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visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: What I
want to do today is to continue where
we left off last time in talking about the empirical
properties of stocks and bonds. I want you to
develop an intuition for how to think about markets. We've already done that over the
course of the last few lectures by looking at market
prices and understanding how to price them,
but I'd like you to get some kind of a
historical perspective now on specific asset classes. Because we're going to be
relying on market prices to make inferences about
other kinds of securities and other decisions
you're going to make. As I told you at the very
beginning of the course, we're going to rely on
markets for information, because it's the wisdom of
crowds that really gets us the information we
need in order to make good financial decisions. So I want to begin that
process of now giving you the intuition about
the wisdom of crowds by looking at the historical
performance of stocks and bonds. And then we're going
to talk about how to quantify risk
more analytically and put it all together in the
very basics of modern portfolio theory. So I want to start by
asking the question, first of all, what characterizes
US equity returns? How do we get our arms around
the behavior of that asset class? And the way I'm
going to do that is to give you some
performance statistics about the volatility, about
the average return, about how predictable they are,
and also patterns of returns across
different kinds of stocks. So we're going to look at
some empirical anomalies before actually turning to
the analytical work of trying to figure out how to make
sense of this from a more formal mathematical framework. Before I do that, let me ask
you to think about the following question, which is, if you are
designing a market for stocks, what properties would you
want that market to have? And I'm going to
argue that there are a few properties
that all of us, I think, can recognize as being good
properties for stock prices. So the first is that
stock market prices are random and unpredictable. Now, that might seem a
little counterintuitive, and certainly I think
you would acknowledge that over the last
several weeks markets have been supremely unpredictable. And that doesn't feel so good. It doesn't seem like
that's a good thing. But in a minute,
I'm going to try to make that a little
bit more clear by looking at the alternative
of predictable-- or unpredictable,
which is predictable. So let me come
back to that point. The second property that
I think you'll agree is a reasonable one
for us to expect is that prices should react
quickly to new information. It should adjust
to new information really without
any kind of delay. And finally, we'd like to
see that investors shouldn't be able to earn abnormal returns
after you adjust for risk. So in other words,
once risk adjustment is taken into account,
there shouldn't be any additional
return left over. That's what we think of as
a well-functioning market. Another way of putting
it is that a market is highly competitive. It's hard to make
money in those markets. Now, they may not be markets
that you would enjoy trading in, but that's not the question. The question is, what
would be a good market, an efficient market? So let me talk about
predictability for a minute, because I said that it seems
a little counterintuitive that a good market is one
that's not predictable. So let's pretend that
this is the stock market. This is the S&P 500. That looks nice-- a
nice, regular curve. Anybody come up with
a prediction for this? How would you go about
predicting the behavior of this kind of a stock market? What's that? STUDENT: Cyclical. PROFESSOR: Cyclical. What kind of curve
would you fit to this? STUDENT: Sine wave. PROFESSOR: Yeah, sine wave. In fact, that's how
I generated this. I used a sine wave, and
then I add a little noise. Now, why might this not be
a good model for a market? If this were the stock
market, what would you do? Yeah? STUDENT: Everybody
would buy on the low and sell them high
[INAUDIBLE] the other end. PROFESSOR: Exactly. After a few of these cycles,
you sort of get the idea. And if you're down here, you're
going to think, well, gee, I think it's likely
to go back up so I'm going to buy a ton over here. And when you get right up there,
you'll say, gee, you know, I think it's time
for me to sell a ton. And you don't have to go
through too many of these before you get richer
than your wildest dreams. Yeah? STUDENT: I would think that
[INAUDIBLE] regular market like that is not
true, because as soon as you want it to raise,
it's going to collapse at 50, 10 points below. PROFESSOR: That's exactly right. So as soon as you
start doing this, as soon as you try to do this,
what happens to the pattern? The pattern
disappears-- exactly. You see, this is
one of the reasons why finance is a lot more
challenging than physics. In physics, if you try to drop
a ball in a gravitational field, it won't change its
mind and say gee, now I'm going to change the
gravitational constant on you just because you're testing me. But in financial
markets, the moment you try to take advantage
of this pattern, the pattern changes. In fact, the more
you try to take advantage of it, the more
quickly the pattern changes. In fact, if you do this a lot-- if there are a lot of people
trying to predict patterns-- then you know what you get? You get no pattern. You get randomness. That's the idea behind an
efficient market being random. If it were not random,
then that means that there aren't
enough people who are bothering to try
to forecast the price and incorporate
information into the price. Now, I said two things that
at first seemed different, but in fact they're opposite
sides of the same coin. When you are forecasting
market prices, you know what you're doing? You're actually
helping markets become more efficient by incorporating
information into that price. How do you do that? Well, if, for example,
you think that having a presidential election
will cause volatility to decline, then if
you know that there's a presidential
election coming up, you will start trading in a way
that will ultimately be betting on volatility declining. As you start that trading, you
force that volatility index to go down. So the fact that
you've got information and you think you
can forecast prices, when you use the
information, what does it mean to
use the information when you buy or sell
securities on the basis of that information? Then the price of the
security ultimately reflects the information, right? So an efficient market is one
where you don't have this. You don't have a very
strong predictability. If it is strongly
predictable, then most likely either the market is rigged,
or there aren't enough people that are trading in order to
make prices fully reflective of all available information. Now, this is the way
markets really look. These are random
walks with drift, drift meaning there's a positive
trend or, in some cases, a negative trend. But otherwise, it's
random around that trend. So you can't really
easily forecast it. And you can see that
prices go up, they go down. There are long periods
where they go up, but there are also, for other
stocks, long periods where they go down. And you don't know what's
going to happen next. This is a sign of a
very efficient market. A while ago, there
was an academic study that was done to try
to test for efficiency, and one of the tests was
that if the underlying price series was not very
volatile, that was considered an efficient market. But it turned out
that was roundly criticized because of the point
that just because a market is not volatile, it doesn't
mean that it's working well. And an example
was, at the time-- this was, like, 20 or 30 years
ago-- the Chinese stock market, the Shanghai Stock Exchange. It was a relatively young
market, and at that time, there were only two
stocks that traded on it. It was the National Railroad
Company and the Bank of China. And at that time,
which is, again, about 15 or 20 years
ago, it was considered unpatriotic to sell the
security if you had bought it. So you could buy it, but you
weren't allowed to sell it. And so the price went
way up and up and up, and that's not an example
of an efficient market. It was not at all volatile. But as a result, there
was no real information reflected in that price. Yeah? STUDENT: India is talking
about getting out. It looks like somebody's doing
one of those roller coaster rides that goes up and
down and up and down. So is volatility a sign of [?
