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PROFESSOR: All
right, let's start.

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00:00:29,720 --> 00:00:34,970
So first of all, I hope you've
been enjoying the class so far.

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00:00:34,970 --> 00:00:38,590
And thank you for
filling out the survey.

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00:00:38,590 --> 00:00:43,610
So we got some very useful
and interesting feedbacks.

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00:00:43,610 --> 00:00:46,240
One of the feedbacks--
this is my impression,

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I haven't gotten a chance
to talk to my co-lecturers

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or colleagues yet, but
I read some comments.

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00:00:54,670 --> 00:00:58,730
You were saying that some of
the problem sets are quite hard.

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00:00:58,730 --> 00:01:03,430
The math part may be a bit more
difficult than the lecture.

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So I'm thinking.

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So this is really the
application lecture.

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And from now, after three
more lectures by Choongbum,

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it will be essentially the
remainder is all applications.

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The original point
of having this class

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is really to show you
how math is applied,

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to show you those cases
in different markets,

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different strategies,
and in the real industry.

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So I'm trying to think, how
do I give today's lecture

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with the right balance?

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00:01:35,480 --> 00:01:37,220
This is, after
all, a math class.

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Should I give you more math,
or should I-- you've had enough

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math.

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I mean, it sounded
like from the survey

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you probably had enough math.

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So I would probably
want to focus a bit more

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on the application side.

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And from the survey also
it seems like most of you

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enjoyed or wanted to listen to
more on the application side.

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So anyway, as you've already
learned from Peter's lecture,

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the so-called Modern
Portfolio Theory.

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00:02:06,680 --> 00:02:08,729
And it's actually
not that modern

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anymore, but we still call
it Modern Portfolio Theory.

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So you probably wonder,
in the real world,

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how actually we use it.

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Do we follow those steps?

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Do we do those calculations?

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00:02:20,870 --> 00:02:25,720
And so today, I'd like to share
with you my experience on that,

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both in the past,
a different area,

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and today probably more
focused on the buy side.

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Oh, come on in.

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Yeah.

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Actually, these
are my colleagues

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from Harvard Management.

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So--

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[CHUCKLES]

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--they will be able to ask
me really tough questions.

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So anyway, so how I'm
going to start this class.

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You wondered why I handed
out to each of you a page.

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So does everyone have
a blank page by now?

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Yeah, actually.

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Yeah.

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Could also pass to--?

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Yeah.

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So I want every one of
you to use that blank page

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to construct a portfolio, OK?

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So you're saying, well, I
haven't done this before.

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That's fine.

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Do it totally from
your intuition,

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from your knowledge
base as of now.

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So what I want you to
do is to write down,

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to break down the
100% of what do you

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want to have in your portfolio.

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OK, you said, give me choices.

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No, I'm not going
to give you choices.

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You think about whatever
you like to put down.

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Wide open, OK?

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And don't even ask me
the goal or the criteria.

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Base it on what you want to do.

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And so totally free
thinking, but I want

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you to do it in five minutes.

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So don't overthink it.

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And hand it back to me, OK?

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So that's really the first part.

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I want you to show
intuitively how you

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can construct a portfolio, OK?

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So what does a portfolio mean?

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That I have to explain to you.

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Let's say for
undergraduates here,

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so your parents give
you some allowance.

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You manage to save a
$1,000 on the side.

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You decided to put into
investments, buying stocks

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or whatever, or gambling,
buy lottery tickets,

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whatever you can do.

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Just break down your percentage.

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That could be $1,000, or you
could be a portfolio manager

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00:04:27,430 --> 00:04:31,140
and have hundreds of billions
of dollars, or whatever.

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Or then and say if they raise
some money, start a hedge fund,

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00:04:35,250 --> 00:04:37,780
they may have $10,000
just to start with.

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00:04:37,780 --> 00:04:40,210
How do you want to use
those money on day one?

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00:04:40,210 --> 00:04:41,740
Just think about it.

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00:04:41,740 --> 00:04:45,610
And then so while you're
filling out those pages,

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please hand it back to me.

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00:04:46,940 --> 00:04:50,320
It's your choice to put
your name down or not.

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00:04:50,320 --> 00:04:56,110
And then I will start
to assemble those ideas

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and put them on the blackboard.

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And sometimes I may come back
to ask you a question-- you

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know, why did you put this?

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00:05:01,400 --> 00:05:02,480
That's OK.

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Don't feel embarrassed.

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00:05:03,910 --> 00:05:05,910
We're not going to
put you on the spot.

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00:05:05,910 --> 00:05:12,440
But the idea is I want to use
those examples to show you

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how we actually connect
theory with practice.

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00:05:19,100 --> 00:05:21,640
I remember when I was a
college student I learned

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a lot of different stuff.

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But I remember one
lecture so well,

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one teacher told me one thing.

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I still remember vividly well,
so I want to pass it on to you.

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00:05:32,030 --> 00:05:34,980
So how do we learn
something useful, right?

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00:05:34,980 --> 00:05:38,560
You always start
with observation.

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So that's kind of
the physics side.

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You collect the data.

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You ask a lot of questions.

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You try to find the patterns.

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Then what you do,
you build models.

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You have a theory.

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You try to explain what is
working, what's repeatable,

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00:06:03,620 --> 00:06:05,680
what's not repeatable.

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So that's where
the math comes in.

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00:06:09,390 --> 00:06:10,690
You solve the equations.

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Sometimes in economics,
lot of times,

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unlike physics, the repeatable
patterns are not so obvious.

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So what you do after this, so
you come back to observations

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again.

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You confirm your theory,
verify your predictions,

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and find your error.

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Then this feeds
back to this rule.

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And a lot of times, the
verification process

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is really about
understanding special cases.

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That's why today I really want
to illustrate the portfolio

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00:06:50,550 --> 00:06:54,540
theory using a lot
of special cases.

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So can you start to hand back
your portfolio construction

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by now?

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00:06:58,920 --> 00:07:02,880
OK, so just hand back
whatever you have.

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00:07:02,880 --> 00:07:05,560
If you have one thing on
the paper, that's fine.

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Or many things on
the paper, or you

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00:07:07,510 --> 00:07:10,360
think as a portfolio manager,
or you think as a trader,

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00:07:10,360 --> 00:07:13,675
or you think simply as
a student, as yourself.

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All right, so I'm
getting these back.

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I will start to write
on the blackboard.

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And you can finish
what you started.

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By the way, that's the only
slide I'm going to use today.

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I'm not concerned-- you realize
if I show you a lot of slides,

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you probably can't
keep up with me.

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So I'm going to write down
everything, just take my time.

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And so hopefully you get a
chance to think about questions

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as well.

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OK, I think-- is
anyone finished?

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Any more?

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OK.

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All right, OK.

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OK, great.

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You guys are awesome.

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OK, so let me just
have a quick look

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to see if I missed any, OK?

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Wow, very interesting.

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So I have to say, some
people have high conviction.

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100% of you, one of those.

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00:11:00,850 --> 00:11:04,080
I think I'm not going to read
your names, so don't worry, OK?

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00:11:07,750 --> 00:11:10,290
OK I'm just going to read the
answers that people put down,

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00:11:10,290 --> 00:11:11,270
OK?

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So small cap equities, bonds,
real estate, commodities.

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Those were there.

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00:11:17,950 --> 00:11:21,000
Qualitative strategies,
selection strategies,

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00:11:21,000 --> 00:11:23,490
deep value models.

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00:11:23,490 --> 00:11:33,120
Food/drug sector models, energy,
consumer, S&P index, ETF fund,

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00:11:33,120 --> 00:11:35,720
government bonds,
top hedge funds.

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00:11:39,600 --> 00:11:43,990
So natural resources,
timber land,

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00:11:43,990 --> 00:11:59,890
farmland, checking account,
stocks, cash, corporate bonds,

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00:11:59,890 --> 00:12:04,140
rare coins, lotteries,
collectibles.

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00:12:04,140 --> 00:12:07,700
That's very unique.

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00:12:07,700 --> 00:12:18,340
And Apple's stock, Google
stock, gold, long term saving

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00:12:18,340 --> 00:12:18,840
annuities.

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00:12:24,000 --> 00:12:28,210
So Yahoo, Morgan Stanley stocks.

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I like that.

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00:12:29,868 --> 00:12:32,000
[LAUGHTER]

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00:12:32,000 --> 00:12:32,500
OK.

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Family trust.

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00:12:38,990 --> 00:12:41,200
OK, I think that
pretty much covered it.

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00:12:41,200 --> 00:12:46,810
OK, so I would say that
list is more or less here.

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00:12:46,810 --> 00:12:50,160
So after you've
done this, when you

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00:12:50,160 --> 00:12:54,010
were doing this, what kind of
questions came to your mind?

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00:12:54,010 --> 00:12:57,181
Anyone wants to-- yeah, please.

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AUDIENCE: [INAUDIBLE] how do I
know what's the right balance

191
00:13:00,127 --> 00:13:02,091
to draw in my portfolio?

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00:13:02,091 --> 00:13:07,010
Whether it would be cash,
bills, or stuff like that?

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00:13:07,010 --> 00:13:08,570
PROFESSOR: How do
you do it, really?

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00:13:08,570 --> 00:13:09,830
What's the criteria?

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00:13:09,830 --> 00:13:12,990
And so before we
answer the question how

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00:13:12,990 --> 00:13:17,420
you do, how do you group
assets or exposures

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00:13:17,420 --> 00:13:22,160
or strategies or even people,
traders, together-- before we

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00:13:22,160 --> 00:13:24,530
ask all those questions,
we have to ask

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00:13:24,530 --> 00:13:26,560
ourselves another question.

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00:13:26,560 --> 00:13:28,020
What is the goal?

201
00:13:28,020 --> 00:13:29,780
What is the objective, right?

202
00:13:29,780 --> 00:13:31,900
So we understand what
portfolio management is.

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00:13:31,900 --> 00:13:34,880
So here in this class,
we're not talking

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00:13:34,880 --> 00:13:38,630
about how to come up with
a specific winning strategy

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00:13:38,630 --> 00:13:40,940
in trading or investments.

206
00:13:40,940 --> 00:13:43,390
But we are talking about
how to put them together.

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00:13:43,390 --> 00:13:45,480
So this is what portfolio
management is about.

208
00:13:45,480 --> 00:13:48,850
So before we answer
how, let's see why.

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00:13:48,850 --> 00:13:49,880
Why do we do it?

210
00:13:49,880 --> 00:13:52,790
Why do we want to have
a portfolio, right?

211
00:13:52,790 --> 00:13:55,100
That's a very, very good point.

212
00:13:55,100 --> 00:14:01,840
So let's understand the goals
of portfolio management.

213
00:14:01,840 --> 00:14:05,000
So before we understand goals
of portfolio management,

214
00:14:05,000 --> 00:14:09,655
let's understand
your situations,

215
00:14:09,655 --> 00:14:10,530
everyone's situation.

216
00:14:32,210 --> 00:14:35,150
So let's look at this chart.

217
00:14:35,150 --> 00:14:38,550
So I'm going to
plot your spending

218
00:14:38,550 --> 00:14:41,220
as a function of your age.

219
00:14:41,220 --> 00:14:47,660
So when you are
age 0 to age 100,

220
00:14:47,660 --> 00:14:49,549
so everyone's spending
pattern is different.

221
00:14:49,549 --> 00:14:51,965
So I'm not going to tell you
this is the spending pattern.

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00:14:51,965 --> 00:14:54,770
So obviously when
kids are young,

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00:14:54,770 --> 00:14:59,650
they probably don't have a
lot of hobbies or tuition,

224
00:14:59,650 --> 00:15:01,730
but they have some basic needs.

225
00:15:01,730 --> 00:15:03,630
So they spend.

226
00:15:03,630 --> 00:15:05,360
And then the spending
really goes up.

227
00:15:05,360 --> 00:15:07,550
Now your parents have
to pay your tuition,

228
00:15:07,550 --> 00:15:10,830
or you have to borrow--
loans, scholarships.

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00:15:10,830 --> 00:15:13,060
And then you have college.

230
00:15:13,060 --> 00:15:14,370
Now you have-- you're married.

231
00:15:14,370 --> 00:15:15,020
You have kids.

232
00:15:15,020 --> 00:15:19,180
You need to buy a house, buy
a car, pay back student loans.

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00:15:19,180 --> 00:15:20,560
You have a lot more spending.

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00:15:20,560 --> 00:15:23,120
Then you go on vacation.

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00:15:23,120 --> 00:15:25,490
You buy investments.

236
00:15:25,490 --> 00:15:27,770
You just have more
spending coming up.

237
00:15:27,770 --> 00:15:30,860
So but it goes to
a certain point.

238
00:15:30,860 --> 00:15:32,610
You will taper down, right?

239
00:15:32,610 --> 00:15:34,590
So you're not going
to keep going forever.

240
00:15:34,590 --> 00:15:37,075
So that's your spending curve.

241
00:15:37,075 --> 00:15:38,950
And with the other curve,
you think about it.

242
00:15:38,950 --> 00:15:42,710
It's what's your income,
what's your earnings curve.

243
00:15:42,710 --> 00:15:47,010
You don't earn anything
where you are just born.

244
00:15:47,010 --> 00:15:48,530
I use earning.

245
00:15:48,530 --> 00:15:49,380
So this is spending.

246
00:15:54,540 --> 00:15:58,810
So let's call this 50.

247
00:15:58,810 --> 00:16:04,100
Your earning probably
typically peaks around age 50,

248
00:16:04,100 --> 00:16:05,970
but it really depends.

249
00:16:05,970 --> 00:16:08,700
Then you probably
go down, back up.

