Name: Ses 15: Portfolio Theory III & The CAPM and APT I
Uploaded: 2018-08-16T07:35:42.000Z
Duration: 1 h 18 min 34 s
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ANDREW LO: Well, let me pick
up where we left off last time

and give you just a very quick
overview of where we're at now,

because we're on the brink of
a very important set of results

that I think will change
your perspective permanently

Last time, remember, we
looked at this trade-off

you combined a bunch
of different securities

what you get is this
bullet-shaped curve in terms

of the possible trade-offs
between that expected return

and riskiness of various
different portfolios.

So every single dot on
this bullet-shaped curve

corresponds to a specific
portfolio, or weighting,

So now what I want to ask you to
do for the next lecture or two

is to exhibit a little
bit of a split personality

I'm going to ask you to
look at the geometry of risk

and expected return,
but at the same time,

In other words, I want
you to keep in mind how we

different weighted
averages of the securities

So every one of these
points on the bullet

change the risk and
return characteristics

So the example that I gave
after showing you this

curve where I argued that the
upper branch of this bullet

is where any rational
person would want to be.

And by rational, I've
defined that as somebody

who prefers more expected
return to less, and somebody

who prefers less risk to
more, other things equal.

So if you've got those
kind of preferences,

You want to be as north,
sorry, Northwest as possible.

And you would never want to be
down in this lower branch when

you could be in the upper
branch because you'd

have a higher expected return
for the same level of risk.

where you've got three
stocks in your universe.

And these are the parameters
that we've estimated

and we've already raised
that question, of how stable

Are they really parameters,
or do they change over time.

And I told you, in reality of
course, they change over time.

But for now, let's play
the game and assume

and see what we can do
with those parameters.

So with the means, the
standard deviations,

and most importantly,
the covariance matrix--

So this is the matrix of
variances and covariances--

The way we do it is of
course, to recognize

that the expected
return of the portfolio

is just a weighted average
of the expected returns

of the component securities,
where the weights are

is how we allocate
the 100% of our wealth

to be given by a somewhat more
complicated expression where

you have the individual
security variances entering here

entering in that same
equation for that variance

And when we put these
two equations together,

the mean and the variance,
and we take the square root

the variance to get
the standard deviation,

This is the curve, the
bullet-shaped curve,

that we generate just
from three securities,

that I pointed out a
couple of things that was

One is that unlike the two asset
example, where when you start

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Ses 15: Portfolio Theory III & The CAPM and APT I

perspective

assume

individual

negative