inefficient ?] [INAUDIBLE]? PROFESSOR: Well, it's not
volatility, per se, but rather the combination of the
predictability per unit volatility. That's really what
you want to focus on. We're going to come back to that
when we talk about portfolio theory and look at this
trade-off between risk and expected return. But no, I wouldn't say that the
Indian market is inefficient. It's undergoing some
pretty significant changes, as is the US and
as is the world. But that's because
the global economy is contracting as
we know it because of this financial crisis. So I wouldn't characterize it
as inefficient at this point, but that remains to be seen. Yeah? STUDENT: [INAUDIBLE] down
the road [INAUDIBLE] market [INAUDIBLE]? PROFESSOR: There isn't any
hard and fast rule, no. But if you take a look
at the trade-off of risk to reward, in other
words that ratio of expected return
to volatility, you can come up
with rules of thumb that will give you a sense
of whether or not a market is efficient or inefficient. So we're going to
come back to that. In fact, we'll look at
that in just a minute. Let me turn to some
data now, and then we can see exactly what those
trade-offs look like. Now, what's going to be
interesting about this part of the talk is that when I
tell you about these numbers, these numbers are
based upon data from I think it was 1946 to 2001. In fact, a lot of the data
that has been collected over the last year is very,
very different from this, so it will be interesting
to sort of compare the two. So there are four
empirical facts that I want you to take with
you about the US stock market. The first is that interest
rates, in general, have been slightly positive
on average, but not by much. In other words, the
real interest rate, the nominal interest rate
minus inflation rate, has been pretty low over
the course of history. So the first fact
is that real rates have been slightly positive. So you can see, for example,
the average rate of return for the one-year T-bill
is about 38 basis points on a monthly basis. This is monthly. I haven't annualized it. But inflation over
that same period is about 32 basis points. So when you subtract
the two, you're going to get six basis
points on a monthly basis as the real rate of interest. On the other hand, if you take
a look at the stock market, which is represented
by VW stock index-- VW doesn't mean
Volkswagen. VW stands for the value weighted index. It's an index of all
the stocks on the NYSE, Amex, and NASDAQ
weighted according to their outstanding
market capitalization. And you can see that
the valuated stock market over this period
is about 1% per month. The equal weighted
stock market, EW, is a little bit higher, 1.18. And Motorola over this period
had an expected rate of return of about 1.66% per month. So the return has been
higher for these indexes. And if you want to get a
sense of why that might be, take a look at the
next column, which is the standard deviation. This, remember, is a measure of
the riskiness of the security. It's a measure of
the fluctuations. And if you take a look
at the equal weighted and the valuated,
the volatility is-- they're both a lot
higher than for T-bills. So this is one of the reasons
we got the idea in finance that there's a
risk-reward trade-off. The more risky, the higher
the expected rate of return. And if you look at Motorola,
the riskiness of Motorola is much larger than that of
any of the stock indexes. Instead of a 5% monthly
standard deviation, you're looking at
double, or 10%, the monthly standard deviation. But look at the rate of return. The rate of return is
commensurately higher. Yeah, Remi? STUDENT: Professor, why
[INAUDIBLE] standard deviation greater than zero? Isn't that [INAUDIBLE]? PROFESSOR: Oh, because it
fluctuates from month to month. So the idea is if you're buying
a T-bill and you're holding it, it still has price fluctuation. The other thing that
I want you to see is something along the lines
of the minimum and the maximum. This is another
way of representing the riskiness of the security. So T-bills are bounded
between 0.03 and 1.34 in terms of their return-- very narrow band. Treasury notes, which
are 10-year instruments, obviously are going to be
swinging around much more, more than a one year T-bill. So the longer the maturity,
the longer the duration, the riskier is the instrument. But if you take a look
at the valuated return and the equal weighted
return and then Motorola, you can see progressively
more and more risk involved in these kinds of securities. Now, if you look at their
compound growth rates, you get what you pay for,
in the sense that you're looking at T-bills down here. So $1 invested in
one of these guys will give you maybe
$10 at the end of 2001, but you're looking at a
much, much larger return for either the valuated
or equal weighted indexes. More risk, more
expected return-- that's the message that you get
from looking at the basic data here. Now, that's just to give
you a sense of where interest rates have been. I think we discussed this
when we did fixed income. Interest rates have really
been all over the map. There was a point
in our history, not that long ago, where
the short-term interest rate, the one year T-bill,
was something like 16% to 17% per year. That's the one-year T-bill. It's astonishing. But that was a
period where there was a large amount of
inflation in the United States. On the other hand, if you take a
look at the more recent period, interest rates have
been extremely low, and that's part of the reason
we're in a credit crisis, is because credit is very cheap. So you can get yourself
into a lot of trouble when it's relatively
easy for you to borrow, and it doesn't cost you that
much in terms of the payments. Now, let me show you what
the total returns look like for these
different asset classes. By total returns, I mean if you
bought one of these instruments and you held it
a month at a time and you computed the return
for holding that instrument. So for a bond, it includes
whatever coupons get paid, plus the price fluctuations. It's the total return. For stocks, it'll include
the dividends that got paid as well as the
price fluctuations. And I'm going to do this
on the exact same scale, from minus 25% to 25%. So these are monthly
returns now that I'm plotting from 1946 to 2001. And so you can see that
the total return for the US 10-year bond actually has
different periods where, in some cases, it's not very
risky but in other cases it bounces around a great deal. When there's a fair amount
of interest rate uncertainty, you get a lot of volatility,
but when markets are not moving around that much
on the interest rate side, you get periods that
are relatively calm. Yes? STUDENT: In the previous
slide, that interest rate are the yield to
maturities, right? PROFESSOR: Yeah, that's right. That's right. Correct. These are yields to maturity. These are total returns, though. These are what you
get as an investor. This is what you get if you
hold a particular security to maturity. Basically, on a given day,
you will get these spot rates. You have a question? STUDENT: [INAUDIBLE] 10 year. So in '81 and '82,
you could buy any bond from the year '86 [INAUDIBLE]. PROFESSOR: Yeah. STUDENT: So [INAUDIBLE] that
incorporates future [INAUDIBLE] interest rates, right? PROFESSOR: Well,
and also inflation. STUDENT: And that inflation--
was it people thinking that inflation was going to be
[INAUDIBLE] 10% of the year, the 10 years out? PROFESSOR: Either
that, or they felt that that, plus whatever
interest rate expectations, was going to be
what you're going to get over a 10-year period. Yep. That's right. STUDENT: And mentally, people
think that stock [INAUDIBLE] [? upon ?] [? death.
