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ANDREW LO:
Well, if you remember last time where we left off, we were talking about risk and return. And
we said that we were going to make the following simplifying assumption, which is that we're
going to assume that investors like expected return, and they do not like risk as measured by
volatility. All right?
And so the way that we depict it graphically is to use a graph where the x-axis is standard
deviation of your entire portfolio, and the y-axis is the expected return of that portfolio. And the
question is, where on this graph can we get to, given the securities that we have access to,
that will maximize our level of happiness. Where happiness, again, is assumed to mean higher
expected rate of return and lower risk, as measured by variance or standard deviation.
So for example, if you take a look at this simple graph and you ask the question, where on the
graph do you want to be, you would like to be always going in the northwest direction. Right?
Because north means higher expected return and west means lower risk. So obviously, if we
could, we'd love to be on this axis all the way, way up. Right? No risk, lots of return. That's an
example of an arbitrage.
And we know that that can't happen very easily because otherwise everybody would be there.
And pretty soon it would wipe out that opportunity. So the question from the portfolio
construction perspective is now a little bit sharper than it was last week when we started down
this path. Now we want to construct a portfolio, we want to take a collection of securities and
weight them in order to be as happy as possible. Meaning, we want to be as northwest as
possible. So let's see how we go about doing that.
One thing we could do is just pick an individual stock. So if you have these four stocks to pick
from, then to go as northwest as possible, you're sort of looking at Merck as, you know, the
extreme. But it's not at all clear whether or not that's something that you really want. Because,
for example, General Motors, while it has a lower expected return than Merck, it does have a
bit of a lower risk. And for some people, that might actually be preferred.
So at this point, we don't have a lot of hard recommendations to provide you with, without any
further analysis. So we're going to do some further analysis today. And the analysis is to ask
the question, all right, what are the properties of mean and variance for a given portfolio, not