250
00:16:08,700 --> 00:16:10,238
Right, so that's your earning.

251
00:16:13,830 --> 00:16:17,240
And do they always match well?

252
00:16:17,240 --> 00:16:18,410
They don't.

253
00:16:18,410 --> 00:16:21,350
So how do you make
up the difference?

254
00:16:21,350 --> 00:16:24,690
You hope to have a fund,
an investment on the side,

255
00:16:24,690 --> 00:16:30,790
which can generate those cash
flows to balance your earning

256
00:16:30,790 --> 00:16:32,220
versus your spending.

257
00:16:32,220 --> 00:16:35,980
OK, so that's only one
simple way to put it.

258
00:16:35,980 --> 00:16:38,500
So you've got to ask
about your situation.

259
00:16:38,500 --> 00:16:41,400
What's your cash flow look like?

260
00:16:41,400 --> 00:16:45,210
So my objective is, I'm
going to retire at age of 50.

261
00:16:45,210 --> 00:16:48,060
Then after the age of
50, I will live free.

262
00:16:48,060 --> 00:16:49,490
I'll travel around the world.

263
00:16:49,490 --> 00:16:51,290
Now I'll calculate
how much money I need.

264
00:16:51,290 --> 00:16:52,712
So that's one situation.

265
00:16:52,712 --> 00:16:55,170
The other situation is, I want
to graduate and pay back all

266
00:16:55,170 --> 00:16:57,780
the student loans in one year.

267
00:16:57,780 --> 00:16:59,520
So that's another.

268
00:16:59,520 --> 00:17:02,710
And typically people
have to plan these out.

269
00:17:02,710 --> 00:17:06,740
And if I'm managing a
university endowment,

270
00:17:06,740 --> 00:17:10,430
so I have to think about what
the university's operating

271
00:17:10,430 --> 00:17:14,060
budget is like, how much money
they need every year drawing

272
00:17:14,060 --> 00:17:15,530
from this fund.

273
00:17:15,530 --> 00:17:18,670
And then by
maintaining, protecting

274
00:17:18,670 --> 00:17:22,190
the total fund for basically
a perpetual purpose, right?

275
00:17:22,190 --> 00:17:24,670
Ongoing and keep growing it.

276
00:17:24,670 --> 00:17:28,920
You ask for more contributions,
but at the same time generating

277
00:17:28,920 --> 00:17:30,380
more return.

278
00:17:30,380 --> 00:17:32,460
If you have a pension
fund, you have

279
00:17:32,460 --> 00:17:37,300
to think about what time frame
lot of the people, the workers,

280
00:17:37,300 --> 00:17:40,670
will retire and will actually
draw from the pension.

281
00:17:40,670 --> 00:17:43,810
And so every situation
is very different.

282
00:17:43,810 --> 00:17:45,370
Let me even expand it.

283
00:17:45,370 --> 00:17:47,520
So you think, oh, this
is all about investment.

284
00:17:47,520 --> 00:17:51,110
No, no, this is not
just about investment.

285
00:17:51,110 --> 00:17:55,330
So I was a trader for a
long time at Morgan Stanley,

286
00:17:55,330 --> 00:17:57,690
and later on a trading manager.

287
00:17:57,690 --> 00:18:01,830
So when I had many
traders working for me,

288
00:18:01,830 --> 00:18:04,640
the question I was
facing is how much money

289
00:18:04,640 --> 00:18:07,710
I need to allocate to each
trader to let them trade.

290
00:18:07,710 --> 00:18:09,250
How much risk do
they take, right?

291
00:18:09,250 --> 00:18:11,390
So they said, oh, I have
this winning strategy.

292
00:18:11,390 --> 00:18:12,840
I can make lots of money.

293
00:18:12,840 --> 00:18:15,250
Why don't you give
me more limits?

294
00:18:15,250 --> 00:18:17,860
No, you're not going
to have all the limits.

295
00:18:17,860 --> 00:18:21,060
You're not going to have all
the capital we can give to you.

296
00:18:21,060 --> 00:18:23,230
Right, so I'm going to explain.

297
00:18:23,230 --> 00:18:24,910
You have to diversify.

298
00:18:24,910 --> 00:18:28,800
At the same time, you have
to compare the strategies

299
00:18:28,800 --> 00:18:33,370
with parameters--
liquidity, volatility,

300
00:18:33,370 --> 00:18:35,510
and many other parameters.

301
00:18:35,510 --> 00:18:39,610
And even if you are
not managing people,

302
00:18:39,610 --> 00:18:43,200
let's say-- I was going to
do this, so Dan, [INAUDIBLE],

303
00:18:43,200 --> 00:18:44,400
Martin and Andrew.

304
00:18:44,400 --> 00:18:46,330
So they start a
hedge fund together.

305
00:18:46,330 --> 00:18:49,560
So each of them had
a great strategy.

306
00:18:49,560 --> 00:18:52,870
Dan has five, Andrew has
four, so they altogether

307
00:18:52,870 --> 00:18:55,410
have 30 strategies.

308
00:18:55,410 --> 00:18:57,600
So they raise an
amount of money,

309
00:18:57,600 --> 00:19:00,420
or they just pool
together their savings.

310
00:19:00,420 --> 00:19:02,150
But how do you
decide which strategy

311
00:19:02,150 --> 00:19:05,620
to put more money on day one?

312
00:19:05,620 --> 00:19:07,240
So those questions
are very practical.

313
00:19:07,240 --> 00:19:08,410
So that's all.

314
00:19:08,410 --> 00:19:10,240
So you understand
your goals, that's

315
00:19:10,240 --> 00:19:15,220
then you're really clear on
how much risk you can take.

316
00:19:15,220 --> 00:19:16,720
So let's come back to that.

317
00:19:16,720 --> 00:19:17,740
So what is risk?

318
00:19:17,740 --> 00:19:19,840
As Peter explained
in his lecture,

319
00:19:19,840 --> 00:19:24,150
risk is actually not
very well defined.

320
00:19:24,150 --> 00:19:27,310
So in the Modern
Portfolio Theory,

321
00:19:27,310 --> 00:19:30,580
we typically talk about
variance or standard deviation

322
00:19:30,580 --> 00:19:32,040
of return.

323
00:19:32,040 --> 00:19:35,380
So today I'm going to
start with that concept,

324
00:19:35,380 --> 00:19:37,470
but then try to
expand it beyond that.

325
00:19:37,470 --> 00:19:39,920
So stay with that
concept for now.

326
00:19:39,920 --> 00:19:45,380
Risk, we use standard
deviation for now.

327
00:19:45,380 --> 00:19:47,170
So what are we trying to do?

328
00:20:16,570 --> 00:20:19,195
So this, you are familiar
with this chart, right?

329
00:20:19,195 --> 00:20:21,880
So return versus
standard deviation.

330
00:20:21,880 --> 00:20:24,190
Standard deviation is
not going to go negative.

331
00:20:24,190 --> 00:20:25,510
So we stop at zero.

332
00:20:25,510 --> 00:20:29,160
But the return
can go below zero.

333
00:20:29,160 --> 00:20:32,970
And I'm going to review one
formula before I go into it.

334
00:20:32,970 --> 00:20:37,380
I think it's useful to review
what previously you learned.

335
00:20:37,380 --> 00:20:40,350
So you let's say you
have-- I will also

336
00:20:40,350 --> 00:20:42,925
clarify the notation as well
so you don't get confused.

337
00:20:47,560 --> 00:20:53,810
So let's say-- so Peter
mentioned the Harry Markowitz

338
00:20:53,810 --> 00:20:56,560
Modern Portfolio Theory
which won him the Nobel

339
00:20:56,560 --> 00:20:59,100
Prize in 1990, right?

340
00:20:59,100 --> 00:21:02,170
Along with Sharpe
and a few others.

341
00:21:02,170 --> 00:21:06,890
So it's a very
elegant piece of work.

342
00:21:06,890 --> 00:21:09,550
But today, I will try to
give you some special cases

343
00:21:09,550 --> 00:21:11,650
to help you understand that.

344
00:21:11,650 --> 00:21:14,780
So let's review
one of the formulas

345
00:21:14,780 --> 00:21:16,780
here, which is really
the definition.

346
00:21:16,780 --> 00:21:18,920
So let's say you
have a portfolio.

347
00:21:18,920 --> 00:21:22,740
Let's call the expected
return of the portfolio

348
00:21:22,740 --> 00:21:37,420
is R of P, equal to the
sum, a weighted sum,

349
00:21:37,420 --> 00:21:41,270
of all the expected
returns of each asset.

350
00:21:41,270 --> 00:21:44,830
You'll basically
linearly allocate them.

351
00:21:44,830 --> 00:21:58,190
Then the variance-- oh, let's
just look at the variance,

352
00:21:58,190 --> 00:21:59,480
sigma_P squared.

353
00:22:13,250 --> 00:22:14,810
So these are vectors.

354
00:22:14,810 --> 00:22:16,390
This is a matrix.

355
00:22:16,390 --> 00:22:19,400
The sigma in the middle
is a covariance matrix.

356
00:22:19,400 --> 00:22:23,170
OK that's all you need to
know about math at this point.

357
00:22:23,170 --> 00:22:27,490
So I want us to go through an
exercise on that piece of paper

358
00:22:27,490 --> 00:22:31,770
I just collected back to put
your choice of the investment

359
00:22:31,770 --> 00:22:33,270
on this chart.

360
00:22:33,270 --> 00:22:36,059
OK, so let's start with one.

361
00:22:36,059 --> 00:22:36,725
So what is cash?

362
00:22:39,340 --> 00:22:41,840
Cash has no standard deviation.

363
00:22:41,840 --> 00:22:45,220
You hold cash-- so it's
going to be on this axis.

364
00:22:45,220 --> 00:22:47,330
It's a positive return.

365
00:22:47,330 --> 00:22:48,290
So that's here.

366
00:22:48,290 --> 00:22:49,290
So let's call this cash.

367
00:22:53,500 --> 00:22:56,280
Where is-- and let's me just
think about another example.

368
00:22:56,280 --> 00:22:57,270
Where's lottery?

369
00:22:57,270 --> 00:23:02,800
Say you buy Powerball, right?

370
00:23:02,800 --> 00:23:04,870
So where's lottery falling?

371
00:23:04,870 --> 00:23:07,600
Let's assume you put
everything in lottery.

372
00:23:11,200 --> 00:23:12,200
So you're going to lose.

373
00:23:12,200 --> 00:23:18,770
So your expected value is
very close to lose 100%.

374
00:23:18,770 --> 00:23:22,790
And your standard deviation
is probably very close to 0.

375
00:23:22,790 --> 00:23:24,070
So you will be here.

376
00:23:24,070 --> 00:23:25,620
So some of you say, oh, no, no.

377
00:23:25,620 --> 00:23:26,980
It's not exactly zero.

378
00:23:26,980 --> 00:23:28,020
So OK, fine.

379
00:23:28,020 --> 00:23:30,880
So maybe it's
somewhere here, OK?

380
00:23:30,880 --> 00:23:34,590
So not 100%, but you still
have a pretty small deviation

381
00:23:34,590 --> 00:23:37,810
from losing all the money.

382
00:23:37,810 --> 00:23:41,510
What is coin flipping?

383
00:23:41,510 --> 00:23:43,890
So let's say you decide to
put all your money to gamble

384
00:23:43,890 --> 00:23:48,620
on a fair coin flip, fair coin.

385
00:23:48,620 --> 00:23:50,320
So expected return is zero.

386
00:23:50,320 --> 00:23:54,278
What is the standard
deviation of that?

387
00:23:54,278 --> 00:23:55,194
AUDIENCE: 100%?

388
00:23:55,194 --> 00:23:56,570
PROFESSOR: Good.

389
00:23:56,570 --> 00:23:58,650
So 100%.

390
00:24:06,230 --> 00:24:10,410
So we got the three
extreme cases covered.

391
00:24:10,410 --> 00:24:17,460
OK, so where is US
government bond?

392
00:24:17,460 --> 00:24:21,600
So let's just call it five-year
note or ten-year bond.

393
00:24:21,600 --> 00:24:26,310
So the return is better than
cash with some volatility.

394
00:24:26,310 --> 00:24:27,110
Let's call it here.

395
00:24:32,870 --> 00:24:37,200
What is investing in a start
up venture capital fund like?

396
00:24:39,900 --> 00:24:41,570
Pretty up there, right?

397
00:24:41,570 --> 00:24:44,540
So you'll probably get
a very high return,

398
00:24:44,540 --> 00:24:45,850
by you can lose all your money.

399
00:24:45,850 --> 00:24:48,810
So probably somewhere
here, you see.

400
00:24:52,320 --> 00:24:54,455
Buying stocks, let's
call it somewhere here.

401
00:24:58,298 --> 00:25:00,580
Our last application
lecture, you

402
00:25:00,580 --> 00:25:02,830
heard about investing
in commodities, right?

403
00:25:02,830 --> 00:25:04,850
Trading gold, oil.

404
00:25:04,850 --> 00:25:10,610
So that has higher volatility,
so sometimes high returns.

405
00:25:10,610 --> 00:25:13,850
So let's call this commodity.

406
00:25:13,850 --> 00:25:19,100
And the ETF is typically lower
than single stock volatility,

407
00:25:19,100 --> 00:25:22,040
because it's just
like index funds.

408
00:25:22,040 --> 00:25:23,840
So here.

409
00:25:23,840 --> 00:25:26,310
Are there any other choices
you'd like to put on this map?

410
00:25:30,770 --> 00:25:31,470
OK.

411
00:25:31,470 --> 00:25:36,220
So let me just look at
what you came up with.

412
00:25:36,220 --> 00:25:38,460
Real estate, OK.