?] [INAUDIBLE]. PROFESSOR: Apparently. And there was a time, in fact,
when the stock market did yield that for quite a bit of time. Absolutely. On the other hand, let me
turn it around and ask you, now that interest rates are at-- I don't know, the 10-year I
think is at-- or the 30 year is at 4.17 this morning-- do you think for the
next 40 years or 30 years that treasury bills are only
going to return 4% a year? Is that realistic? I mean, it's not so
easy to say, is it? When you're in the midst of
it, it's not so easy to say. Based upon historical
evidence, it seems crazy to think
that we could possibly be in such a low interest rate
environment over the next 30 years, especially given
that we're printing money like it's going
out of style now. And we're going to be doing that
over the next couple of years. We've got to, because
somebody's got to pay for all of
these rescue packages. And so we basically
have to engage in some kind of inflationary
monetary and fiscal policy. But it's still saying
4.17 as of this morning. So the market does the best
it can, given the data, but it's hard to forecast. And we just said at the
beginning of this class that it better be
hard to forecast, because if it's not
hard to forecast, then something's wrong. Then it means that
it's not reflecting all available information. Yeah? STUDENT: When you showed that
graph in the previous slide of the stocks going way up,
I'm wondering how much of that is due to the fact that this
was just a really good period of the United States and if
you compare to other countries at other times. PROFESSOR: Yeah, that
is definitely a factor. So I'm not trying to
explain the numbers, and I'm not trying
to justify them. You're absolutely right. This is a very special country
in a very special time. So you can either thank your
good fortune that you're here, or you can argue that, well,
it's not going to persist and time to move to wherever. But I don't know. I don't know which that is. But it is very unusual. If you look at other
countries, there are other countries that
are having difficulties during this time period, but
there are other countries that are growing even faster. If you look at China
over the last 10 years, the growth rate of
the Chinese economy is double to triple
what the US economy. Now, it was a smaller
economy, but still over an extended
period of time it's got tremendous growth rate. So that really is
the challenge, is to try to understand
what's going on in the context of where we're
living and how we're living. So let me go through and
show you some more numbers, and then we can talk about
some of the interpretations. So this is the total
return for the US 10-year. You've get a sense
of the scale-- minus 25 to 25. Now, this is the
return of the US stock market during that same
period using that same scale-- more risky. So you can see the
difference in fluctuations. And if this weren't
exciting enough for you, this is Motorola. And there are many
stocks like Motorola. So when you invest in
an individual stock, you're getting not just the
fluctuations of the economy, but you're getting
the fluctuations that affect that specific company. So you should expect, if
you're taking on more risk, that you're going to be getting
a reward for these kinds of incredible bouncing around. And in fact, you do. The average return of
Motorola is quite a bit higher than that of the market. Now let me show you a little
bit about predictability. We talked about a market
that's random as one that is a good or efficient market. This plots the return
today versus tomorrow, or yesterday versus today if
you want to think about that-- pairs of returns for the
aggregate stock market. And this is done
on a daily basis. Now, if you look at it on
a monthly basis for the S&P 500 from 1926 to 1997,
you've got something that also looks kind of random-- so not much predictability here,
not much predictability there. But suppose we were to graph
the return of General Motors against the S&P 500. Well, now, all of a sudden,
it looks like there's a little bit of a pattern-- not totally random. Sort of looks like there
is kind of a line that goes through that scatter of points. There is a
relationship on a given day between General Motors
and the broad market index. But over the course of
two days or two months, there's very little
predictability. Now let me talk
about volatility. Your question? STUDENT: So on the last graph,
GM is included in there, right? PROFESSOR: That's right. GM is one of the
stocks in the S&P 500. STUDENT: So would you still
see that relationship if it was everything but GM in the S&P? PROFESSOR: Oh, absolutely. In other words, it's
not any one stock that gives this random
scatter of points. In other words, this
random scatter of points is really all 500 stocks
put into a portfolio. But remember, we're asking
a different question. This is a question about the
relationship between the S&P 500 last month
versus this month. There's no real relationship. This, on the other
hand, is a question about the relationship
between S&P this month and GM this month,
the same month. Now, you're right that S&P has
GM as one of the components, but it's only one of them. If it weren't in there, you
would actually still see this kind of a relationship. Yeah? STUDENT: On slide
16, you showed us the one-year and
10-year interest rate. What does it mean when the
two figures cross each other? PROFESSOR: There's no
particular significance. It just means that that
one-year rate happens to be identical to
the 10-year rate, so people are just assuming that
that rate is going to continue over a period of time. So there's no particular
economic significance to when they cross. These are all
annualized, remember. So you're asking the question,
over a 10-year period what is the average
interest rate you're going to get paid by
the US Government, versus over a one
year period what is the interest rate you're
going to get paid by the US Government? That's all. Now let me talk
about volatility. These are monthly estimates
of US Stock Market daily volatility
from 1926 to 1997. So every month I've
got 20 days or 21 days. I'm going to take
the daily returns and calculate the
standard deviation for those daily returns, and I
plot it and it looks like this. Now, these are monthly, so
if you want to annualize it you have to multiply it
by the square root of 12 to get the annualized
volatility. But the point of this is that
there are periods of time where the market is
extremely volatile, and there are periods of time
where it's relatively quiet. And if I would have extended
this to the most recent period, you would see that within
the last several weeks we had a spike that was about
as big as this spike over here. Anybody know what this spike is? You can sort of guess. Yeah, October 1987. That was the big stock
market crash that occurred during that month. Volatility shot way up during
that month-- lots of risk. And right now we're
in a situation where there is lots of risk as well. Now, I'm going to just
conclude my overview with a few interesting anomalies
that I want to tease you with to get you to think
a little bit more carefully about stock markets. What I'm going to
show you are just a bunch of factoids, factoids
meaning that they are empirical facts in the data. But if you change some of
the assumptions or the sample that you use, these
facts could change. So these are not
universal constants that, for some theoretical
reason, has to be true. This is just
properties of the data. What I've done here is
to take all the stocks in the NYSE, Amex, and
NASDAQ from 1964 to 2004. And on a monthly
basis, I'm going to rank them by
market capitalization, break them up into 10 equal
numbers of securities, and then average the
returns in those deciles and then compute it
over time and then average those decile returns. That sounds a
little complicated, but pretty straightforward. Let me tell you, for example,
what this means here. This particular bin
over here is the bin of all stocks that
have the largest market capitalizations among all
of the stocks in my sample. I've divided them up
into 10 equal groups. This is the largest
10th, and I'm going to compute the
returns monthly for that bin and then average that
across my entire sample. And I get an annual
