:23:28.810 align:middle line:84% like Hermes having a lot of people 02:23:28.810 --> 02:23:30.370 align:middle line:84% wear Birkins, especially people who 02:23:30.370 --> 02:23:32.250 align:middle line:84% aren't like their ideal clientele 02:23:32.250 --> 02:23:38.590 align:middle line:90% is tanking their luxury status. 02:23:38.590 --> 02:23:41.090 align:middle line:84% And so then I was trying to figure out 02:23:41.090 --> 02:23:46.170 align:middle line:84% where does that line start between resellers and not 02:23:46.170 --> 02:23:50.610 align:middle line:84% resellers because there's a lot of different types of resellers. 02:23:50.610 --> 02:23:51.710 align:middle line:90% That's kind of my-- 02:23:51.710 --> 02:23:54.043 align:middle line:84% HAZHIR RAHMANDAD: So this is a very interesting problem. 02:23:54.043 --> 02:23:56.790 align:middle line:84% I think it's a good problem in the sense that it is dynamic. 02:23:56.790 --> 02:23:58.670 align:middle line:84% It kind of has important trade-offs. 02:23:58.670 --> 02:24:01.150 align:middle line:84% It has stocks and flows that you can imagine. 02:24:01.150 --> 02:24:02.350 align:middle line:90% So good space. 02:24:02.350 --> 02:24:04.110 align:middle line:84% I don't know enough about the topic, 02:24:04.110 --> 02:24:09.010 align:middle line:84% but from just that 30-second introduction that you gave, 02:24:09.010 --> 02:24:16.490 align:middle line:84% it feels to me you may need to have two categories of customers 02:24:16.490 --> 02:24:20.330 align:middle line:84% based on their willingness to pay something that might be 02:24:20.330 --> 02:24:24.510 align:middle line:90% the one piece of the story. 02:24:24.510 --> 02:24:29.550 align:middle line:84% You may care about your product's life 02:24:29.550 --> 02:24:34.750 align:middle line:84% in the sense of some quality versus how long it 02:24:34.750 --> 02:24:39.230 align:middle line:84% will last trade-off, and something about price 02:24:39.230 --> 02:24:40.210 align:middle line:90% that you assign. 02:24:40.210 --> 02:24:42.550 align:middle line:84% So for a product, you decide on the price, 02:24:42.550 --> 02:24:45.530 align:middle line:84% and you decide on that quality measure. 02:24:45.530 --> 02:24:49.630 align:middle line:84% And you might bring down the price 02:24:49.630 --> 02:24:51.310 align:middle line:90% and bring down the quality. 02:24:51.310 --> 02:24:56.270 align:middle line:84% You may get more of the low willingness 02:24:56.270 --> 02:24:59.710 align:middle line:84% to pay customer sector segment, which is much bigger customer 02:24:59.710 --> 02:25:00.210 align:middle line:90% segment. 02:25:00.210 --> 02:25:03.150 align:middle line:84% And you may still have a good margin on that, 02:25:03.150 --> 02:25:06.470 align:middle line:84% but then that may erode your attractiveness 02:25:06.470 --> 02:25:11.150 align:middle line:90% for the high brand group. 02:25:11.150 --> 02:25:17.390 align:middle line:84% So think about a model where you have adopter, nonadopter 02:25:17.390 --> 02:25:21.970 align:middle line:84% for two groups of customers, and then 02:25:21.970 --> 02:25:25.930 align:middle line:84% you have something about their attractiveness for each 02:25:25.930 --> 02:25:31.130 align:middle line:84% of these groups that comes from your price, your quality, 02:25:31.130 --> 02:25:34.290 align:middle line:84% and your exclusivity, or how much 02:25:34.290 --> 02:25:36.410 align:middle line:90% the other group is using it. 02:25:36.410 --> 02:25:39.530 align:middle line:84% So for the low willingness to pay customers, 02:25:39.530 --> 02:25:41.890 align:middle line:84% having high willingness to pay customers 02:25:41.890 --> 02:25:44.470 align:middle line:84% becomes a factor of attractiveness, 02:25:44.470 --> 02:25:47.410 align:middle line:84% but the reverse is actually negative. 02:25:47.410 --> 02:25:51.730 align:middle line:84% So that becomes kind of the heart of your model. 