413
00:25:38,460 --> 00:25:42,690
Real estate, I would say
probably somewhere around here.

414
00:25:45,310 --> 00:25:54,760
Private equity probably
somewhere here.

415
00:25:54,760 --> 00:25:57,060
Or investing in hedge
funds somewhere.

416
00:25:57,060 --> 00:26:01,000
So I think that's enough
examples to cover.

417
00:26:01,000 --> 00:26:06,060
So now let me turn the table
around and ask you a question.

418
00:26:06,060 --> 00:26:13,170
Given this map, how would you
like to pick your investments?

419
00:26:13,170 --> 00:26:16,880
So you learned about
the portfolio theory.

420
00:26:16,880 --> 00:26:19,280
As a so-called
rational investor,

421
00:26:19,280 --> 00:26:22,360
you try to maximize your return.

422
00:26:22,360 --> 00:26:28,140
At the same time, minimize
your standard deviation, right?

423
00:26:28,140 --> 00:26:30,260
I hesitate to use
the term "risk," OK?

424
00:26:30,260 --> 00:26:33,690
Because as I said, we
need to better define it.

425
00:26:33,690 --> 00:26:36,800
But let's just say you
try to minimize this

426
00:26:36,800 --> 00:26:40,170
but maximize this,
the vertical axis.

427
00:26:40,170 --> 00:26:43,610
OK, so let's just say you
try to find the highest

428
00:26:43,610 --> 00:26:46,590
possible return
for that portfolio

429
00:26:46,590 --> 00:26:50,890
with the lowest possible
standard deviation.

430
00:26:50,890 --> 00:26:53,360
So would you pick this one?

431
00:26:53,360 --> 00:26:55,680
Would you pick this one?

432
00:26:55,680 --> 00:26:58,920
OK, so eliminate those two.

433
00:26:58,920 --> 00:27:03,270
But for this, that's
actually all possible, right?

434
00:27:03,270 --> 00:27:06,610
So then that's where we learn
about the efficient frontier?

435
00:27:12,580 --> 00:27:14,330
So what is the
efficient frontier?

436
00:27:14,330 --> 00:27:18,120
It's really the
possible combinations

437
00:27:18,120 --> 00:27:22,070
of those investments you
can push out to the boundary

438
00:27:22,070 --> 00:27:27,100
that you can no longer find
another combination-- given

439
00:27:27,100 --> 00:27:30,760
the same standard
deviation, you can no longer

440
00:27:30,760 --> 00:27:31,940
find a higher return.

441
00:27:31,940 --> 00:27:33,460
So you reached the boundary.

442
00:27:33,460 --> 00:27:36,890
And the same is true
that for the same return,

443
00:27:36,890 --> 00:27:40,820
you can no longer minimize
your standard deviation

444
00:27:40,820 --> 00:27:42,830
by finding another combination.

445
00:27:42,830 --> 00:27:45,645
OK, so that's called
efficient frontier.

446
00:27:55,800 --> 00:27:58,090
How do you find the
efficient frontier?

447
00:27:58,090 --> 00:28:01,325
That's what essentially
those work were done

448
00:28:01,325 --> 00:28:04,260
and it got them the
Nobel Prize, obviously.

449
00:28:04,260 --> 00:28:07,110
It's more than that,
but you get the flavor

450
00:28:07,110 --> 00:28:09,860
from the previous lectures.

451
00:28:09,860 --> 00:28:13,130
So what I'm going to do
today is really reduce

452
00:28:13,130 --> 00:28:17,500
all of these to the
special case of two assets.

453
00:28:17,500 --> 00:28:21,050
Now we can really derive a
lot of intuition from that.

454
00:28:53,700 --> 00:28:56,930
So we have sigma, R.
We're going to ignore

455
00:28:56,930 --> 00:28:58,250
what's below this now, right?

456
00:28:58,250 --> 00:28:59,480
We don't want to be there.

457
00:28:59,480 --> 00:29:02,310
And we want to stay
on the up-right.

458
00:29:02,310 --> 00:29:05,790
So let's consider
one special case.

459
00:29:05,790 --> 00:29:09,210
So again for that, let's
write out for the two assets.

460
00:29:09,210 --> 00:29:11,932
So what is R of P?

461
00:29:11,932 --> 00:29:19,010
It's w_1 R_1 plus 1
minus w_1 R_2, right?

462
00:29:19,010 --> 00:29:20,816
Very simple math.

463
00:29:20,816 --> 00:29:24,100
And what is sigma_P?

464
00:29:24,100 --> 00:29:27,940
So the standard deviation of
the portfolio-- or the variance

465
00:29:27,940 --> 00:29:46,710
of that, which is a
square-- we know that's

466
00:29:46,710 --> 00:29:49,620
for the two asset
class special case.

467
00:29:49,620 --> 00:29:55,840
So let me give you a further
restriction-- which, let's

468
00:29:55,840 --> 00:30:06,860
consider if R_1 equal to R_2.

469
00:30:06,860 --> 00:30:08,830
Again, here meaning
expected return.

470
00:30:08,830 --> 00:30:12,220
I'm simplifying some
of the notations.

471
00:30:12,220 --> 00:30:21,210
And sigma_1 equal
to 0, and sigma_2

472
00:30:21,210 --> 00:30:25,956
not equal to 0, so what is rho?

473
00:30:25,956 --> 00:30:26,955
What is the correlation?

474
00:30:31,060 --> 00:30:32,310
Zero, right?

475
00:30:32,310 --> 00:30:35,890
Because you have no
volatility on it.

476
00:30:35,890 --> 00:30:41,057
OK, so what is-- what's that?

477
00:30:41,057 --> 00:30:42,390
AUDIENCE: It's really undefined.

478
00:30:42,390 --> 00:30:44,028
PROFESSOR: It's
really undefined, yes.

479
00:30:44,028 --> 00:30:44,884
Yeah.

480
00:30:44,884 --> 00:30:47,250
AUDIENCE: [INAUDIBLE]
no covariance.

481
00:30:47,250 --> 00:30:49,080
PROFESSOR: There's no--
yeah, that's right.

482
00:30:49,080 --> 00:30:51,100
OK, so let's look at this.

483
00:30:51,100 --> 00:30:53,970
So you have sigma_2 here.

484
00:30:53,970 --> 00:30:55,345
Sigma_1 is 0.

485
00:30:57,970 --> 00:31:03,070
And you have R_1 equal to R_2.

486
00:31:03,070 --> 00:31:04,728
What is all R of P?

487
00:31:07,540 --> 00:31:08,380
It's R, right?

488
00:31:11,250 --> 00:31:13,300
Because the weighting
doesn't matter.

489
00:31:13,300 --> 00:31:18,170
So you know it's going
to fall along this line.

490
00:31:18,170 --> 00:31:22,710
So here is when
weight one equal to 0.

491
00:31:22,710 --> 00:31:25,940
So you weight everything
on the second asset.

492
00:31:25,940 --> 00:31:31,170
Here you weight the
first asset 100%.

493
00:31:31,170 --> 00:31:34,120
So you have a possible
combination along this line,

494
00:31:34,120 --> 00:31:36,160
along this flat line.

495
00:31:36,160 --> 00:31:37,750
Very simple, right?

496
00:31:37,750 --> 00:31:41,000
I like to start with a
really a simple case.

497
00:31:41,000 --> 00:31:53,280
So what if sigma_1 also is
not 0, but sigma_1 equal

498
00:31:53,280 --> 00:31:54,830
to sigma_2.

499
00:31:54,830 --> 00:32:00,714
And further, I impose-- impose--
the correlation to be 0, OK?

500
00:32:00,714 --> 00:32:01,880
What is this line look like?

501
00:32:01,880 --> 00:32:04,980
So I have sigma_2
equal to sigma_1.

502
00:32:09,140 --> 00:32:12,950
And R_1 is still equal
to R_2, so R_P is still

503
00:32:12,950 --> 00:32:15,750
equal to R_1 or R_2, right?

504
00:32:15,750 --> 00:32:17,000
What does this line look like?

505
00:32:27,070 --> 00:32:29,740
So volatility is the same.

506
00:32:29,740 --> 00:32:32,740
Return is those are the same
of each of the asset class.

507
00:32:32,740 --> 00:32:36,500
You have two strategies
or two instruments.

508
00:32:36,500 --> 00:32:39,810
They are zero-ly correlated.

509
00:32:39,810 --> 00:32:43,580
How would you combine them?

510
00:32:43,580 --> 00:32:47,800
So you take the derivative
of this variance

511
00:32:47,800 --> 00:32:50,800
with regarding to
the weight, right?

512
00:32:50,800 --> 00:32:52,870
And then you minimize that.

513
00:32:52,870 --> 00:33:01,390
So what you find is that
this point is R_1 equal to 0,

514
00:33:01,390 --> 00:33:06,100
or-- I'm sorry, w_1,
or w_1 equal to 1.

515
00:33:06,100 --> 00:33:08,021
You're at this point, right?

516
00:33:08,021 --> 00:33:08,520
Agreed?

517
00:33:08,520 --> 00:33:11,460
So you choose either, you will
be ending up-- the portfolio

518
00:33:11,460 --> 00:33:16,530
exposure in terms of return and
variance will be right here.

519
00:33:16,530 --> 00:33:19,600
But what if you
choose-- so when you

520
00:33:19,600 --> 00:33:22,612
try to find the minimum
variance, you actually end up--

521
00:33:22,612 --> 00:33:23,820
I'm not going to do the math.

522
00:33:23,820 --> 00:33:24,930
You can do it afterwards.

523
00:33:24,930 --> 00:33:26,320
You check by yourself, OK?

524
00:33:26,320 --> 00:33:32,950
You will find at
this point, that's

525
00:33:32,950 --> 00:33:37,760
when they are equally
weighted, half and half.

526
00:33:42,190 --> 00:33:49,130
So you get square root of that.

527
00:33:49,130 --> 00:33:53,400
So you actually have a
significant reduction

528
00:33:53,400 --> 00:33:57,780
of the variance of the portfolio
by choosing half and half,

529
00:33:57,780 --> 00:34:00,060
zero-ly correlated portfolio.

530
00:34:00,060 --> 00:34:01,020
So what's that called?

531
00:34:01,020 --> 00:34:02,340
What's that benefit?

532
00:34:02,340 --> 00:34:03,740
Diversification, right?

533
00:34:03,740 --> 00:34:06,920
When you have less than
perfectly correlated,

534
00:34:06,920 --> 00:34:09,110
positively correlated
assets, you

535
00:34:09,110 --> 00:34:13,800
can actually achieve the same
return but having a lower

536
00:34:13,800 --> 00:34:16,110
standard deviation.

537
00:34:16,110 --> 00:34:18,520
I'll say, OK, that's
fairly straightforward.

538
00:34:18,520 --> 00:34:21,679
So let's look at a few
more special cases.

539
00:34:21,679 --> 00:34:25,454
I want really to have you
establish this intuition.

540
00:34:28,880 --> 00:34:34,780
So let's think about what
if in the same example,

541
00:34:34,780 --> 00:34:38,330
what if rho equals to
1, perfectly correlated?

542
00:34:43,719 --> 00:34:45,150
Then you can't, right?

543
00:34:45,150 --> 00:34:49,389
So you end up at
just this one point.

544
00:34:49,389 --> 00:34:50,761
You agree?

545
00:34:50,761 --> 00:34:51,260
OK.

546
00:34:55,250 --> 00:34:59,002
What if it's totally
negatively correlated?

547
00:34:59,002 --> 00:35:00,335
Perfectly negatively correlated.

548
00:35:04,330 --> 00:35:05,790
What's this line look like?

549
00:35:17,750 --> 00:35:18,250
Right?

550
00:35:24,640 --> 00:35:27,190
So you if you weight
everything to one side,

551
00:35:27,190 --> 00:35:29,690
you're going to
still get this point.

552
00:35:29,690 --> 00:35:33,460
But if you weight
half and half, you're

553
00:35:33,460 --> 00:35:37,416
going to achieve
basically zero variance.

554
00:35:37,416 --> 00:35:40,450
I think we showed
that last time,

555
00:35:40,450 --> 00:35:41,790
you learned that last time.

556
00:35:41,790 --> 00:35:46,070
OK, so let's look
beyond those cases.

557
00:35:46,070 --> 00:35:46,740
So what now?

558
00:35:46,740 --> 00:35:58,980
Let's look at-- so R_1 does
not equal to R_2 anymore.

559
00:36:09,010 --> 00:36:11,020
Sigma_1 equal to 0.

560
00:36:11,020 --> 00:36:14,170
There's no volatility
of the first asset.

561
00:36:14,170 --> 00:36:15,760
So that's cash, OK?

562
00:36:15,760 --> 00:36:19,240
So that's a riskless
asset in the first one.

563
00:36:19,240 --> 00:36:22,740
So let's even call that
R_1 is less than R_2.

564
00:36:22,740 --> 00:36:24,530
So that's the-- right?

565
00:36:24,530 --> 00:36:28,170
You have the cash asset, and
then you have a non-cash asset.

566
00:36:28,170 --> 00:36:30,539
Rho equal to 0,
zero correlation.

567
00:36:30,539 --> 00:36:32,330
So let's look at what
this line looks like.

568
00:36:54,400 --> 00:36:58,971
So R_1, R_2, sigma_2 here.

569
00:36:58,971 --> 00:37:06,450
When you weight asset
two 100%, you're

570
00:37:06,450 --> 00:37:08,490
going to get this point, right?

571
00:37:08,490 --> 00:37:15,020
When you weight asset
one 100%, you're

572
00:37:15,020 --> 00:37:17,940
going to get this point, right?