return of close to 10%. This is annualized now. It's not monthly-- annualized. If I now compute that
same rate of return for the smallest
stocks, the stocks that are the smallest
part of my sample-- that's down here-- I get a return of something
like 15% per year. 15% versus 10%, that's
a huge difference. That's like a 6 percentage
point difference. No, it's more like 9%
versus 15%-plus something. Five percentage points,
500 basis points a year-- that's the gap between small
stocks and large stocks. This is known as the size
effect or the size premium. Small stocks seem to do
better than large stocks. Now, there are lots of stories
you could tell about why. I'm not going to
tell those stories, but I just want you
to see the data. Now, you want to know
what's weird about this? What's weird about
this picture is that I'm going to change
the sample ever so slightly. What I'm going to
do is I'm going to compute this graph only
for the month of January and then for all the other
months outside of January. And I'll show you what happens. The yellow bars-- those
are the January returns, and the blue bars are all
of the non-January returns. So I don't really think there's
that much of a size effect once you delete the Januarys. You get a little bit of a
difference between the biggest and the smallest,
but the difference that we're talking
about now is very small. But look at the January effect. That's big. And it turns out that this
seems to be a phenomenon that has become a little bit
less pronounced recently, but for many years it was
quite strong and reliable. And people actually traded
on this particular pattern, buying stocks in January,
holding them in December, and holding them until January,
or doing a spread where you basically tried to go long-- small stocks in December
and large stocks in December and hold that spread. And then it widened. So this is a really
puzzling anomaly. Again, you can come up
with explanations for this. I'm not going to tell
you what they are. You can think about them and
possibly even trade on them over the next month or so. Now, the second anomaly that
I want you to be aware of-- and this, depending
on who you speak to, may not be considered
an anomaly. For example, Warren
Buffett would call this genius and fact. This is the value premium. What this suggests is that
there are certain stocks that, for whatever reason, are
just simply undervalued systematically--
or, alternatively, other stocks that are
systematically overvalued. The value premium is where
you take the same universe of stocks that I showed
you before, but instead of sorting according to
market capitalization, you sort it according to
another characteristic. And the characteristic is
the price-equity ratio, or the reverse of that is
what you usually hear about, book-to-market-- book value divided
by market value. Now, you all know what
that difference is by now. Book value is the
value of the company as it was initially formed
and as it accrues either cash or profitability, but based
upon its accounting book value. Whereas the market value
is what the market thinks the company is worth. And in many cases,
with technology stocks and other growth
stocks, the price gets way, way ahead of the
value of the company's assets. And so those are
situations where you've got a very large
price-to-book ratio. If you have a very large
price-to-book ratio, that means that
you're going to be on the right hand
of this spectrum. And that says,
according to this chart, that the expected rate of
return is generally pretty low. On the other hand, low
book-to-market or high book-to-price-- sorry, the other way around-- high book-to-market,
low price-to-book is on the left-hand side. These are what Warren
Buffett and Graham and Dodd would call "value stocks." These are stocks where you've
got lots of good book value, but somehow the market
doesn't really appreciate it. And so the price is low
relative to the book value. In other words, the
price-to-book ratio is low. And look at the returns there. The value premium
is the difference between the high price-to-book
and the low price-to-book, and you're looking at a premium
of about 600 to 700 basis points, on an annualized basis. That's a big difference,
because in both of these bins it turns out the risks are
actually roughly comparable. So it's not as if the
stocks on the left are way more risky than
the stocks on the right. That actually is true of the
market capitalization effect. Small stocks actually
have higher volatility than large stocks. But that's not true
of value and growth. So that's another puzzle, or,
depending on who you talk to, this is a way to invest. Momentum-- this is something
that academics discovered maybe 10 or 15 years ago, which
is also really anomalous. By momentum, we mean
simply last year's return. If that's positive, does it
tend to persist over the next 12 months? So the stocks with low
momentum on the left-hand side seem to do worse than the
stocks that have high momentum. So the momentum effect
seems to be really strong. And again, look at
that difference. That difference is something
on the order of a 15% spread, if not more. It's a very, very big spread. So this might lead you to
try to construct a trading strategy based upon this. And there are a bunch
of other anomalies that have been reported in
the academic literature. In fact, for a while,
certain academic journals were accused of never meeting an
anomaly that they didn't love, because they just kept
publishing one after another. And in a way, you have to be
a bit skeptical about this, because there are so many
different ways of looking at stocks, so many
characteristics. And you know that in a sample
of 100 random variables, 5% of them are going to be
statistically significant, even if none of them are in
terms of being significantly different from zero. So you've got to take these
anomalies with a grain of salt, but what I've
presented to you are the ones that seem
to be the most persistent, the ones that
people spin stories about, the ones that people
construct mutual funds around. And so you'll have to think a
little bit about whether or not you believe any of
these anomalies, but I wanted to make you
aware that they're there. And if you take
15433, investments, you'd actually end up spending
a fair bit of time digging through each one of these
to see whether or not there's something in
there that you could use for investment purposes. The last thing I want to mention
with this introductory lecture is mutual funds. These anomalies were
obviously very, very exciting from the perspective of
active portfolio management, because once you identify
one of these anomalies you could argue, I want
to take advantage of it. Of course, then the argument
that was raised earlier comes into play. If you're going to
take advantage of it, isn't that going to disappear? And the answer is, in
general, yes, it will, but it may take a while. And along the way,
you'll do quite well. So the question was
asked, well, if that's the case, if there are
all these anomalies and if you can take
advantage of them, well, then mutual
fund managers ought to be able to outperform
simple buy and hold strategies. Because they can take
advantage of these anomalies. If you do a histogram
of mutual fund returns that are in excess
of their risks-- so if you make some kind
of a simple risk adjustment and you look at the mutual
funds' additional value added above and beyond those
risk adjustments-- those excess returns are
given by this histogram. For data from 1972 to 1991,
the histogram of excess returns has basically this
kind of a distribution. You've got some positives,
you've got some negatives, you've got more
negatives than positives, and on average it's
actually less than zero. Mutual funds net of fees are
actually losing money for you on average. That was the conclusion by these
academics as of a few years ago. Yeah? STUDENT: In defense
of the big ones, isn't part of the
purpose to lower your risk of your portfolio
to lower the volatility? For example, you might be able
to get the return plus zero. But then the next
year you might be able to get the
return minus five. Well, I think
mutual fund managers aim to get you steady terms
that are [? being ?] exactly the term, plus zero. PROFESSOR: Well, so first of
all, that's not necessarily the objective of