02:25:51.730 --> 02:25:53.750 align:middle line:90% I would say that works well. 02:25:53.750 --> 02:25:55.630 align:middle line:84% And don't go anywhere beyond that. 02:25:55.630 --> 02:25:57.610 align:middle line:90% That's already pretty-- 02:25:57.610 --> 02:26:03.370 align:middle line:84% AUDIENCE: I guess my question for when you're optimizing where 02:26:03.370 --> 02:26:08.890 align:middle line:84% should this brand position themselves is it's not 02:26:08.890 --> 02:26:10.810 align:middle line:84% profitability because, obviously, 02:26:10.810 --> 02:26:14.890 align:middle line:84% a Macy's is much more profitable than a Gucci. 02:26:14.890 --> 02:26:17.690 align:middle line:84% But they choose to stay in that space 02:26:17.690 --> 02:26:20.270 align:middle line:84% because they value something about it, 02:26:20.270 --> 02:26:22.230 align:middle line:84% whether it's the status or the artistic value 02:26:22.230 --> 02:26:25.310 align:middle line:84% that they perceive that they're gaining from being there. 02:26:25.310 --> 02:26:27.803 align:middle line:90% So I don't-- 02:26:27.803 --> 02:26:29.970 align:middle line:84% HAZHIR RAHMANDAD: That's an interesting observation. 02:26:29.970 --> 02:26:35.110 align:middle line:84% So don't worry about optimizing in that sense, 02:26:35.110 --> 02:26:41.390 align:middle line:84% but worry about whether they can thrive in their desired market 02:26:41.390 --> 02:26:42.010 align:middle line:90% segment. 02:26:42.010 --> 02:26:45.250 align:middle line:84% That is, if they are targeting the high customers, 02:26:45.250 --> 02:26:49.070 align:middle line:84% can they thrive there and still have a foothold 02:26:49.070 --> 02:26:52.230 align:middle line:84% in the other market, under what conditions? 02:26:52.230 --> 02:26:55.270 align:middle line:84% So keep it to that level of I'm interested in this question 02:26:55.270 --> 02:26:59.310 align:middle line:84% rather than optimizing for the whole market. 02:26:59.310 --> 02:27:00.850 align:middle line:90% I think that's a good problem. 02:27:00.850 --> 02:27:02.430 align:middle line:90% It would work out well. 02:27:02.430 --> 02:27:04.590 align:middle line:90% Good. 02:27:04.590 --> 02:27:05.610 align:middle line:90% Anybody else? 02:27:05.610 --> 02:27:10.510 align:middle line:90% 02:27:10.510 --> 02:27:15.390 align:middle line:84% AUDIENCE: I was thinking about there's a contrast-- 02:27:15.390 --> 02:27:19.610 align:middle line:84% basically, book sales are up but reading rates are down, 02:27:19.610 --> 02:27:24.930 align:middle line:84% and my hypothesis for why that is that the reason for buying 02:27:24.930 --> 02:27:30.450 align:middle line:84% a book is less so for the human capital of consuming it but more 02:27:30.450 --> 02:27:33.450 align:middle line:84% so for the signaling and cultural and social benefits 02:27:33.450 --> 02:27:38.010 align:middle line:84% that you get from having it and carrying it around 02:27:38.010 --> 02:27:42.530 align:middle line:84% and having it on your shelf when people come over, et cetera. 02:27:42.530 --> 02:27:50.170 align:middle line:84% And yeah, so I think it's more so like a simple paradox 02:27:50.170 --> 02:27:53.370 align:middle line:84% explanation with some reinforcing dynamics 02:27:53.370 --> 02:27:57.770 align:middle line:84% around social value of book makes it 02:27:57.770 --> 02:27:59.550 align:middle line:84% so that reading the book doesn't matter, 02:27:59.550 --> 02:28:04.550 align:middle line:84% makes it harder and less important to you to read books. 02:28:04.550 --> 02:28:07.850 align:middle line:84% And so that's how we get these sales increasing, reading-- 02:28:07.850 --> 02:28:10.330 align:middle line:84% HAZHIR RAHMANDAD: So just for me to understand 02:28:10.330 --> 02:28:13.730 align:middle line:84% the sales of physical books are up 02:28:13.730 --> 02:28:17.830 align:middle line:84% or sales of books, audio and physical together are, 02:28:17.830 --> 02:28:18.610 align:middle line:90% but not physical-- 02:28:18.610 --> 02:28:20.950 align:middle line:84% AUDIENCE: All formats sales are up. 02:28:20.950 --> 02:28:23.350 align:middle line:84% HAZHIR RAHMANDAD: So each format alone is also growing. 