573
00:37:17,940 --> 00:37:24,440
So what's in the
middle of your return

574
00:37:24,440 --> 00:37:27,510
as a function of variance?

575
00:37:27,510 --> 00:37:30,500
Can someone guess?

576
00:37:30,500 --> 00:37:31,824
AUDIENCE: A parabola?

577
00:37:31,824 --> 00:37:33,640
Should it be a parabola?

578
00:37:33,640 --> 00:37:35,655
PROFESSOR: Try again.

579
00:37:35,655 --> 00:37:36,530
AUDIENCE: A parabola.

580
00:37:36,530 --> 00:37:37,890
PROFESSOR: Yeah, I know, I know.

581
00:37:37,890 --> 00:37:38,665
Thank you.

582
00:37:38,665 --> 00:37:40,270
Are there any other answers?

583
00:37:45,640 --> 00:37:47,540
OK, this is actually
I-- let me just

584
00:37:47,540 --> 00:37:50,140
derive very quickly for you.

585
00:37:50,140 --> 00:37:52,736
Sigma_1 equal to
0, rho equal to 0.

586
00:37:52,736 --> 00:37:53,360
What's sigma_P?

587
00:38:03,080 --> 00:38:05,240
Right?

588
00:38:05,240 --> 00:38:16,780
And sigma_P is essentially
proportional to sigma_2

589
00:38:16,780 --> 00:38:19,750
with the weighting.

590
00:38:19,750 --> 00:38:21,914
OK, and what's R?

591
00:38:26,090 --> 00:38:30,130
R is a linear combination
of R_1 and R_2.

592
00:38:30,130 --> 00:38:37,190
So it's still-- so it's linear.

593
00:38:41,770 --> 00:38:47,060
OK, so because in these
cases, you actually-- you

594
00:38:47,060 --> 00:38:52,220
essentially-- your return
is a linear function.

595
00:38:52,220 --> 00:38:55,000
And the slope, what
is the slope of this?

596
00:39:00,620 --> 00:39:02,410
Oh, let's wait on the slope.

597
00:39:02,410 --> 00:39:04,060
So we can come back to this.

598
00:39:04,060 --> 00:39:09,080
This actually relates back to
the so-called capital market

599
00:39:09,080 --> 00:39:12,515
line or capital
allocation line, OK?

600
00:39:12,515 --> 00:39:14,890
Because last time we talked
about the efficient frontier.

601
00:39:19,810 --> 00:39:25,450
That's when we have no riskless
assets in the portfolio, right?

602
00:39:25,450 --> 00:39:31,860
When you add on cash, then
you actually can select.

603
00:39:31,860 --> 00:39:34,990
You can combine the
cash into the portfolio

604
00:39:34,990 --> 00:39:42,490
by having a higher boundary,
higher Efficient Frontier,

605
00:39:42,490 --> 00:39:45,240
and essentially a higher
return with the same exposure.

606
00:39:50,370 --> 00:39:52,510
So let's look at a
couple more cases, then

607
00:39:52,510 --> 00:40:02,280
I will tell you-- so I
think let's look at-- so R_1

608
00:40:02,280 --> 00:40:04,350
is less than R_2.

609
00:40:04,350 --> 00:40:08,390
And volatilities are not 0.

610
00:40:08,390 --> 00:40:13,070
Also, sigma_1 is
less than sigma_2,

611
00:40:13,070 --> 00:40:28,920
but it has a negative
correlation of 1.

612
00:40:28,920 --> 00:40:32,660
So you'll have asset
one, asset two.

613
00:40:32,660 --> 00:40:38,720
And as we know, where you pick
half and half, this goes to 0.

614
00:40:38,720 --> 00:40:41,070
So this is a quadratic function.

615
00:40:41,070 --> 00:40:43,950
You can verify and
prove it later.

616
00:40:43,950 --> 00:40:54,830
And what if when
rho is equal to 0--

617
00:40:54,830 --> 00:41:02,840
and actually, I want to-- so
sigma_1 should be here, OK?

618
00:41:02,840 --> 00:41:06,680
So when rho is equal
to zero, this no longer

619
00:41:06,680 --> 00:41:10,135
goes to-- the variance can
no longer be minimized to 0.

620
00:41:13,920 --> 00:41:16,470
So this is your efficient
frontier, this part.

621
00:41:23,260 --> 00:41:27,150
I think that's enough
examples of two assets

622
00:41:27,150 --> 00:41:28,520
for the efficient frontier.

623
00:41:28,520 --> 00:41:30,080
So you get the idea.

624
00:41:30,080 --> 00:41:32,847
So then what if we
have three assets?

625
00:41:32,847 --> 00:41:34,680
So let me just touch
upon that very quickly.

626
00:41:34,680 --> 00:41:38,880
If you have one more
asset here, essentially

627
00:41:38,880 --> 00:41:41,020
you can solve the
same equations.

628
00:41:41,020 --> 00:41:48,770
And when the-- special case:
you can verify afterwards,

629
00:41:48,770 --> 00:41:50,580
if all the
volatilities are equal,

630
00:41:50,580 --> 00:41:54,540
and zero correlation
among the assets.

631
00:41:54,540 --> 00:42:00,500
You're going to be able to
minimize sigma_P equal to 1

632
00:42:00,500 --> 00:42:03,550
over the square root
of three of sigma_1.

633
00:42:03,550 --> 00:42:04,050
OK.

634
00:42:07,690 --> 00:42:09,050
So it seems pretty neat, right?

635
00:42:09,050 --> 00:42:13,100
The math is not hard
and straightforward.

636
00:42:13,100 --> 00:42:16,540
But it gives you the idea
how to answer your question,

637
00:42:16,540 --> 00:42:20,570
how to select them when
you start with two.

638
00:42:20,570 --> 00:42:23,580
So why are two
assets so important?

639
00:42:23,580 --> 00:42:26,270
What's the implication
in practice?

640
00:42:26,270 --> 00:42:31,230
It's actually a very
popular combination.

641
00:42:31,230 --> 00:42:34,180
Lot of the asset
managers, they simply

642
00:42:34,180 --> 00:42:38,070
benchmark to bonds
versus equity.

643
00:42:38,070 --> 00:42:41,290
And then one famous
combination is really 60/40.

644
00:42:41,290 --> 00:42:42,990
They call it a
60/40 combination.

645
00:42:42,990 --> 00:42:46,130
60% in equity, 40% in bonds.

646
00:42:46,130 --> 00:42:49,890
And even nowadays, any fund
manager, you have that.

647
00:42:49,890 --> 00:42:52,140
People will still ask you
to compare your performance

648
00:42:52,140 --> 00:42:53,170
with that combination.

649
00:42:53,170 --> 00:42:59,020
So the two-asset examples seem
to be quite easy and simple,

650
00:42:59,020 --> 00:43:05,440
but actually it's a very
important one to compare.

651
00:43:05,440 --> 00:43:09,700
And that will lead me to
get into the risk parity

652
00:43:09,700 --> 00:43:10,390
discussion.

653
00:43:10,390 --> 00:43:13,330
But before I get to
risk parity discussion,

654
00:43:13,330 --> 00:43:17,080
I want to review the concept
of beta and the Sharpe ratio.

655
00:44:21,530 --> 00:44:28,260
So your portfolio return,
this is your benchmark return,

656
00:44:28,260 --> 00:44:29,840
R of m, expected return.

657
00:44:29,840 --> 00:44:36,520
R_f is the risk-free return,
so essentially a cash return.

658
00:44:36,520 --> 00:44:41,150
And alpha is what you can
generate additionally.

659
00:44:41,150 --> 00:44:45,650
So let's even not to worry
about these small other terms--

660
00:44:45,650 --> 00:44:48,870
or not necessarily small,
but for the simplicity,

661
00:44:48,870 --> 00:44:50,550
I'll just reveal that.

662
00:44:50,550 --> 00:44:52,660
So that's your beta.

663
00:44:52,660 --> 00:44:53,910
Now what is your Sharpe ratio?

664
00:45:14,710 --> 00:45:15,330
OK.

665
00:45:15,330 --> 00:45:21,020
And you can-- so
sometimes Sharpe

666
00:45:21,020 --> 00:45:26,315
ratio is also called
risk-weighted return,

667
00:45:26,315 --> 00:45:30,380
or risk-adjusted return.

668
00:45:30,380 --> 00:45:36,670
And how many of you have
heard of Kelly's formula?

669
00:45:36,670 --> 00:45:39,680
So Kelly's formula
basically gives you

670
00:45:39,680 --> 00:45:44,460
that when you have-- let's
say in the gambling example,

671
00:45:44,460 --> 00:45:47,540
you know your winning
probability is p.

672
00:45:55,220 --> 00:45:59,600
So this basically tells
you how much to size up,

673
00:45:59,600 --> 00:46:01,270
how much you want to bet on.

674
00:46:01,270 --> 00:46:03,130
So it's a very simple formula.

675
00:46:07,260 --> 00:46:13,010
So you have a winning
probability of 50/50,

676
00:46:13,010 --> 00:46:16,300
how much you bet on?

677
00:46:16,300 --> 00:46:17,330
Nothing.

678
00:46:17,330 --> 00:46:23,850
So if you have p equal to 100%,
you bet 100% of your position.

679
00:46:23,850 --> 00:46:28,170
If you have a winning
probability of negative 100%,

680
00:46:28,170 --> 00:46:29,560
so what does it mean?

681
00:46:29,560 --> 00:46:32,760
That means you have a 100%
probability of losing it.

682
00:46:32,760 --> 00:46:34,290
What do you do?

683
00:46:34,290 --> 00:46:36,080
You bet the other
way around, right?

684
00:46:36,080 --> 00:46:40,665
You bet the other side, so that
when p is equal to negative--

685
00:46:40,665 --> 00:46:42,040
I'm sorry, actually
what I should

686
00:46:42,040 --> 00:46:46,480
say is when p equal to 0, your
losing probability becomes

687
00:46:46,480 --> 00:46:47,710
100%, right?

688
00:46:47,710 --> 00:46:51,370
So you bet 100%
the other way, OK?

689
00:46:51,370 --> 00:46:54,560
So that I leave to
you to think about.

690
00:46:54,560 --> 00:46:59,200
That's when you have
discrete outcome case.

691
00:46:59,200 --> 00:47:00,900
But when you
construct a portfolio,

692
00:47:00,900 --> 00:47:02,800
this leads to the next question.

693
00:47:02,800 --> 00:47:08,240
It's in addition to the
efficient frontier discussion,

694
00:47:08,240 --> 00:47:11,000
is that really all
about asset allocation?

695
00:47:11,000 --> 00:47:14,830
Is that how we calculate
our weights of each asset

696
00:47:14,830 --> 00:47:17,270
or strategy to choose from?

697
00:47:17,270 --> 00:47:19,080
The answer is no, right?

698
00:47:19,080 --> 00:47:22,765
So let's look at a
60/40 portfolio example.

699
00:47:42,800 --> 00:47:44,220
So again, two asset stock.

700
00:47:46,780 --> 00:47:56,150
Stock is, let's say,
60% percent, 40% bonds.

701
00:48:06,570 --> 00:48:31,280
So on this-- so typically
your stock volatility

702
00:48:31,280 --> 00:48:35,190
is higher than the bonds, and
the return, expected return,

703
00:48:35,190 --> 00:48:36,530
is also higher.

704
00:48:36,530 --> 00:48:41,770
So your 60/40 combinations
likely fall on the higher

705
00:48:41,770 --> 00:48:45,070
return and the higher
standard deviation

706
00:48:45,070 --> 00:48:48,500
part of the efficient frontier.

707
00:48:48,500 --> 00:48:50,760
So the question was--
so that's typically

708
00:48:50,760 --> 00:48:52,920
what people do before 2000.

709
00:48:52,920 --> 00:48:56,470
A real asset manager, the
easiest way or the passive way

710
00:48:56,470 --> 00:49:00,100
is just to allocate 60/40.

711
00:49:00,100 --> 00:49:05,600
But after 2000, what happened
was when after the equity

712
00:49:05,600 --> 00:49:12,750
market peaked and the bond had
a huge rally as first Greenspan

713
00:49:12,750 --> 00:49:20,150
cut interest rates before
the Y2K in the year 2000.

714
00:49:20,150 --> 00:49:22,900
You think it's kind of funny,
but at that time everybody

715
00:49:22,900 --> 00:49:25,210
worried about the year 2000.

716
00:49:25,210 --> 00:49:27,490
All the computers
are going to stop

717
00:49:27,490 --> 00:49:32,740
working because old software
were not prepared for crossing

718
00:49:32,740 --> 00:49:34,920
this millennium event.

719
00:49:34,920 --> 00:49:37,660
So they had to cut interest
rates for this event.

720
00:49:37,660 --> 00:49:41,060
But actually nothing happened,
so everything was OK.

721
00:49:41,060 --> 00:49:43,860
But that left the market
with plenty of cash,

722
00:49:43,860 --> 00:49:46,960
and also after the
tech bubble burst.

723
00:49:46,960 --> 00:49:50,650
So that was a good
portfolio, but then obviously

724
00:49:50,650 --> 00:49:54,300
in 2008 when the
equity market crashed,

725
00:49:54,300 --> 00:49:57,040
the bond market, the
government bond hybrid market,

726
00:49:57,040 --> 00:49:58,240
had a huge rally.

727
00:49:58,240 --> 00:50:03,610
And so that made
people question that.

728
00:50:03,610 --> 00:50:09,890
Is this 60/40 allocation of
asset simply by the market

729
00:50:09,890 --> 00:50:12,240
value the optimal
way of doing it,

730
00:50:12,240 --> 00:50:15,910
even though you are falling
on the Efficient Frontier?