every mutual fund right there are mutual
funds that are not trying to give you
lower volatility, but rather they're
trying to give you access to broader investment
vehicles and instruments. So the original index
fund that was set up by Wells Fargo in the 1970s-- the purpose was to
allow an investor to get access to 100 securities
without having to actually go out and buy 100 securities. STUDENT: Thereby
diversifying, right? PROFESSOR: Right,
by diversifying. But it doesn't lower
the volatility, except through diversification. So you're right. Diversification will lower
it, versus buying Motorola. But the question
is, how does this do versus buying 100
stocks, or rather buying a mutual fund like
Vanguard, the Vanguard 500 Index Trust, where
you're not trying to outperform the market you're
trying to match the market? And the argument is that the
mutual funds that have been trying to beat the market,
on average they don't. They don't beat the market. Some of them do;
some of them don't. But as a group, they
don't add any extra value. That's the argument
that was made. Now, that's not to say that
there aren't good mutual funds and there aren't
bad mutual funds. There may be. So somewhere in here is
Peter Lynch's Magellan Fund-- terrific fund, very
talented portfolio manager. But on the other
hand, if you can't tell in advance who is going
to be the next Peter Lynch and who's going to be the next-- I don't know who; I won't
cast any aspersions. But if you can't tell in
advance who's going to do bad, then you're essentially throwing
a dart at this histogram. You may be lucky and you'll
get on the right side, or you may be unlucky
and hit the left side. But on average, you
should do better by putting your money
in a passive index fund. Now, that's the
argument of Vanguard and all of the passive
investment vehicles. I'm not going to take a
stand on that, because we're going to come back and
talk a bit about that at the end of the course. And then as part of
investments, you're going to re-look into that. I just want you to get a feeling
for the data that's out there. And the data that's
out there says it's very hard to
tell whether or not mutual funds, as an aggregate,
are adding any value. By the way, you realize
that there are actually more mutual funds out there
than there are stocks. You know that? Yeah, there are about
10,000 mutual funds. There are about 8,000
stocks out there, including the penny stocks
and pink sheet stocks. There are probably only
4,000 or 5,000 stocks that you would actually ever
invest in as a retail investor yourself. And so the number
of mutual funds far exceeds the
number of stocks. The way that mutual
fund managers justify that is by
saying, look, there are 31 flavors of
Baskin Robbins and so we want to provide
investors with lots of different possibilities. Not everybody wants the S&P 500. Some people want the S&P 100. Some people want the S&P 250. Some people want the S&P 385. And so I'm going to construct a
fund for every clientele that's out there. That's a legitimate
argument, as long as investors understand that
when you buy into a mutual fund you're buying something that
may cost you more than if you try to do this on your own. So the key points that
I want you to take away is that the average return on
US stocks from 1926 to 2004 was 11.2%. Now that's considered the
good old days, so no more. The average risk
premium was about 8%-- again, the good old days. That's probably not going
to happen for a while. Stocks are quite risky. Standard deviation of returns
for the market is about 16% annually. That isn't risky anymore. That, again, is
the good old days. The market today, using the
implied volatility of the VIX index, the implied volatility
of S&P at the money options, was about 49%. So the annual forward-looking
S&P 500 stock market volatility right now is about 49%, which
by the way is down from 80% a couple of weeks ago. So as I predicted,
volatility was going to decline once
the election was clear. That eliminated a
piece of uncertainty, but there is still
a remaining piece, which is what's going to
happen to our economy. That's why the volatility is at
49% versus a historical average of 16% to 20%. Stocks on an individual
basis are clearly much more risky than as a group,
so you're absolutely right, Remi, that when you
put it into a portfolio you reduce the risk. And so the S&P 500 is a lot
less risky than Motorola. Also, stocks tend to
move together over time. Over time, from one
day to the next, there is very
little relationship, but on a given day stocks
tend to move together in groups, General
Motors seemingly to be correlated with the
S&P as well as other stocks. And obviously, market
volatility changes over time, and
financial ratios that can be used to create these
different kinds of bins for sorting stocks and
constructing these anomalies-- they actually do seem to have
some kind of predictive value. Why, we don't know
in many cases, but the anomalies are there. And so that's something
to be aware of. Other questions? Now that you have a
feel for the data, I want to take a step
back and ask the question, how do we make use
of this information in a way that can help
the typical investor and also help the
individual trying to decide on a corporate
financial decision? How do we use these kinds
of empirical insights in our theory? So to do that, I'm going to
turn now to lectures 13 and 14 and focus on how to measure
risk and return in a more systematic way and
then incorporate that into portfolios. So we're going to talk
a bit about motivating the idea behind
portfolio analysis and then use some of
the theoretical concepts that we introduced last
time, like mean, variance, and covariances and use
it to piece together a good portfolio. So the motivation for what
we're trying to do now is to figure out how
to combine securities into a group that will
have attractive properties. If you're an investor or a
corporate financial manager, this is a decision that you've
got to do almost every day. For example, all of you have
already made that decision today, whether you
know it or not. Because if you didn't do
anything between yesterday and today to rebalance
your portfolio, you've made an affirmative
decision to let the debt ride. Let it ride. You're going to be
taking another roll of the dice at 4:00
today, and let's hope it turns out well for you. But you've made a decision. Every day you don't do
anything with your portfolio, you are making a decision. So what we want to
do is to see if we can think about making that
decision a little bit more systematically. To do that, I want to define
what I mean by a portfolio. So the definition,
in very simple terms, is just a specific weighting or
combination of securities, such that the weights add up to one. It's just a way to
divide up the pie. If you've got a certain
amount of wealth, you're going to allocate it
among different securities into a portfolio. A portfolio is defined as a set
of weights of those securities where the weights add up to one. Now, this is sort
of the framework that we use in terms
of the notation. So omega, the
Greek letter omega, when you write it
as a vector, it denotes the set of weights
for your portfolio. So if you've got n securities,
then this vector omega, which is equal to omega one,
comma, omega two, dot, dot, dot, omega n, that
is a portfolio. And if you want to be clear
about how to define it, it's simply the number
of shares of security I multiplied by
that price, divided by the sum of all of the
values of your securities in your entire collection. Any questions about this? Very basic stuff, but
it's important to get it right upfront. Now, by the way,
the number of shares NI, I'm going to let
that be a real number, meaning it could be zero, it
could be five, it could be 500, it could be minus 200. Minus 200 means that
you have short-sold 200 shares of that security. So these weights,
they all sum to one, but they don't have to
be all non-negative. Some of these weights
could be zero. Some of these weights
could be negative. If some of these weights
are negative, then what do you know about
some of the other weights? Well, yes, they have to
be positive because they have to add up to one. But tell me more
about the weights. STUDENT: Greater than one. PROFESSOR: Right. Because in order
for it to add up to one, if some of these