02:28:23.350 --> 02:28:25.690 align:middle line:84% Physical books also have been growing. 02:28:25.690 --> 02:28:27.310 align:middle line:84% AUDIENCE: Physical books are growing. 02:28:27.310 --> 02:28:28.230 align:middle line:90% Audio-- yeah. 02:28:28.230 --> 02:28:30.022 align:middle line:84% HAZHIR RAHMANDAD: OK, so that's number one. 02:28:30.022 --> 02:28:33.990 align:middle line:84% Then you're saying reading of it is actually declining. 02:28:33.990 --> 02:28:38.230 align:middle line:90% Is it reading across all-- 02:28:38.230 --> 02:28:40.430 align:middle line:84% AUDIENCE: So the survey question is, 02:28:40.430 --> 02:28:42.350 align:middle line:84% in the last 12-- or two survey questions. 02:28:42.350 --> 02:28:45.430 align:middle line:84% In the last 12 months, have you read a book 02:28:45.430 --> 02:28:47.230 align:middle line:90% not for work or school? 02:28:47.230 --> 02:28:50.832 align:middle line:84% And then second question is, how many books 02:28:50.832 --> 02:28:53.290 align:middle line:84% have you read in the last 12 months not for work or school? 02:28:53.290 --> 02:28:55.710 align:middle line:84% And both of those, it's like 50% of people 02:28:55.710 --> 02:28:58.110 align:middle line:84% now haven't read a book in the last year. 02:28:58.110 --> 02:29:04.140 align:middle line:84% And the average number of books has gone from 20-ish to 8. 02:29:04.140 --> 02:29:05.390 align:middle line:90% HAZHIR RAHMANDAD: Interesting. 02:29:05.390 --> 02:29:08.390 align:middle line:84% But when you say, have you read a book, 02:29:08.390 --> 02:29:12.690 align:middle line:84% people report their audiobook consumption as reading a book? 02:29:12.690 --> 02:29:15.240 align:middle line:90% Is that how the survey is-- 02:29:15.240 --> 02:29:18.520 align:middle line:84% AUDIENCE: I think the question hasn't been consistent 02:29:18.520 --> 02:29:21.360 align:middle line:84% over the 30 years, but I think in the recent surveys 02:29:21.360 --> 02:29:26.240 align:middle line:84% they say audiobooks count, and they should 02:29:26.240 --> 02:29:27.798 align:middle line:90% report audiobooks [INAUDIBLE]. 02:29:27.798 --> 02:29:28.840 align:middle line:90% HAZHIR RAHMANDAD: Got it. 02:29:28.840 --> 02:29:31.440 align:middle line:90% Got it. 02:29:31.440 --> 02:29:34.280 align:middle line:84% AUDIENCE: So I don't think this is a book format story. 02:29:34.280 --> 02:29:36.800 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:29:36.800 --> 02:29:39.600 align:middle line:84% AUDIENCE: I think this is a book like a BookTok, which 02:29:39.600 --> 02:29:43.400 align:middle line:84% is like the TikTok book phenomenon that really blew up 02:29:43.400 --> 02:29:45.100 align:middle line:90% across the pandemic story. 02:29:45.100 --> 02:29:47.623 align:middle line:90% 02:29:47.623 --> 02:29:49.040 align:middle line:84% HAZHIR RAHMANDAD: So the story you 02:29:49.040 --> 02:29:55.760 align:middle line:84% are telling as this is a story of social boasting 02:29:55.760 --> 02:29:59.400 align:middle line:84% that I have some books or I read books or whatever, 02:29:59.400 --> 02:30:05.620 align:middle line:90% that is interesting. 02:30:05.620 --> 02:30:09.600 align:middle line:90% It's probably not that complex. 02:30:09.600 --> 02:30:13.580 align:middle line:84% There is a feedback loop of people 02:30:13.580 --> 02:30:15.740 align:middle line:84% see books as a status symbol, and that 02:30:15.740 --> 02:30:22.200 align:middle line:84% may get reified as more people use it with that idea. 02:30:22.200 --> 02:30:24.420 align:middle line:90% And that drives demand. 02:30:24.420 --> 02:30:29.940 align:middle line:84% But then what is bringing down the actual consumption 02:30:29.940 --> 02:30:31.740 align:middle line:90% of books-- 02:30:31.740 --> 02:30:33.060 align:middle line:90% AUDIENCE: [INAUDIBLE] 02:30:33.060 --> 02:30:34.920 align:middle line:84% HAZHIR RAHMANDAD: --is a different story. 