731
00:50:15,910 --> 00:50:18,420
But how do you compare
different points?

732
00:50:18,420 --> 00:50:22,870
Is that simple choice of your
objectives, your situation,

733
00:50:22,870 --> 00:50:28,070
or there's actually other
ways to optimize it.

734
00:50:28,070 --> 00:50:32,290
So that's where the risk
parity concept was really--

735
00:50:32,290 --> 00:50:34,340
the concept has been
around, but the term

736
00:50:34,340 --> 00:50:39,210
was really coined in
2005, so quite recently,

737
00:50:39,210 --> 00:50:41,940
by a guy named Edward Qian.

738
00:50:41,940 --> 00:50:46,840
He basically said, OK,
instead of allocating 60/40

739
00:50:46,840 --> 00:50:49,870
based on market value,
why shouldn't we

740
00:50:49,870 --> 00:50:52,060
consider allocating risk?

741
00:50:52,060 --> 00:50:55,070
Instead of targeting a return,
targeting asset amount--

742
00:50:55,070 --> 00:50:58,020
let's think about
a case where we

743
00:50:58,020 --> 00:51:02,270
can have equal weighting of
risk between the two assets.

744
00:51:02,270 --> 00:51:06,780
So risk parity really means
equal risk weighting rather

745
00:51:06,780 --> 00:51:09,650
than equal market exposure.

746
00:51:09,650 --> 00:51:17,250
And then the further step
he took was he said, OK.

747
00:51:17,250 --> 00:51:19,980
So this actually,
OK, is equal risk.

748
00:51:19,980 --> 00:51:24,619
So you have lower return
and a lower risk, a lower

749
00:51:24,619 --> 00:51:25,410
standard deviation.

750
00:51:25,410 --> 00:51:29,040
But sometimes you will really
want a higher return, right?

751
00:51:29,040 --> 00:51:31,570
How do you satisfy both?

752
00:51:31,570 --> 00:51:36,060
Higher return and lower risk.

753
00:51:36,060 --> 00:51:37,460
Is there a free lunch?

754
00:51:37,460 --> 00:51:39,850
So he was thinking, right?

755
00:51:39,850 --> 00:51:42,370
There is, actually.

756
00:51:42,370 --> 00:51:45,366
It's not quite free, but
it's the closest thing.

757
00:51:45,366 --> 00:51:47,240
You've probably heard
this phrase many times.

758
00:51:47,240 --> 00:51:50,770
The closest thing in
investment to a free lunch

759
00:51:50,770 --> 00:51:55,430
is diversification.

760
00:51:55,430 --> 00:52:00,720
OK, and so he's using a
leverage here as well.

761
00:52:00,720 --> 00:52:03,540
let me talk about it a bit
more, about diversification,

762
00:52:03,540 --> 00:52:07,330
give you a couple
more examples, OK?

763
00:52:07,330 --> 00:52:11,230
That phrase about the free
lunch and diversification

764
00:52:11,230 --> 00:52:14,850
was actually from-- was
that from Markowitz?

765
00:52:14,850 --> 00:52:18,620
Or people gave him that term.

766
00:52:18,620 --> 00:52:19,800
OK, but anyway.

767
00:52:19,800 --> 00:52:24,690
So let me give you another
simple example, OK?

768
00:52:24,690 --> 00:52:34,840
So let's consider two
assets, A and B. In year one,

769
00:52:34,840 --> 00:52:39,970
A goes up to-- it
basically doubles.

770
00:52:39,970 --> 00:52:44,730
And in year two,
it goes down 50%.

771
00:52:44,730 --> 00:52:46,334
So where does it end up?

772
00:52:58,530 --> 00:53:00,160
So it started with 100%.

773
00:53:00,160 --> 00:53:04,250
It goes up to 200%.

774
00:53:04,250 --> 00:53:10,010
Then it goes down
50% on the new base,

775
00:53:10,010 --> 00:53:11,650
so it returns nothing, right?

776
00:53:11,650 --> 00:53:12,930
It comes back.

777
00:53:12,930 --> 00:53:21,750
So asset B in year one loses
50%, then doubles, up 100%

778
00:53:21,750 --> 00:53:22,930
in year two.

779
00:53:22,930 --> 00:53:30,950
So asset B basically
goes down to 50%

780
00:53:30,950 --> 00:53:35,780
and it goes back up to 100%.

781
00:53:35,780 --> 00:53:39,200
So that's when you look
at them independently.

782
00:53:39,200 --> 00:53:44,170
But what if you had a 50/50
weight of the two assets?

783
00:53:44,170 --> 00:53:46,600
So if someone who is
quick on math can tell me,

784
00:53:46,600 --> 00:53:49,240
what does it change?

785
00:53:49,240 --> 00:53:53,450
So A goes up like that,
B goes down like that.

786
00:53:53,450 --> 00:53:59,010
Now you have a 50/50 A and
B. So let's look at magic.

787
00:53:59,010 --> 00:54:05,520
So in year one, A,
you have only 50%.

788
00:54:08,050 --> 00:54:10,320
So it goes up 100%.

789
00:54:12,890 --> 00:54:17,320
So that's up 50%
on the total basis.

790
00:54:17,320 --> 00:54:25,240
B, you'll also weight
50%, but it goes down 50%.

791
00:54:25,240 --> 00:54:29,150
So you have lost 25%.

792
00:54:29,150 --> 00:54:31,340
So at the end of
year one, you're

793
00:54:31,340 --> 00:54:38,620
actually-- so this is a combined
50/50 portfolio, year one

794
00:54:38,620 --> 00:54:39,480
and year two.

795
00:54:39,480 --> 00:54:41,990
So you started with 100.

796
00:54:41,990 --> 00:54:48,850
You're up to 1.25
at this point, OK?

797
00:54:48,850 --> 00:54:52,600
So at the end of year
one, you rebalance, right?

798
00:54:52,600 --> 00:54:55,150
So you have to
come back to 50/50.

799
00:54:55,150 --> 00:54:56,580
So what do you do?

800
00:54:56,580 --> 00:55:01,780
So this becomes 75, right?

801
00:55:01,780 --> 00:55:05,350
So you no longer have
the 50/50 weight equal.

802
00:55:05,350 --> 00:55:08,750
So you have to sell
A to come back to 50

803
00:55:08,750 --> 00:55:11,810
and use the money to buy B.

804
00:55:11,810 --> 00:55:17,670
So you have a new 50/50
percent weight asset.

805
00:55:17,670 --> 00:55:19,570
Again, you can
figure out the math.

806
00:55:19,570 --> 00:55:23,800
But what happens in
the following year

807
00:55:23,800 --> 00:55:27,450
when you have this move,
this comes back 50%,

808
00:55:27,450 --> 00:55:29,230
this goes up 100%.

809
00:55:29,230 --> 00:55:36,740
You return another 25%
positively without volatility.

810
00:55:39,420 --> 00:55:40,910
So you have a straight line.

811
00:55:40,910 --> 00:55:43,850
You can keep-- so
this two year is

812
00:55:43,850 --> 00:55:48,560
a-- so that's so-called
diversification benefit.

813
00:55:48,560 --> 00:55:53,120
And in the 60/40 bond market,
that's really the idea

814
00:55:53,120 --> 00:55:56,670
people think about
how to combine them.

815
00:55:56,670 --> 00:56:00,900
And so let me talk a little
bit about risk parity

816
00:56:00,900 --> 00:56:02,370
and how you actually
achieve them.

817
00:56:06,050 --> 00:56:09,380
I'll try to leave plenty
of time for questions.

818
00:56:12,070 --> 00:56:17,510
So that's the return, and
so let's forget about these.

819
00:56:24,330 --> 00:56:27,260
So let's leave cash here, OK?

820
00:56:27,260 --> 00:56:35,900
So the previous example I gave
you, when you have two assets,

821
00:56:35,900 --> 00:56:43,170
one is cash, R_1,
the other is not.

822
00:56:43,170 --> 00:56:45,070
The other has a
volatility of sigma_2.

823
00:56:48,100 --> 00:56:49,820
You have this point, right?

824
00:56:49,820 --> 00:56:52,960
So and I said,
what's in between?

825
00:56:52,960 --> 00:56:54,510
It's a straight line.

826
00:56:54,510 --> 00:56:57,870
That's your asset allocation,
different combination.

827
00:57:00,800 --> 00:57:04,350
Did it occur to you, why
can't we go beyond this point?

828
00:57:08,230 --> 00:57:16,590
So this point is when we weight
w_2 equal to 1, w_1 equal to 0.

829
00:57:16,590 --> 00:57:21,570
That's when you weight
everything into the asset two.

830
00:57:21,570 --> 00:57:22,940
What if you go beyond that?

831
00:57:22,940 --> 00:57:24,060
What does that mean?

832
00:57:24,060 --> 00:57:24,750
OK.

833
00:57:24,750 --> 00:57:31,330
So let's say, can we have w_1
equal to minus 1, w_2 equal

834
00:57:31,330 --> 00:57:33,990
to plus 2?

835
00:57:33,990 --> 00:57:37,500
So they still add up to 100%.

836
00:57:37,500 --> 00:57:41,524
But what's negative 1 mean?

837
00:57:41,524 --> 00:57:42,580
Borrow, right?

838
00:57:42,580 --> 00:57:48,380
So you went short cash
100%, you borrow money.

839
00:57:48,380 --> 00:57:53,120
You borrow 100% of cash,
then put into to buy

840
00:57:53,120 --> 00:57:56,020
equity or whatever,
risky assets, here.

841
00:57:56,020 --> 00:57:58,540
So you have plus 2 minus 1.

842
00:57:58,540 --> 00:58:02,130
What does the return looks
like when you do this?

843
00:58:02,130 --> 00:58:10,840
So R_P equal to w_1
R_1 plus w_2 R_2.

844
00:58:14,640 --> 00:58:19,900
So minus R_1 plus 2R_2.

845
00:58:19,900 --> 00:58:21,220
That's your return.

846
00:58:21,220 --> 00:58:23,810
It's this point here.

847
00:58:23,810 --> 00:58:28,220
What's your variance look
like, or standard deviation

848
00:58:28,220 --> 00:58:29,142
look like?

849
00:58:32,370 --> 00:58:34,000
As we did before, right?

850
00:58:34,000 --> 00:58:39,040
So sigma_P simply
equal to w_2 sigma_2.

851
00:58:39,040 --> 00:58:41,650
So in this case, it's 2sigma_2.

852
00:58:41,650 --> 00:58:47,980
So you're two times more
risky, two times as risky

853
00:58:47,980 --> 00:58:53,110
as the asset two.

854
00:58:53,110 --> 00:58:56,310
So this introduces the
concept of leverage.

855
00:58:56,310 --> 00:58:59,580
Whenever you go short,
you introduce leverage.

856
00:58:59,580 --> 00:59:02,170
You actually-- on
your balance sheet,

857
00:59:02,170 --> 00:59:05,950
you have two times of asset two.

858
00:59:05,950 --> 00:59:09,370
You're also short one of
the other instrument, right?

859
00:59:09,370 --> 00:59:11,230
OK so that's your liability.

860
00:59:11,230 --> 00:59:12,710
So your net is still one.

861
00:59:15,760 --> 00:59:21,470
So what this risk
parity says is, OK,

862
00:59:21,470 --> 00:59:26,140
so we can target on the
equal risk weighting, which

863
00:59:26,140 --> 00:59:31,940
will give you somewhere
around-- let's called it 25.

864
00:59:31,940 --> 00:59:39,690
25% bonds, 75%-- 25%
equity, 75% of fixed income.

865
00:59:39,690 --> 00:59:44,420
Or in other words, 25%
of stocks, 75% of bonds.

866
00:59:44,420 --> 00:59:45,970
So you have lower return.

867
00:59:45,970 --> 00:59:51,940
But if you leverage
it up, you actually

868
00:59:51,940 --> 00:59:58,800
have higher return,
higher expected return,

869
00:59:58,800 --> 01:00:03,500
given the same amount
of standard deviation.

870
01:00:03,500 --> 01:00:05,260
You achieved by leveraging up.

871
01:00:05,260 --> 01:00:08,120
Obviously, you
leverage up, right?

872
01:00:08,120 --> 01:00:10,360
That's the other
implication of that.

873
01:00:10,360 --> 01:00:12,260
We haven't talked about
the liquidity risk,

874
01:00:12,260 --> 01:00:16,210
but that's a different topic.

875
01:00:16,210 --> 01:00:23,905
So what's your Sharpe ratio look
like for risk parity portfolio?

876
01:01:08,180 --> 01:01:12,520
So you essentially
maximized the Sharpe ratio,

877
01:01:12,520 --> 01:01:17,320
or risk-adjusted return, by
achieving the risk parity

878
01:01:17,320 --> 01:01:18,340
portfolio.

879
01:01:18,340 --> 01:01:20,090
So 60/40 is here.

880
01:01:20,090 --> 01:01:28,729
You actually maximize that, and
this is-- does leverage matter?

881
01:01:28,729 --> 01:01:31,020
When you leverage up, does
Sharpe ratio change, or not?

882
01:01:35,412 --> 01:01:36,876
AUDIENCE: It splits in half.

883
01:01:36,876 --> 01:01:41,770
So you've got twice the
[? variance ?] [INAUDIBLE].

884
01:01:41,770 --> 01:01:46,084
PROFESSOR: So let's look at that
straight line, this example,

885
01:01:46,084 --> 01:01:46,584
OK?

886
01:01:51,460 --> 01:02:02,944
So we said Sharpe
ratio equal to-- right?

887
01:02:07,390 --> 01:02:17,200
So R_P, what is sigma_P?