things are less than zero, then some of these other things
are greater than one. What does it mean for a
security to be greater than one, a weight to be greater than one? Does that make sense? What's the interpretation? Yeah, Lucas? STUDENT: Does it mean
you're leveraged? PROFESSOR: It means
that you're leveraged, that's right-- leveraged
meaning that you're buying more than you have money. Where are you getting
that money from? You're basically getting
a loan, but who's loaning you the money? Andy? STUDENT: Well, the
stocks that you sold short gave
you the extra cash that you can buy long stock. PROFESSOR: That's right. So nobody loaned you money, but
somebody loaned you something. They loaned you a stock. So this simple little
framework already has given us one
interesting insight, which is that when we short sell
a stock and buy another one, we're actually getting
a loan from somebody who's lending the stock
to us that we've sold. We've taken that cash and we're
putting it into another stock. So we're getting a
loan of one security and turning around
and using those funds to buy another security. That's a new transaction
as far as we're concerned, but it's one that's going to be
very important in how we think about portfolio construction. If you didn't understand
that, go back and take a look at these nodes and try to
work out a numerical example for yourself. And if you still don't
understand it, ask again next time or ask the
TA during recitation. It is a very important point. Now, there is a
case that I'm not going to talk
about in this class where the weights can
actually sum to zero. I don't want to talk about
that because that's a much more complex situation,
where basically you have a portfolio with no money down. This is sort of like
the arbitrage portfolios that I described to you
in earlier settings. We're not going to analyze
that in the context of stocks, but there are a
very large number of hedge fund strategies
that are based upon just these portfolios. And so this will be a
very important concept that you'll cover in
433, but we're not going to talk about it now. I just want to make
you aware of that, that you can have the weights
summing not to one but actually to zero. Now, the assumption that
I'm making implicitly is that the
portfolio weights are summarizing everything there is
to know about your investment. So once you know the
portfolio weights and you know the
stocks, then you know what your
portfolio is about. So as an example, you
have an investment account with $100,000, and you've
got three stocks in there-- 200 shares of A, 1,000
shares of B, 700 shares of C, so that your portfolio is
summarized by the weights 10%, 60%, and 30%. So from now on, we're not
going to worry about prices and shares anymore. We're going to focus
just on portfolio weights and the returns of your
securities multiplied by those weights. It's just simplification. Yeah, Megan? STUDENT: I'm just wondering what
you think about a 130-30 type portfolio in the context
of the last slide. PROFESSOR: Yeah, sure. So you're already
asking a question that's quite a bit more advanced
than what we're going to cover. What's a 130-30 portfolio? Can you explain
that, or have you just heard that in the news? STUDENT: I understand, I
guess, the basic concept, which is you're 130%
long and are 30% short, so you're headed back to
a net exposure of zero. PROFESSOR: Right. That's right, exactly. So let me describe
a product that's out there that's been developed
just over the last few years. It's called a 130-30
portfolio, and what 130-30 stands for is 130%
long and 30% short. Now, you can have
a 120-20 portfolio or a 180-80 portfolio. But the idea is that you have
weights that add up to 100%, but the long positions
are no greater than 130%. And the short positions
are no less than minus 30%. Now, the reason that this is an
interesting product is that-- I have to give you a
little bit of history. This is getting a
little out of our area, but I'll give you a
preview of Investments 433. Typically, when
institutional investors like pension funds or mutual
funds, when they invest, they are not allowed
to short sell. This has nothing
to do with the SEC. It has nothing to do with law. It has to do with the
particular entities that are investing, because
short selling was viewed way back as being a very risky
endeavor because you could lose everything and more. There's unlimited
amounts that you could lose because your short
selling a stock can go way up and you could lose
tremendous amounts. So mutual funds
were originally not allowed to short sell at all. So for a mutual fund,
the portfolio weights were restricted to
be non-negative, and certain pension funds were
not allowed to short sell. So if you were a pension
plan or a state university and you gave your money
to investment manager xyz, that investment manager would
be required not to short sell for your portfolio. It was discovered over
the last several years that this kind of
constraint artificially dampened the return
of a portfolio-- not surprisingly, because
when the market goes down, if you're long-only
you're going down with it. But if you have a
short position, then at least the shorts would
be able to buffer some of the losses on the long side. So institutions have started
getting more and more sophisticated,
thanks to hedge funds pushing them into this
area because, of course, hedge funds can do anything. They can short, they can long,
they can go sideways, whatever. So hedge funds led
the pack by saying, we're going to
actually short sell some of your long-only
portfolio to help you get a little bit of
extra return on the downside. And so pretty soon,
institutional investors said, well, I actually
like the idea of you short selling a little bit but I don't
want you to do it too much. Because I don't really
know what the risks are. I'm new to this. I don't want to get the
risks out of control, so I'm going to limit how
much you can short sell. The limit of how much
you can short sell imposes a limit on how much
more long you can go than 100%. Just like we said, if
something's negative, then some of the weights have
got to be greater than one, or they got to add up
to greater than one. So when you have
that situation where you have a limit on the total
negative position you can have, that limit puts a symmetric
upper bound beyond the number one of what you can go long. And so for reasons that are
probably a little bit too far afield to get into
here, 130-30 seems to be a bit of a sweet spot
for managers out there. So they said, we will
limit our short positions to no more than
30% of the capital. So you give us $100
million to manage, we will take no more than
$30 million of shorts. And therefore, we will take
no more than $130 million of longs. But when you add them up,
you still get back to 100%. So that's 130-30. It's very popular,
and it's something that is likely to grow,
particularly given this current market environment. Because 130-30 has done better
than the S&P, not surprisingly, because of that
30% short position. So here's the example
of your own portfolio and how you get those weights. That's pretty straightforward. Here's another example
where you've now got some short positions
here, and the short positions are not from short selling. But the short positions
are in riskless bonds. In other words, now instead
of shorting a stock, you're shorting a bond or
selling a bond or borrowing money from a broker
and getting leverage. So this is leverage where
the security that you're levering up is using bonds,
and you're levering up the equity positions. So your portfolio
weights look like this. Your equity positions,
when you add up the equity positions, those portfolio
weights, you get 200%. But your riskless bonds,
you shorted $50,000. You're borrowing
$50,000 from the broker, so you've got minus 100%. When you add those two, you
get back 100%, or in this case, $50,000. So you start out
with $50,000 cash and then you buy
$100,000 worth of stocks by borrowing an extra
$50,000 from your broker. Yeah? STUDENT: I understand
the [? degree ?] of the portfolio [INAUDIBLE],
but I thought, fundamentally, it's to have different
risks and to manage that. PROFESSOR: Yes. STUDENT: So when
you are actually structuring portfolios, do you
have these risks [INAUDIBLE]? Because I would just be