02:30:34.920 --> 02:30:38.700 align:middle line:84% That is, basically, it becomes a little bit exogenous-y. 02:30:38.700 --> 02:30:40.700 align:middle line:84% What I mean by exogenous is that there 02:30:40.700 --> 02:30:43.640 align:middle line:84% is a mechanism that is driving one reference mode, 02:30:43.640 --> 02:30:48.242 align:middle line:84% and that is books are becoming status symbols in some circles. 02:30:48.242 --> 02:30:49.700 align:middle line:84% And then there is another mechanism 02:30:49.700 --> 02:30:53.920 align:middle line:84% that is bringing down books consumption in your story. 02:30:53.920 --> 02:30:58.000 align:middle line:84% And that might be people are busy with other things, 02:30:58.000 --> 02:31:00.460 align:middle line:84% or there is so much of time going to social media 02:31:00.460 --> 02:31:02.360 align:middle line:90% or they are not literate enough. 02:31:02.360 --> 02:31:05.620 align:middle line:84% I don't know what, but you come up with some hypothesis, 02:31:05.620 --> 02:31:11.640 align:middle line:84% and then you can code it into your model and get it to work. 02:31:11.640 --> 02:31:15.540 align:middle line:84% But because they are kind of detached from each other, 02:31:15.540 --> 02:31:20.800 align:middle line:90% these two parts of the puzzle-- 02:31:20.800 --> 02:31:23.080 align:middle line:84% AUDIENCE: I guess I was thinking of connecting them 02:31:23.080 --> 02:31:26.480 align:middle line:84% because you're spending time talking about it, 02:31:26.480 --> 02:31:29.540 align:middle line:84% and you're spending time on social media kind of hunting 02:31:29.540 --> 02:31:35.240 align:middle line:84% what's the next thing I need to get to signal my continuing 02:31:35.240 --> 02:31:37.560 align:middle line:90% reader status. 02:31:37.560 --> 02:31:40.560 align:middle line:84% And you're spending time-- one is spending time 02:31:40.560 --> 02:31:44.000 align:middle line:84% doing that instead of actually consuming the thing that they 02:31:44.000 --> 02:31:45.560 align:middle line:90% bought. 02:31:45.560 --> 02:31:50.200 align:middle line:84% AUDIENCE: I was wondering, is the reading rates go down, 02:31:50.200 --> 02:31:51.720 align:middle line:90% is that among everyone? 02:31:51.720 --> 02:31:55.760 align:middle line:84% I guess my question would be, among people who are actually 02:31:55.760 --> 02:31:58.600 align:middle line:84% in BookTok, if you only surveyed them, 02:31:58.600 --> 02:32:00.340 align:middle line:84% their reading rates might actually be up. 02:32:00.340 --> 02:32:02.740 align:middle line:90% So that might not be related. 02:32:02.740 --> 02:32:04.160 align:middle line:84% It might just be like, in general, 02:32:04.160 --> 02:32:07.240 align:middle line:84% people would rather watch YouTube or scroll Instagram, 02:32:07.240 --> 02:32:08.780 align:middle line:90% so reading rates are down. 02:32:08.780 --> 02:32:12.480 align:middle line:84% But among BookTok people, yes, it's a social status symbol, 02:32:12.480 --> 02:32:14.740 align:middle line:84% but they also are probably also reading books. 02:32:14.740 --> 02:32:16.407 align:middle line:84% AUDIENCE: Yeah, no, that's a fair point. 02:32:16.407 --> 02:32:18.560 align:middle line:84% The reading rate surveys are US adults, 02:32:18.560 --> 02:32:20.880 align:middle line:84% and then they break it just by the standard things 02:32:20.880 --> 02:32:22.380 align:middle line:84% that you break down by, but it's not 02:32:22.380 --> 02:32:25.440 align:middle line:84% surveying people who are in these communities. 