888
01:02:17,200 --> 01:02:20,555
It's 2sigma_2, right,
when you leverage up.

889
01:02:24,590 --> 01:02:34,474
So this equals to R_2 minus
R_1, divide by sigma_2.

890
01:02:38,330 --> 01:02:41,940
So that's the same
as at this point.

891
01:02:41,940 --> 01:02:45,290
So that's essentially the
slope of the whole line.

892
01:02:45,290 --> 01:02:47,010
It doesn't change.

893
01:02:47,010 --> 01:02:50,430
OK, so now you can
see the connection

894
01:02:50,430 --> 01:02:55,280
between the slope of this
curve and the Sharpe ratio

895
01:02:55,280 --> 01:02:58,670
and how that links back to beta.

896
01:02:58,670 --> 01:03:00,430
So let me ask you
another question.

897
01:03:00,430 --> 01:03:08,850
When the portfolio has higher
standard derivation of sigma_P,

898
01:03:08,850 --> 01:03:12,544
will beta to a specific
asset increase or decrease?

899
01:03:16,890 --> 01:03:19,240
So what's the
relationship intuitively

900
01:03:19,240 --> 01:03:23,880
between beta-- so let's take
a look at the 60/40 example.

901
01:03:23,880 --> 01:03:28,210
Your portfolio, you have
stocks, you have bonds in it.

902
01:03:28,210 --> 01:03:32,090
So I'm asking you, what is
really the beta of this 60/40

903
01:03:32,090 --> 01:03:34,740
portfolio to the equity market?

904
01:03:34,740 --> 01:03:38,300
When equity market, it
becomes-- when the portfolio

905
01:03:38,300 --> 01:03:40,850
becomes more volatile.

906
01:03:40,850 --> 01:03:43,390
Is your beta increasing
or decreasing?

907
01:03:48,040 --> 01:03:49,820
So you can derive that.

908
01:03:49,820 --> 01:03:51,240
I'm going to tell
you the result,

909
01:03:51,240 --> 01:03:54,370
but I'm not going
to do the math here.

910
01:03:54,370 --> 01:04:06,170
So beta equals to-- [INAUDIBLE]
in this special case,

911
01:04:06,170 --> 01:04:09,271
is sigma_P over sigma_2.

912
01:04:09,271 --> 01:04:09,770
OK.

913
01:04:13,060 --> 01:04:15,550
All right, so so
much for all these.

914
01:04:15,550 --> 01:04:19,320
I mean, it sounds like
everything is nicely solved.

915
01:04:19,320 --> 01:04:22,100
And so coming back
to the real world,

916
01:04:22,100 --> 01:04:24,480
and let me bring you back, OK?

917
01:04:24,480 --> 01:04:27,380
So are we all set for
portfolio management?

918
01:04:27,380 --> 01:04:30,140
We can program, make
a robot to do this.

919
01:04:30,140 --> 01:04:31,880
Why do we need all
these guys working

920
01:04:31,880 --> 01:04:32,980
on portfolio management?

921
01:04:37,070 --> 01:04:44,800
Or why do we need anybody
to manage a hedge fund?

922
01:04:44,800 --> 01:04:46,390
You can just give money, right?

923
01:04:46,390 --> 01:04:49,410
So why do you need somebody,
anybody, to put it together?

924
01:04:49,410 --> 01:04:50,920
So before I answer
this question,

925
01:04:50,920 --> 01:04:52,100
let me show you a video.

926
01:05:01,581 --> 01:05:05,074
[VIDEO PLAYBACK]

927
01:05:51,980 --> 01:05:54,475
[HORN BLARING]

928
01:06:02,080 --> 01:06:04,110
[END VIDEO PLAYBACK]

929
01:06:04,110 --> 01:06:04,610
OK.

930
01:06:08,300 --> 01:06:13,840
Anyone heard about the
London Millennium Bridge?

931
01:06:13,840 --> 01:06:16,590
So it was a bridge
built around that time

932
01:06:16,590 --> 01:06:21,650
and thought it had
the latest technology.

933
01:06:21,650 --> 01:06:26,150
And it would really
perfectly absorb--

934
01:06:26,150 --> 01:06:28,550
you heard about soldiers just
marching across a bridge,

935
01:06:28,550 --> 01:06:30,900
and they'll crush the bridge.

936
01:06:30,900 --> 01:06:33,190
When everybody's
walking in sync,

937
01:06:33,190 --> 01:06:35,920
your force gets synchronized.

938
01:06:35,920 --> 01:06:37,830
Then the bridge was
not designed to take

939
01:06:37,830 --> 01:06:42,250
that synchronized force, so the
bridge collapsed in the past.

940
01:06:42,250 --> 01:06:45,730
So when they designed this,
they took all that into account.

941
01:06:45,730 --> 01:06:49,510
But what they hadn't
taken into account

942
01:06:49,510 --> 01:06:52,850
was the support of
that is actually--

943
01:06:52,850 --> 01:06:59,450
so they allow the horizontal
move to take that tension away.

944
01:06:59,450 --> 01:07:02,190
But the problem is
when everybody's sees

945
01:07:02,190 --> 01:07:07,290
more people walking in
sync, then the whole bridge

946
01:07:07,290 --> 01:07:09,460
starts to swell, right?

947
01:07:09,460 --> 01:07:11,360
Then the only way
to keep a balance

948
01:07:11,360 --> 01:07:13,970
for you standing
on the bridge is

949
01:07:13,970 --> 01:07:17,760
to walk in sync
with other people.

950
01:07:17,760 --> 01:07:20,685
So that's a survival instinct.

951
01:07:20,685 --> 01:07:22,670
And so I got this--
I mean, that's

952
01:07:22,670 --> 01:07:25,310
actually my friend at
Fidelity, Ren Cheng.

953
01:07:25,310 --> 01:07:26,910
Dr. Ren Cheng brought
this up to me.

954
01:07:26,910 --> 01:07:29,080
He said, oh, you're
doing-- how do

955
01:07:29,080 --> 01:07:32,720
you think about the
portfolio risk, right?

956
01:07:32,720 --> 01:07:37,330
This is what happened in the
financial market in 2008.

957
01:07:37,330 --> 01:07:40,060
When you think you got
everything figured out,

958
01:07:40,060 --> 01:07:42,460
you have the optimal strategy.

959
01:07:42,460 --> 01:07:44,820
When everybody
starts to implement

960
01:07:44,820 --> 01:07:50,210
the same optimal strategy
for your own as individual,

961
01:07:50,210 --> 01:07:53,660
the whole system is
actually not optimized.

962
01:07:53,660 --> 01:07:54,950
It's actually in danger.

963
01:07:54,950 --> 01:07:56,260
Let me show you another one.

964
01:07:56,260 --> 01:07:56,926
[VIDEO PLAYBACK]

965
01:07:56,926 --> 01:07:58,300
[CLACKING]

966
01:07:58,300 --> 01:07:59,680
OK.

967
01:07:59,680 --> 01:08:02,336
These are metronomes, right?

968
01:08:02,336 --> 01:08:04,816
So can start anywhere you like.

969
01:08:09,280 --> 01:08:12,752
Are they in sync?

970
01:08:12,752 --> 01:08:13,744
Not yet.

971
01:08:18,208 --> 01:08:20,192
What is he doing?

972
01:08:39,040 --> 01:08:41,752
You only have to listen to it.

973
01:08:41,752 --> 01:08:44,395
You don't have to see it.

974
01:08:44,395 --> 01:08:46,272
So what's going on here?

975
01:08:46,272 --> 01:08:49,840
This is not-- metronomes
don't have brains, right?

976
01:08:49,840 --> 01:08:52,160
They don't really
follow the herd.

977
01:08:52,160 --> 01:08:53,700
Why are they synchronizing?

978
01:09:11,450 --> 01:09:14,648
OK, if you're expecting they
are getting out of sync,

979
01:09:14,648 --> 01:09:15,689
it's not going to happen.

980
01:09:15,689 --> 01:09:17,910
OK, so I'm going
to stop right here.

981
01:09:17,910 --> 01:09:19,564
OK.

982
01:09:19,564 --> 01:09:20,460
[END VIDEO PLAYBACK]

983
01:09:20,460 --> 01:09:25,180
You can try as many--
how do I get out of this?

984
01:09:30,310 --> 01:09:32,410
OK, so you can try it.

985
01:09:32,410 --> 01:09:36,140
You can look at-- there's
actually a book written on this

986
01:09:36,140 --> 01:09:36,810
as well, so.

987
01:09:36,810 --> 01:09:41,460
But the phenomena
here is nothing new.

988
01:09:41,460 --> 01:09:46,649
But what when he did
this, what's that mean?

989
01:09:46,649 --> 01:09:49,479
When he actually raised
that thing on the plate

990
01:09:49,479 --> 01:09:53,149
and put it on the Coke cans?

991
01:09:53,149 --> 01:09:54,240
What happened?

992
01:09:54,240 --> 01:09:56,545
Why is that is so significant?

993
01:09:59,034 --> 01:10:00,700
AUDIENCE: Because now
they're connected.

994
01:10:00,700 --> 01:10:01,600
PROFESSOR: They're connected.

995
01:10:01,600 --> 01:10:02,100
Right.

996
01:10:02,100 --> 01:10:03,780
So they are interconnected.

997
01:10:03,780 --> 01:10:05,720
Before, they were individuals.

998
01:10:05,720 --> 01:10:07,770
Now they're connected.

999
01:10:07,770 --> 01:10:12,560
And why did I show you
the London Bridge and this

1000
01:10:12,560 --> 01:10:13,360
at the same time?

1001
01:10:13,360 --> 01:10:16,660
What's this to do with
portfolio management?

1002
01:10:16,660 --> 01:10:19,132
What's this to do with
portfolio management?

1003
01:10:19,132 --> 01:10:22,802
AUDIENCE: [INAUDIBLE]
people who are trading,

1004
01:10:22,802 --> 01:10:25,385
if they have the same strategy,
[INAUDIBLE] affect each other,

1005
01:10:25,385 --> 01:10:26,843
they become connected
in that way--

1006
01:10:26,843 --> 01:10:27,685
PROFESSOR: Right.

1007
01:10:27,685 --> 01:10:29,317
AUDIENCE: If as
an individual, you

1008
01:10:29,317 --> 01:10:31,150
are doing a different
strategy, if everybody

1009
01:10:31,150 --> 01:10:32,608
has been doing
something different,

1010
01:10:32,608 --> 01:10:35,620
you can maximize
[? in the space. ?]

1011
01:10:35,620 --> 01:10:37,140
PROFESSOR: Very well said.

1012
01:10:37,140 --> 01:10:41,720
So if you're looking
for this stationary best

1013
01:10:41,720 --> 01:10:44,920
way of optimizing
your portfolio,

1014
01:10:44,920 --> 01:10:47,240
chances are everybody
else is going

1015
01:10:47,240 --> 01:10:48,509
to figure out the same thing.

1016
01:10:48,509 --> 01:10:50,300
And eventually, you
end up in the situation

1017
01:10:50,300 --> 01:10:52,450
and you actually get killed.

1018
01:10:52,450 --> 01:10:58,250
OK, so that's the thing.

1019
01:10:58,250 --> 01:11:01,120
What you learned today,
what you walk away was this.

1020
01:11:01,120 --> 01:11:06,610
OK, today is not what I
want you to know that all

1021
01:11:06,610 --> 01:11:07,750
the problems are solved.

1022
01:11:12,410 --> 01:11:12,910
Right?

1023
01:11:12,910 --> 01:11:14,451
So you say, oh, the
problem's solved.

1024
01:11:14,451 --> 01:11:16,290
The Nobel Prize was given.

1025
01:11:16,290 --> 01:11:18,770
So let's just program them.

1026
01:11:18,770 --> 01:11:22,170
No, you actually-- it's
a dynamic situation.

1027
01:11:22,170 --> 01:11:23,195
You have to.

1028
01:11:23,195 --> 01:11:25,070
So that makes the problem
interesting, right?

1029
01:11:25,070 --> 01:11:27,780
As a younger generation,
you're coming to the field.

1030
01:11:27,780 --> 01:11:29,370
The excitement is
there are still

1031
01:11:29,370 --> 01:11:32,390
a lot of interesting
problems out there unsolved.

1032
01:11:32,390 --> 01:11:36,300
You can beat the others
already in the field.

1033
01:11:36,300 --> 01:11:39,920
And so that's one takeaway.

1034
01:11:39,920 --> 01:11:42,240
And what are the
takeaways you think

1035
01:11:42,240 --> 01:11:46,470
by listening to all these?

1036
01:11:49,900 --> 01:11:52,350
AUDIENCE: Diversification
is a free lunch.

1037
01:11:52,350 --> 01:11:52,850
[CHUCKLES]

1038
01:11:52,850 --> 01:11:54,850
PROFESSOR: Diversification
is a free lunch, yes.

1039
01:11:54,850 --> 01:11:56,410
Not so free, right, in the end.

1040
01:11:56,410 --> 01:11:58,510
It's free to a certain extent.

1041
01:11:58,510 --> 01:12:00,870
But it's something--
you know, it's better

1042
01:12:00,870 --> 01:12:02,970
than not diversified, right?

1043
01:12:02,970 --> 01:12:04,540
It depends on how you do it.

1044
01:12:04,540 --> 01:12:07,810
But there is a way
you can optimize.

1045
01:12:07,810 --> 01:12:10,920
And so it's-- I want
to leave with you,

1046
01:12:10,920 --> 01:12:13,710
I actually want to finish a few
minutes earlier so that you can

1047
01:12:13,710 --> 01:12:15,010
ask me questions.