willing to do them separately. There is no reason for you
to have them as [INAUDIBLE]. PROFESSOR: Well, the
reason that I have them here is I want to show
you exactly how you would compute the
portfolio weights of your entire portfolio. So basically, what this is
is your equity portfolio, but in addition, your fixed
income position's added in. I mean, your whole
portfolio could be anything. It could be stocks, bonds,
options, currencies, real state. So I'm just including all of
this in the portfolio itself. STUDENT: So basically, it is to
try to handle different risks-- I mean, different stocks or
bonds or whatever they have, various risks? PROFESSOR: Yes, absolutely,
and you are doing that. Stocks A, B, and C
have different risks, as does the bond. And so you're mixing and
matching and putting them together into what
hopefully will be an attractive portfolio. Now, we mentioned before
that when you get a mortgage, that's leverage, too. So this is an example
of a situation where you buy a home for
$500,000, but you only have a $100,000 payment. Your equity in the
home is only $100,000. The bank has loaned
you $400,000. Your leverage ratio
is 5:1, so if you were to look at your
portfolio weights it would be 500% house minus
400% bank or bonds or mortgage. That's very high leverage. And in that case, when
you're leveraged five to one, if the house price goes down by
something like, I don't know, 2%, you've lost 10% of
the value of your home-- or the value of
your equity, rather. If the house price declines by
15%, that's really bad news. So leverage is a
two-edged sword. When things are working
well, it gives you a boost. When things are
not working well, it can hurt you on
the downside as well. Here's another example
where you've got a zero net investment strategy. You can work that
out for yourself. This is a little bit trickier
because the portfolio weights now add up to zero. You've got to think a little
bit about what it means to have portfolio weights at all. So I'll leave that
for you to look at. That's something
that, as I said, we won't cover this
course in great detail. So now motivation--
what we're trying to do now that you know the
basic language of portfolio weights and how to manipulate
them to some degree, I want to ask the question,
why bother with the portfolio? Well, we've already got
a couple of comments about why you want a portfolio. You want to have stocks with
different kinds of risks so you have diversification. But there's another approach,
and the other approach is championed by Warren Buffett. Warren Buffett has criticized
this idea of diversification, not putting all your eggs
in one basket, by saying, you should put all
your eggs in one basket and then simply just watch
that basket really carefully. Isn't that better? Well, that sounds
good, but what if it's the case that you
don't really know how to pick the right basket? And so therefore, whatever
basket you're watching may not be
particularly attractive because you picked
the wrong basket. So that's really the idea
behind portfolio theory. It's that not all of
us are Warren Buffett. Not all of us want to
become Warren Buffetts. We want to have a relatively
systematic approach to making a good investment decision. We don't want to try
to beat the market. We want to figure out
whether we can come up with a responsible and
attractive way of investing that has some kind of
economic logic to it. So the point is that we don't
know which stock is best, and so we don't want to pick
just one stock like Motorola. Because there are periods
where Motorola looks fantastic and periods where
Motorola looks horrible. So we want to be able to
pick a portfolio that's got good characteristics. So diversification is
one way to do that. It's to basically
spread your risk across a number of securities,
and portfolios can do that. But at the same time, they
can also create focused bets. So it's not just
the case that you have to buy every possible stock
there is out there in order to diversify. For example, you
may have information or you may have conviction that
information technology is going to do really well over
the next couple of years because somebody's
got to figure out how to process all of these
bad loans and problem banks. And IT is going to
ultimately be the solution. Well, if that's the case,
you can make a bet on IT without having to make a bet
on any one firm or one stock. The way you do that is to
form a portfolio of stocks that are all in the IT sector. And so you get diversification,
but at the same time, you're able to make
a bet in an area where you think you have
particular expertise. And finally, portfolios
can customize and manage your own personal
risk-reward tradeoffs. So for some of you,
you want a lot of risk, you want it concentrated in
a small number of industries, and you want to do it with
relatively small priced stocks. You can do that. Somebody else might have a very
different set of preferences. Portfolios allow you to tailor
the risk-reward tradeoffs to your particular preferences. So now we have a
motivation for portfolios. Then the next question is,
that sounds great; now tell me, how do I construct one
of these good portfolios? And in order to
answer that question, I've got to tell you
what "good" means, or you've got to tell
me what "good" means. So typically, what we say
about a good portfolio is it's a portfolio that
has high mean and low risk. That's what "good" means. There are two characteristics
that we tend to focus on for purely statistical reasons. It's because those
are easy to compute, and they are the
first two statistics that one would
look at when you're looking at an
investment-- the mean and the standard deviation. So you might think that,
naturally, it would make sense to pick a portfolio
that's got high mean and low standard deviation. That's an assumption. In other words, we're
assuming that we're going to measure risk
by standard deviation, and we're assuming that
we're measuring return by the actual expected
rate of return. For certain investors,
those are not appropriate. For example, there
are some investors that are really keen on
socially aware investing so they don't want to
invest in companies that pollute the environment. They don't want to
invest in companies that engage in nonunion
workers, or they don't want to
invest in companies that happen to be exploiting
labor in unregulated markets. Those are examples of
non-pecuniary characteristics that figure into this
choice of stocks. We're going to
abstract from that. So for our purposes, the
characteristics that we're going to look at
for a good portfolio is, does it have a high
return, does it have low risk? And the way we're
going to measure risk is in terms of the volatility
or standard deviation. Now, here, again, there's lots
of ways of measuring risk. We can measure by the
upper quartile, the 5% loss or spread, but in fact,
what we're going to use is this standard
deviation measure. For symmetric distributions
like the normal, it turns out that that's
not a bad measure, but some people have argued
that by looking at spread you're confusing the
upside with the downside. Nobody has any problem
with upside risk or upside distribution. I haven't run across
anybody that said, gee, this year I'm really
making too much money and that's just
not a good thing. If you meet anybody
like that, introduce me. I'll help them out
with their problem. But the point is that for
a symmetric distribution, it doesn't matter, and in
more advanced approaches to investments people have
used one-sided measures. But we're not going to
do that in this course. So we're going to focus on
variance or standard deviation as the measure of risk. And the assumptions
that I'm going to make for the
remainder of the course is that all investors like
higher mean and all investors like higher variance. Now, that's a really
reasonable assumption, but you could
challenge it if you wanted to argue that investors
care about other things. So just be aware that I'm
making an approximation, and the approximation is exactly
that, that mean and variance are the only things that
our prototypical investor is going to care about. So now, we actually are
pretty close to being able to come up with an
answer to the question, what's a good portfolio and