02:32:25.440 --> 02:32:29.783 align:middle line:84% So totally that could be a breaker here. 02:32:29.783 --> 02:32:31.200 align:middle line:84% HAZHIR RAHMANDAD: So then, I mean, 02:32:31.200 --> 02:32:36.660 align:middle line:84% it could be that Oriana's kind of hypothesis is more of a 02:32:36.660 --> 02:32:38.900 align:middle line:84% now you have these concentrated groups that 02:32:38.900 --> 02:32:41.660 align:middle line:84% consume a lot of books, and then you 02:32:41.660 --> 02:32:44.160 align:middle line:84% have the general population that is not consuming much. 02:32:44.160 --> 02:32:47.580 align:middle line:84% And it's kind of a question of heterogeneity more 02:32:47.580 --> 02:32:54.220 align:middle line:84% than a question of the two mechanisms you're highlighting. 02:32:54.220 --> 02:32:56.280 align:middle line:84% Now that is actually an interesting-- 02:32:56.280 --> 02:32:58.980 align:middle line:84% that might be even more interesting for a modeling 02:32:58.980 --> 02:33:01.680 align:middle line:90% practice type of situation. 02:33:01.680 --> 02:33:04.940 align:middle line:84% That is, how do you capture this type of heterogeneity? 02:33:04.940 --> 02:33:09.440 align:middle line:84% That is, it is happening, perhaps across other product 02:33:09.440 --> 02:33:14.760 align:middle line:84% categories, that as people become more focused 02:33:14.760 --> 02:33:18.720 align:middle line:84% in their narrow niche areas, you may 02:33:18.720 --> 02:33:23.580 align:middle line:84% get more consumption of something among some groups 02:33:23.580 --> 02:33:25.440 align:middle line:90% but less among others. 02:33:25.440 --> 02:33:31.200 align:middle line:84% So trying to actually capture that heterogeneity in a stock 02:33:31.200 --> 02:33:35.840 align:middle line:84% and flow structure with minimum complexity 02:33:35.840 --> 02:33:37.920 align:middle line:90% is pretty interesting. 02:33:37.920 --> 02:33:41.600 align:middle line:84% It becomes, again, kind of exogenously driven. 02:33:41.600 --> 02:33:47.320 align:middle line:84% It might not be feedback-rich, but see 02:33:47.320 --> 02:33:51.440 align:middle line:84% what you can tell about the feedback mechanisms that 02:33:51.440 --> 02:33:52.920 align:middle line:90% can be important. 02:33:52.920 --> 02:33:56.000 align:middle line:84% And then capturing just the stock and flow part of it 02:33:56.000 --> 02:33:58.780 align:middle line:84% that generates the heterogeneity is also interesting. 02:33:58.780 --> 02:34:03.880 align:middle line:90% So that would be my suggestion. 02:34:03.880 --> 02:34:06.480 align:middle line:84% I think we are running out of time. 02:34:06.480 --> 02:34:11.140 align:middle line:84% So with that, if you haven't submitted your problem 02:34:11.140 --> 02:34:12.400 align:middle line:90% statement, please do. 02:34:12.400 --> 02:34:16.900 align:middle line:84% I will try to work on it on the feedback next week 02:34:16.900 --> 02:34:19.940 align:middle line:84% and get it back to you so you have a little bit more time 02:34:19.940 --> 02:34:23.580 align:middle line:84% to go back to it, edit it, and these problem 02:34:23.580 --> 02:34:26.060 align:middle line:84% definitions that I mentioned over the email, 02:34:26.060 --> 02:34:29.860 align:middle line:84% they are for you to be a little bit more connected 02:34:29.860 --> 02:34:36.940 align:middle line:84% with the problem but also have create more of diverse models 02:34:36.940 --> 02:34:41.700 align:middle line:84% that we can look at in the last couple of sessions. 02:34:41.700 --> 02:34:44.740 align:middle line:84% If you are OK with it, we will share those for others 02:34:44.740 --> 02:34:47.900 align:middle line:84% to also make it a concrete problem that others 02:34:47.900 --> 02:34:52.660 align:middle line:84% can tackle it as a modeling challenge if they get a chance. 02:34:52.660 --> 02:34:54.900 align:middle line:84% So those are the purposes, but you 02:34:54.900 --> 02:34:57.820 align:middle line:84% don't have to share it broadly if you don't want to. 02:34:57.820 --> 02:34:59.080 align:middle line:90% OK, cool. 02:34:59.080 --> 02:35:00.890 align:middle line:90% Thank you. 02:35:00.890 --> 02:35:04.000 align:middle line:90%