1048
01:12:15,010 --> 01:12:15,750
You can ask.

1049
01:12:15,750 --> 01:12:19,320
It's probably better to
have this open discussion.

1050
01:12:19,320 --> 01:12:23,710
And so I want you to
walk away, to really keep

1051
01:12:23,710 --> 01:12:27,180
in mind is in the
field of finance,

1052
01:12:27,180 --> 01:12:32,730
and particularly in the
quantitative finance,

1053
01:12:32,730 --> 01:12:34,230
it's not mechanical.

1054
01:12:34,230 --> 01:12:37,010
It's not like solving
physics problems.

1055
01:12:37,010 --> 01:12:39,390
It's not like you can get
everything figured so it

1056
01:12:39,390 --> 01:12:41,480
becomes predictable, right?

1057
01:12:41,480 --> 01:12:47,590
So the level of predictability
is actually very much linked

1058
01:12:47,590 --> 01:12:48,970
to a lot of other things.

1059
01:12:48,970 --> 01:12:51,600
Physics, you solve
Newton's equations.

1060
01:12:51,600 --> 01:12:53,480
You have a controlled
environment

1061
01:12:53,480 --> 01:12:55,780
and you know what you're
getting in the outcome.

1062
01:12:55,780 --> 01:12:59,750
But here, when you
participate in the market,

1063
01:12:59,750 --> 01:13:01,720
you are changing the market.

1064
01:13:01,720 --> 01:13:04,620
You are adding on
other factors into it.

1065
01:13:04,620 --> 01:13:09,180
So think more from a
broader scope kind of view

1066
01:13:09,180 --> 01:13:12,860
rather than just
solve the mathematics.

1067
01:13:12,860 --> 01:13:14,860
That's why I come
back to the original--

1068
01:13:14,860 --> 01:13:17,100
if you walk away
from this lecture,

1069
01:13:17,100 --> 01:13:19,520
you'll remember what I
said at the very beginning.

1070
01:13:19,520 --> 01:13:22,730
Solving problems
is about observe,

1071
01:13:22,730 --> 01:13:25,290
collecting data,
building models,

1072
01:13:25,290 --> 01:13:28,140
then verify and observe again.

1073
01:13:28,140 --> 01:13:31,230
OK, so I'll end right
here, so questions.

1074
01:13:35,150 --> 01:13:37,110
AUDIENCE: Yeah, just
[INAUDIBLE] question.

1075
01:13:37,110 --> 01:13:40,600
Does this have anything to
do with-- it kind of sounds

1076
01:13:40,600 --> 01:13:43,026
like game theory, but
I'm not exactly too sure.

1077
01:13:43,026 --> 01:13:45,460
Because you have
a huge population

1078
01:13:45,460 --> 01:13:48,470
and no stable equilibrium.

1079
01:13:48,470 --> 01:13:51,130
Does it have anything to do
with game theory, by any chance?

1080
01:13:51,130 --> 01:13:53,088
PROFESSOR: It has a lot
to do with game theory,

1081
01:13:53,088 --> 01:13:55,740
but not only to game theory.

1082
01:13:55,740 --> 01:13:59,680
So game theory, you have
a pretty well-defined set

1083
01:13:59,680 --> 01:14:01,150
of rules.

1084
01:14:01,150 --> 01:14:03,760
Two people play chess
against each other.

1085
01:14:03,760 --> 01:14:07,490
That's where a computer actually
can become smarter, right?

1086
01:14:07,490 --> 01:14:11,760
So in this market situation,
you have so many people

1087
01:14:11,760 --> 01:14:16,610
participating without
clearly defined rules.

1088
01:14:16,610 --> 01:14:20,270
There are some rules, but
not always clearly defined.

1089
01:14:20,270 --> 01:14:26,190
And so it's much more
complex than game theory.

1090
01:14:26,190 --> 01:14:30,510
But it's part of it, yeah.

1091
01:14:30,510 --> 01:14:31,140
Dan, yeah?

1092
01:14:31,140 --> 01:14:33,723
AUDIENCE: Can you talk a little
bit about why some of the risk

1093
01:14:33,723 --> 01:14:36,046
parity portfolios that did
so poorly in May and June

1094
01:14:36,046 --> 01:14:38,750
when rates started to rise
and what about their portfolio

1095
01:14:38,750 --> 01:14:39,750
allowed them do that?

1096
01:14:39,750 --> 01:14:41,083
PROFESSOR: Good question, right.

1097
01:14:41,083 --> 01:14:47,840
So as you can see here, what
the risk parity approach does

1098
01:14:47,840 --> 01:14:53,250
is essentially to weight more
on the lower volatility asset.

1099
01:14:53,250 --> 01:14:56,610
In this case, the question
is, how do you know

1100
01:14:56,610 --> 01:14:58,340
which asset has low volatility?

1101
01:14:58,340 --> 01:15:02,130
So you look at
historical data, which

1102
01:15:02,130 --> 01:15:05,410
you conclude bonds have
the lower volatility.

1103
01:15:05,410 --> 01:15:06,850
So you overweight bonds.

1104
01:15:06,850 --> 01:15:08,280
That's the essence
of them, right?

1105
01:15:08,280 --> 01:15:11,140
So then when bonds
to start to sell off

1106
01:15:11,140 --> 01:15:14,190
after Bernanke, Fed
chairman Bernanke,

1107
01:15:14,190 --> 01:15:17,310
said he's going to taper
quantitative easing.

1108
01:15:17,310 --> 01:15:22,954
So bonds from a very low high
yield, a very low yield level,

1109
01:15:22,954 --> 01:15:25,370
the yield went much higher,
the interest rate went higher.

1110
01:15:25,370 --> 01:15:26,390
Bonds got sold off.

1111
01:15:26,390 --> 01:15:30,420
So this portfolio did poorly.

1112
01:15:30,420 --> 01:15:34,310
So now the question
is, does that

1113
01:15:34,310 --> 01:15:39,070
prove the risk parity approach
wrong, or does it prove right?

1114
01:15:39,070 --> 01:15:42,040
Does the financial
crisis of 2008

1115
01:15:42,040 --> 01:15:46,020
prove the risk parity
approach a superior approach,

1116
01:15:46,020 --> 01:15:48,925
or does the June/May
experience prove this

1117
01:15:48,925 --> 01:15:53,640
as the less-favored approach?

1118
01:15:53,640 --> 01:15:55,870
What does it tell us?

1119
01:15:55,870 --> 01:15:56,980
Think about it.

1120
01:15:56,980 --> 01:16:00,710
So it really is inconclusive.

1121
01:16:00,710 --> 01:16:05,380
So you observe, you extrapolate
from your historical data.

1122
01:16:05,380 --> 01:16:10,020
But what you are
really doing is you're

1123
01:16:10,020 --> 01:16:15,870
trying to forecast volatility,
forecast return, forecast

1124
01:16:15,870 --> 01:16:20,120
correlation, all based
on historical data.

1125
01:16:20,120 --> 01:16:22,790
It's like-- a lot of
people use that example.

1126
01:16:22,790 --> 01:16:27,900
It's like driving by looking
at the rear view mirror.

1127
01:16:27,900 --> 01:16:29,750
That's the only thing
you look at, right?

1128
01:16:29,750 --> 01:16:33,010
You don't know what's going
on, happening in front of you.

1129
01:16:33,010 --> 01:16:34,345
You have another question?

1130
01:16:34,345 --> 01:16:36,520
AUDIENCE: Given all
this new information,

1131
01:16:36,520 --> 01:16:38,220
do you find that
people are still

1132
01:16:38,220 --> 01:16:43,170
playing similar [INAUDIBLE]
strategy with portfolio

1133
01:16:43,170 --> 01:16:44,590
management?

1134
01:16:44,590 --> 01:16:46,920
PROFESSOR: Very much true.

1135
01:16:46,920 --> 01:16:47,480
Why?

1136
01:16:47,480 --> 01:16:51,150
Right, so you said, people
should be smarter than that.

1137
01:16:51,150 --> 01:16:55,350
It's very difficult to
discover new asset classes.

1138
01:16:55,350 --> 01:16:58,400
It's also very
difficult to invent

1139
01:16:58,400 --> 01:17:02,780
new strategies in which you have
a better winning probability.

1140
01:17:02,780 --> 01:17:05,670
The other risk, the other
very interesting phenomenon,

1141
01:17:05,670 --> 01:17:08,895
is most of the traders and
the portfolio managers,

1142
01:17:08,895 --> 01:17:12,300
the investors, they
are career investors--

1143
01:17:12,300 --> 01:17:16,460
meaning just like if
I'm a baseball coach,

1144
01:17:16,460 --> 01:17:21,460
I'm hired to coach
a baseball team.

1145
01:17:21,460 --> 01:17:23,300
My performance is
really measured

1146
01:17:23,300 --> 01:17:27,410
against the other teams
when I win or lose, right?

1147
01:17:27,410 --> 01:17:30,470
A portfolio manager
or investor is also

1148
01:17:30,470 --> 01:17:32,460
measured against their peers.

1149
01:17:32,460 --> 01:17:37,990
So the safest way for them to
do is to benchmark to an index,

1150
01:17:37,990 --> 01:17:39,260
to the herd.

1151
01:17:39,260 --> 01:17:43,720
So there's very little
incentive for them to get out

1152
01:17:43,720 --> 01:17:47,080
of the crowd, because
if they are wrong,

1153
01:17:47,080 --> 01:17:48,550
they get killed first.

1154
01:17:48,550 --> 01:17:49,910
They lose their jobs.

1155
01:17:49,910 --> 01:17:53,760
So the tendency is to
stay with the crowd.

1156
01:17:53,760 --> 01:17:55,110
It's for survival instinct.

1157
01:17:55,110 --> 01:17:57,550
It's, again, the other example.

1158
01:17:57,550 --> 01:17:59,410
It's actually the
optimal strategy

1159
01:17:59,410 --> 01:18:04,290
for individual portfolio manager
is really to do the same thing

1160
01:18:04,290 --> 01:18:06,850
as other people are
doing because you

1161
01:18:06,850 --> 01:18:10,430
stay with the force.

1162
01:18:10,430 --> 01:18:16,217
AUDIENCE: So you said given
that we have all these groups,

1163
01:18:16,217 --> 01:18:18,672
in the end, it's not just
that we could leave it

1164
01:18:18,672 --> 01:18:19,654
to the computers.

1165
01:18:19,654 --> 01:18:20,940
We need managers.

1166
01:18:20,940 --> 01:18:23,680
So what different
are the managers

1167
01:18:23,680 --> 01:18:25,960
doing, other than [INAUDIBLE]?

1168
01:18:25,960 --> 01:18:28,550
PROFESSOR: Can you try to
answer that question yourself?

1169
01:18:28,550 --> 01:18:31,440
What's the difference between
a human and a computer?

1170
01:18:31,440 --> 01:18:35,610
That's really-- what
can human add value

1171
01:18:35,610 --> 01:18:37,940
to what a computer can do?

1172
01:18:37,940 --> 01:18:41,910
AUDIENCE: Consider the factors,
the market factors and news

1173
01:18:41,910 --> 01:18:43,230
and what's going on.

1174
01:18:43,230 --> 01:18:45,340
PROFESSOR: So taking more
information, processing

1175
01:18:45,340 --> 01:18:51,010
information, make a judgment
on a more holistic approach.

1176
01:18:51,010 --> 01:18:52,730
So it's an interesting question.

1177
01:18:52,730 --> 01:18:56,500
I have to say that
computers are beating

1178
01:18:56,500 --> 01:18:59,310
humans in many different ways.

1179
01:18:59,310 --> 01:19:04,105
Can a computer ever get to
the point actually beating

1180
01:19:04,105 --> 01:19:06,080
a human in investment?

1181
01:19:06,080 --> 01:19:10,780
I can't confidently tell you
that it's not going to happen.

1182
01:19:10,780 --> 01:19:12,640
It may happen.

1183
01:19:12,640 --> 01:19:13,500
So I don't know.

1184
01:19:18,987 --> 01:19:19,820
Any other questions?

1185
01:19:19,820 --> 01:19:20,318
Yeah?

1186
01:19:20,318 --> 01:19:21,568
AUDIENCE: Just to add to that.

1187
01:19:21,568 --> 01:19:25,316
I think there is some more to
management than just investing.

1188
01:19:25,316 --> 01:19:33,066
I think managers also have key
roles in their HR, key roles in

1189
01:19:33,066 --> 01:19:35,190
just like managing people
and ensuring that they're

1190
01:19:35,190 --> 01:19:37,790
maximizing their
talents, not just like,

1191
01:19:37,790 --> 01:19:39,640
oh, how much money did you make?

1192
01:19:39,640 --> 01:19:42,540
But I mean, are you moving
forward in your career

1193
01:19:42,540 --> 01:19:43,400
while you're there?

1194
01:19:43,400 --> 01:19:46,267
So I think management has a
role to play in that as well,

1195
01:19:46,267 --> 01:19:47,100
not just investment.

1196
01:19:49,830 --> 01:19:52,730
PROFESSOR: Yeah, I think
that's a good point.

1197
01:19:52,730 --> 01:19:55,300
Yeah.

1198
01:19:55,300 --> 01:19:57,120
All right, so-- oh, sure.

1199
01:19:57,120 --> 01:19:57,620
Jesse?

1200
01:19:57,620 --> 01:19:59,440
AUDIENCE: What is your
portfolio breakdown?

1201
01:19:59,440 --> 01:20:01,960
PROFESSOR: My
personal portfolio?