how do we pick stocks. One of the things that
we're going to answer over the course of the
next few slides is, how much does
a stock contribute to the risk and the expected
return of a portfolio? So if you're thinking about
investing in a new stock, it's like inviting
somebody into your club. You want to ask,
well, what are you going to contribute to my club? What are you going to
contribute to the portfolio? What will you add to
what I already have? Are you going to help me
with my expected return? Are you going to help
me lower my risk? And if the answer is no to both
of them, then I don't want you. You're not going to
do anything for me. Why should you be
in my portfolio? So that's the kind
of argument we're going to make to be able to
construct a good portfolio. So let's get a little bit
more specific about that. Here's a graph, and you're
going to see this a lot. This graph is going
to be one that we use for all of portfolio analysis. It's where we plot on
two-dimensional space the average return
of the stock as well as its risk, where
risk is now being measured by standard deviation. So I've got five
assets plotted here. Merck is one and General
Motors is another one. Motorola is a third,
McDonald's a fourth, and I've got T-bills down
there on the lower left. This gives you a sense of the
different trade-offs there are. Clearly General Motors is
lower risk that Motorola, but it's also lower return. And McDonald's is
definitely going to be higher risk than Merck,
but notice that McDonald's is also lower return than Merck. So at least in this setting,
nobody in their right mind-- by that I mean, no
rational investor-- would ever want to hold
McDonald's over Merck-- by our assumption. We're assuming that investors
like expected return and they don't like risk. Question? Yeah? STUDENT: This [INAUDIBLE]
think that McDonald's will perform better. PROFESSOR: Exactly,
that's right. So I was waiting for
somebody to say that. Warren Buffett would
say that's the stupidest thing I've ever heard,
because all you're doing is plotting history
on this chart. And this tells you nothing
about what might happen over the next 12, 24 months. It could be that health
care is going to just become a real problem,
pharmaceutical companies are going to get
battered because of the Democratic
administration. That's going to force
them to reduce the prices. And so over the next
six to 12 months, the only thing that
people will be able to do is to go to their neighborhood
McDonald's and just enjoy a nice hamburger and
complain about what's been going on with the
pharmaceutical industry. In that case, McDonald's
is a great bet and Merck is a
terrible investment. We abstract from all of that. We are not in the business
of forecasting stock returns. Why? Because I just showed you
in the previous set of slides that it's
hard to forecast. In fact, you told me that
in an efficient market it's actually hard
to tell what's going to happen with these stocks. And if you could
tell, then people are going to start
using that information, and then the
information is worthless because it'll have already
been taken into account. So you see, this
is a very important philosophical difference between
Warren Buffett and academics. Warren Buffett
believes that there are systematic mispricings
out there that can be found and taken advantage of. Academic finance, as
of the 1960s and 70s when this theory was developed,
started from the point that you just came
to very quickly, which is that there are
no patterns in the data. If there were, someone
would have already done it-- which, by the way, Warren
Buffett would answer by saying, you know what, that sounds
like a joke about the economist walking down the road,
sees a $100 bill, and walks right by it. And when somebody
says, why didn't you pick up the $100 bill, they
said, well, if it were real, someone would have
already picked it up. I mean, that's the argument
that we made together. We made that argument, that if
there was a pattern somebody would take advantage of
it and then the pattern can't be there. And then, again,
Warren Buffet would say, that's the stupidest
thing I ever heard, because in fact, I've done
it, I saw the patterns, I took advantage of it,
and I have a bit more money than you do, so there. Who do you believe? Well, it's kind of hard to
argue with a $40-something billionaire. I think that's his
wealth, $40 billion. But that's not the
perspective of this analysis. Mike? STUDENT: Well, let's say
the expected return was you had perfect
information and that's what was going to be a
perfect crystal ball. It would still be irrational
to buy McDonald's versus Merck, so you'd short
McDonald's and long Merck until the returns became equal. PROFESSOR: Exactly. So I'm going to talk about
that for a little while, but you're right. So if you could short,
then what you'd want to do is exactly what you said. You want to basically long the
low risk, high yield asset, short the high risk, low
yield asset, make that spread, and make it as
riskless as you can buy including other securities. Yes? STUDENT: Yeah, but
eventually it would collapse, and then the
relationship would-- PROFESSOR: And then it should. That's right. So the argument that
economists would make is that this picture is
the equilibrium of where these returns should be, given
what the market determines their fair rates of return
are, relative to their risks. So that's, again, a very big
philosophical difference. An economist would say,
all of these securities are exactly where
they should be. And they may change over
time, but at any point in time they are where they should be. Supply equals demand,
market's clear, everything is equilibrium,
and our decision is simply to figure
out what to make of the portfolio of
these securities. What is the best portfolio
of these securities? So I'm just warning you, this
is a philosophical departure from what you're used
to thinking and reading in the newspapers. Because the newspapers
would say, well, let's take a look at the
earnings at McDonald's. Let's take a look at Merck. Let's talk to the
macroeconomists and see what's going to happen
over the next 12 months. Let's talk to the
earnings analysts and see whether they
forecast higher earnings, lower earnings. The whole point of the academic
infrastructure that we set up is that you can't
predict these things. And if you believe that,
then basically Warren Buffett is just one really lucky guy. So I'm going to have to justify
this academic position to you. And I won't do that until
the end of the semester, because first of all, I have
a lot of material to cover. And I want to cover all of the
material in the basic form, and then in the end I'm going
to give you a sense of where things really stand. It's a fiction. It's a fiction that you
can't forecast stock prices, but it's a fiction that actually
is pretty close to reality for 99% of the public. Now, you guys are not
99% of the public. But for the people
that will someday be your clients
or your investors, it will be true, that
the typical individual has no hope of being able to
out-forecast Warren Buffett. And if you can't
out-forecast somebody, then you may as well
assume that they're random and they're perfectly priced. And then you still
have the problem, OK, if you assume that,
then what do you do? That's all we're going
to try to figure out. I'm going to tell you what
you do with portfolio theory. Now, since we're
almost out of time, I want to just tell
you where we're going. What we're going to do
is look at this graph and ask the question,
what do people want? They want higher return,
they want to go north, and they want lower risk. They want to go west. So the northwest is
where we're going to be heading in this
graph, and the question is, how can we get there? How can we get as
northwest as possible using these securities? And the answer will
shock you, I think, because you're going
to see that by doing a very simple little bit
of high school algebra we can actually create
a portfolio that beats all of these things. That is, if you
didn't know anything about portfolio theory, you
would be severely worse off, because you'd be stuck having to
be on one of these five points. And if you knew a little
bit of high school algebra and some finance, you
could actually do a lot better. So we'll see that on Monday.