1202
01:20:01,960 --> 01:20:04,900
Well, I am actually very
conservative at this point,

1203
01:20:04,900 --> 01:20:10,820
because if you look at my curve
of those spending and earning

1204
01:20:10,820 --> 01:20:16,520
curve, I'm basically trying
to protect principals rather

1205
01:20:16,520 --> 01:20:19,570
than try to maximize
return at this point.

1206
01:20:19,570 --> 01:20:25,480
So I would be sliding down
more towards this part

1207
01:20:25,480 --> 01:20:29,500
rather than try to go
to this corner, yeah.

1208
01:20:29,500 --> 01:20:32,110
So I haven't really
talked much about risk.

1209
01:20:32,110 --> 01:20:33,580
What is risk, right?

1210
01:20:33,580 --> 01:20:37,500
So I talk about volatility
or standard deviation.

1211
01:20:37,500 --> 01:20:41,200
But as we all know that, as
Peter mentioned last time as

1212
01:20:41,200 --> 01:20:46,550
well, there are many other ways
to look at risk-- value at risk

1213
01:20:46,550 --> 01:20:51,290
or half distribution or
truncated distribution,

1214
01:20:51,290 --> 01:20:55,160
or simply maximum loss you
can afford to take, right?

1215
01:20:58,500 --> 01:21:01,660
But looking at standard
deviation or volatility

1216
01:21:01,660 --> 01:21:02,680
is an elegant way.

1217
01:21:02,680 --> 01:21:04,310
You can see.

1218
01:21:04,310 --> 01:21:09,170
I can really show you in
very simple math about how

1219
01:21:09,170 --> 01:21:11,440
the concept actually plays out.

1220
01:21:11,440 --> 01:21:14,600
But in the end,
actually volatility

1221
01:21:14,600 --> 01:21:18,420
is really not the best
measure, in my view, of risk.

1222
01:21:18,420 --> 01:21:18,920
Why?

1223
01:21:18,920 --> 01:21:24,368
Let me give you another simple
example before we leave.

1224
01:21:28,670 --> 01:21:31,450
So let's say this is over time.

1225
01:21:34,400 --> 01:21:43,700
This is your cumulative
return or you dollar amount.

1226
01:21:43,700 --> 01:21:46,090
So you start from here.

1227
01:21:46,090 --> 01:21:53,489
If you go flat,
then-- does anyone

1228
01:21:53,489 --> 01:21:55,155
like to have this
kind of a performance?

1229
01:21:58,300 --> 01:21:59,230
Right?

1230
01:21:59,230 --> 01:22:00,410
Of course, right?

1231
01:22:00,410 --> 01:22:01,240
This is very nice.

1232
01:22:01,240 --> 01:22:02,190
You keep going up.

1233
01:22:02,190 --> 01:22:03,930
You never go down.

1234
01:22:03,930 --> 01:22:08,940
But what's the
volatility of that?

1235
01:22:08,940 --> 01:22:12,890
The volatility is
probably not low, right?

1236
01:22:12,890 --> 01:22:16,345
And then on the
other hand, you could

1237
01:22:16,345 --> 01:22:26,840
have-- what I'm
trying to say, when

1238
01:22:26,840 --> 01:22:30,010
you look at expected
return matching expected

1239
01:22:30,010 --> 01:22:38,190
return and the volatility,
you can still really not

1240
01:22:38,190 --> 01:22:40,630
selecting the best combination.

1241
01:22:40,630 --> 01:22:43,530
Because what you really
should care about

1242
01:22:43,530 --> 01:22:46,540
is not just your volatility.

1243
01:22:46,540 --> 01:22:51,820
And again, bear in mind all
the discussion about the Modern

1244
01:22:51,820 --> 01:22:54,920
Portfolio Theory is based
on one key assumption here.

1245
01:22:54,920 --> 01:22:59,220
It's about Gaussian
distribution, OK?

1246
01:22:59,220 --> 01:23:01,240
Normal distribution.

1247
01:23:01,240 --> 01:23:04,800
The two parameters, mean
and standard deviation,

1248
01:23:04,800 --> 01:23:06,850
categorize the distribution.

1249
01:23:06,850 --> 01:23:11,780
But in reality, you have many
other sets of distributions.

1250
01:23:11,780 --> 01:23:17,400
And so it's a concept
still up for a lot

1251
01:23:17,400 --> 01:23:19,460
of discussion and debate.

1252
01:23:19,460 --> 01:23:24,710
But I want to leave
that with you as well.

1253
01:23:24,710 --> 01:23:25,690
Yeah?

1254
01:23:25,690 --> 01:23:28,385
AUDIENCE: Just going back to
the same question about what

1255
01:23:28,385 --> 01:23:30,590
these guys were asking
about management

1256
01:23:30,590 --> 01:23:33,060
and how do they add
value, I think the people

1257
01:23:33,060 --> 01:23:35,170
who added value-- there
were some people who

1258
01:23:35,170 --> 01:23:38,430
added a tremendous amount of
value in the financial crisis.

1259
01:23:38,430 --> 01:23:40,400
And they were doing
the same mathematics.

1260
01:23:40,400 --> 01:23:42,455
But a difference was in
their expected return

1261
01:23:42,455 --> 01:23:44,910
of various assets was
different from the entire--

1262
01:23:44,910 --> 01:23:46,360
the broad market.

1263
01:23:46,360 --> 01:23:50,500
So if you can just know what
expected return is that,

1264
01:23:50,500 --> 01:23:52,810
probably that is the only
answer to the whole portfolio

1265
01:23:52,810 --> 01:23:53,590
management debate.

1266
01:23:53,590 --> 01:23:54,370
PROFESSOR: Yes.

1267
01:23:54,370 --> 01:24:00,900
If you can forecast expected
return, then that's-- yeah,

1268
01:24:00,900 --> 01:24:01,920
now you know the game.

1269
01:24:01,920 --> 01:24:02,760
You solved it.

1270
01:24:02,760 --> 01:24:04,605
You solved the big
part of the puzzle.

1271
01:24:04,605 --> 01:24:05,105
Yeah?

1272
01:24:05,105 --> 01:24:07,250
AUDIENCE: What
management does is

1273
01:24:07,250 --> 01:24:10,370
how good it can do [INAUDIBLE]
expected return, full stop.

1274
01:24:10,370 --> 01:24:10,980
Nothing more.

1275
01:24:14,200 --> 01:24:15,470
PROFESSOR: I disagree on that.

1276
01:24:15,470 --> 01:24:16,490
That's the only thing.

1277
01:24:16,490 --> 01:24:21,040
Because given two managers, they
have the same expected return,

1278
01:24:21,040 --> 01:24:24,710
but you can still further
differentiate them, right?

1279
01:24:24,710 --> 01:24:25,650
So that's-- yeah.

1280
01:24:25,650 --> 01:24:29,500
And that's what all this
discussion is about.

1281
01:24:29,500 --> 01:24:33,940
But yes, expected return will
drive lot of these decisions.

1282
01:24:33,940 --> 01:24:37,530
If you know one manager's good
expected return, three years

1283
01:24:37,530 --> 01:24:41,122
later, he's going to make 150%.

1284
01:24:41,122 --> 01:24:43,080
You don't really care
what's in between, right?

1285
01:24:43,080 --> 01:24:45,140
You're just going
to ride it through.

1286
01:24:45,140 --> 01:24:48,840
But the problem is you
don't know for sure.

1287
01:24:48,840 --> 01:24:52,287
You will never be sure.

1288
01:24:52,287 --> 01:24:53,870
AUDIENCE: I'd like
to comment on that.

1289
01:24:53,870 --> 01:24:54,220
PROFESSOR: Sure.

1290
01:24:54,220 --> 01:24:55,595
AUDIENCE: What
[INAUDIBLE] looked

1291
01:24:55,595 --> 01:24:58,330
at in simplified
settings, estimating

1292
01:24:58,330 --> 01:25:00,560
returns and volatilities.

1293
01:25:00,560 --> 01:25:04,820
And the problem, the
conclusion for the problem,

1294
01:25:04,820 --> 01:25:09,770
was basically cannot
estimate returns very well,

1295
01:25:09,770 --> 01:25:12,240
even with more data,
over a historical period.

1296
01:25:12,240 --> 01:25:15,950
But you can estimate volatility
much better with more data.

1297
01:25:15,950 --> 01:25:19,060
So there's really an
issue of perhaps luck

1298
01:25:19,060 --> 01:25:23,160
in getting the return estimates
right with different managers,

1299
01:25:23,160 --> 01:25:26,480
which are hard to prove
that there was really

1300
01:25:26,480 --> 01:25:28,580
an expertise behind that.

1301
01:25:28,580 --> 01:25:33,910
Although with volatility, you
can have improved estimates.

1302
01:25:33,910 --> 01:25:37,290
And I think possibly with
a risk parity portfolio,

1303
01:25:37,290 --> 01:25:40,750
those portfolios are focusing
not on return expectations,

1304
01:25:40,750 --> 01:25:43,870
but saying if we're going to
consider different choices

1305
01:25:43,870 --> 01:25:46,560
based on just how
much risk they have

1306
01:25:46,560 --> 01:25:51,400
and equalize that risk, then
the expected return should

1307
01:25:51,400 --> 01:25:54,116
be comparable across
those, perhaps.

1308
01:25:54,116 --> 01:25:55,800
PROFESSOR: Yeah.

1309
01:25:55,800 --> 01:25:57,290
So that highlights
the difficulty

1310
01:25:57,290 --> 01:25:59,840
of forecasting return,
forecasting volatility,

1311
01:25:59,840 --> 01:26:01,440
forecasting correlation.

1312
01:26:01,440 --> 01:26:04,780
So risk parity appears
to be another elegant way

1313
01:26:04,780 --> 01:26:07,800
of proposing the
optimal strategy

1314
01:26:07,800 --> 01:26:10,122
but it has the same problems.

1315
01:26:10,122 --> 01:26:10,782
Yeah?

1316
01:26:10,782 --> 01:26:12,740
AUDIENCE: Actually, I
also wanted to highlight.

1317
01:26:12,740 --> 01:26:14,930
You mentioned the
Kelly criterion,

1318
01:26:14,930 --> 01:26:18,470
which we haven't covered the
theory for that previously.

1319
01:26:18,470 --> 01:26:21,100
But I encourage people
to look into that.

1320
01:26:21,100 --> 01:26:24,840
It deals with issues of
multi-period investments

1321
01:26:24,840 --> 01:26:26,830
as opposed to
single-period investments.

1322
01:26:26,830 --> 01:26:30,945
And most-- all this classical
theory we've been discussing,

1323
01:26:30,945 --> 01:26:34,600
or that I discuss, covers
just a single period analysis,

1324
01:26:34,600 --> 01:26:38,020
which is an oversimplification
of an investment.

1325
01:26:38,020 --> 01:26:41,952
And when you are investing
over multiple periods,

1326
01:26:41,952 --> 01:26:45,790
the Kelly criterion tells you
how to optimally basically

1327
01:26:45,790 --> 01:26:47,780
bet with your bank roll.

1328
01:26:47,780 --> 01:26:53,380
And actually there's an
excellent book, at least

1329
01:26:53,380 --> 01:26:56,120
I like it, called
Fortune's Formula

1330
01:26:56,120 --> 01:26:58,510
that talks about--
[? we already ?]

1331
01:26:58,510 --> 01:27:00,830
said the origins of
options theory in finance.

1332
01:27:00,830 --> 01:27:02,760
But it does get into
the Kelly criterion.

1333
01:27:02,760 --> 01:27:08,780
And there was a rather major
discussion between Shannon,

1334
01:27:08,780 --> 01:27:12,280
a mathematician at MIT, who
advocated applying the Kelly

1335
01:27:12,280 --> 01:27:17,139
criterion, and Paul Samuelson,
one of the major economists.

1336
01:27:17,139 --> 01:27:18,180
PROFESSOR: Also from MIT.

1337
01:27:18,180 --> 01:27:19,790
AUDIENCE: Also from MIT.

1338
01:27:19,790 --> 01:27:23,710
And there was a great
dispute about how you should

1339
01:27:23,710 --> 01:27:26,339
do portfolio optimization.

1340
01:27:26,339 --> 01:27:27,630
PROFESSOR: That's a great book.

1341
01:27:27,630 --> 01:27:30,090
And a lot of
characters in that book

1342
01:27:30,090 --> 01:27:34,840
actually are from MIT--
and Ed Thorp, for example.

1343
01:27:34,840 --> 01:27:41,530
And it's really about people
trying to find the Holy Grail

1344
01:27:41,530 --> 01:27:44,540
magic formula-- not
really to that extent,

1345
01:27:44,540 --> 01:27:47,910
but finding something other
people haven't figured out.

1346
01:27:47,910 --> 01:27:50,900
But it's very
interesting history.

1347
01:27:50,900 --> 01:27:56,830
Big names like Shannon, very
successful in other fields.

1348
01:27:56,830 --> 01:28:01,000
In his later part of his
career and life really devoted

1349
01:28:01,000 --> 01:28:06,915
most of his time to
studying this problem.

1350
01:28:06,915 --> 01:28:08,710
You know Shannon, right?

1351
01:28:08,710 --> 01:28:09,940
Claude Shannon?

1352
01:28:09,940 --> 01:28:15,270
He's the father of
information theory

1353
01:28:15,270 --> 01:28:18,520
and has a lot to do with
the later information age

1354
01:28:18,520 --> 01:28:23,540
invention of computers
and very successful, yeah.

1355
01:28:23,540 --> 01:28:25,980
So anyway, so we'll end
the class right here.

1356
01:28:25,980 --> 01:28:27,810
No homework for today, OK?

1357
01:28:27,810 --> 01:28:31,050
So you just need to-- yeah, OK.

1358
01:28:31,050 --> 01:28:33,100
All right, thank you.