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In the Investments part of the book, we will use the terms “stock” and “security” very loosely.
Side Note:
Our concern is really the choice among many investment opportunities, which includes bonds, options, fu-
tures, real estate, etc. It is just more convenient to use the phrase stock, rather than “any possible investment
opportunity.”




Please be aware that I have recently changed the naming of securities, and that I am trying
to make most security names appear in mathitalic (e.g., A). This has neither been double-
checked, yet, nor fully completed (speci¬cally, ¬rms 1 through N must be italic). Please
bring mistakes and issues to my attention.
270


What we want to Accomplish in this Part
The goal of this part of the book is to teach you how public investors think. This is important
not only when you are an investor who wants to decide how to allocate money among the
thousands of possible ¬nancial investments, but also for the corporate manager who wants to
get you and other investors to part with their money in order to ¬nance new corporate projects.

• Chapter 11 gives a short tour of historical rates of returns to whet your appetite, and
explains some of the setup of equity markets.

Typical questions: Did stocks, bonds, or cash perform better over the last thirty
years? How safe were stocks compared to bonds or cash?

• Chapter 12 describes how you can trade equity securities (a.k.a. “stocks”) , and how
securities can be combined into portfolios.

Typical questions: what was the rate of return on a portfolio that invested
money into the 30 stocks that form the Dow-Jones Industrial Average (DJIA)
index?

• Chapter 13 shows how to measure the risk and reward of securities.

Typical questions: if you held a portfolio of the 30 stocks that form the DJIA,
what would your risk be?

• Chapter 14 shows how to measure the risk and reward of portfolios.

Typical questions: How would the risk change if you rearrange how much money
you put into each of the 30 stocks of the Dow Jones?

• Chapter 15 shows how holding many stocks in your portfolio can reduce your risk.

Typical questions: How much lower would your risk be if you held all 30 stocks
in the DJIA instead of just a single stock in the DJIA?

• Chapter 16 shows how you can determine the best portfolio.

Typical questions: Can you invest better than just into the 30 stocks in the DJIA?
How much risk does PepsiCo contribute to your portfolio? Would it be better if
you shifted more money into PepsiCo stock, or should you stick to your current
portfolio?

• Chapter 17 shows what expected rates of return securities have to o¬er if investors make
smart investment decisions. It gives the formula (cookbook) version of the “Capital Asset
Pricing Model” (CAPM) model, which answers this question.

Typical questions: What is a fair reward for PepsiCo™s stock investors, given how
much risk it contributes to the overall market portfolio?

• Chapter 18 explains more of the theory behind the CAPM.

• Chapter 19 expands on the e¬cient markets concept, ¬rst mentioned in the introduction.
It also explains the di¬erence between arbitrage and good bets.

Typical questions: what kind of information can you use to beat the market?
CHAPTER 11
A First Look at Investments

Historical Rates of Returns
last ¬le change: Feb 23, 2006 (14:17h)

last major edit: Jan 2005




The subject of investments is so interesting that we are going to break our rule of starting
simple. Instead of laying all the foundations before we look at the evidence, we shall ¬rst look
at some evidence: the world of returns on stocks, bonds, and “cash.” My plan is to show you
the annual returns on these investment classes (and on some individual stocks), so that you can
visualize the main patterns that matter”patterns of risk, reward, and covariation. Don™t worry
if you cannot follow everything in this chapter. It will all be explained in due course”and you
can always come back later.




271
¬le=invmotive.tex: LP
272 Chapter 11. A First Look at Investments.

11·1. Stocks, Bonds, and Cash, 1970“2004

Financial investment opportunities are often classi¬ed into just a few large categories: cash,
Common categories.
bonds, and stocks. Cash is actually a misnomer, because it usually designates not physical
bills under your mattress, but bonds that are very liquid, very low-risk, and very short-term.
Another common designation for cash is money-market, a catch-all designation that includes
not only very short-term Treasury bills but also a number of other securities (such as CDs,
savings deposits, and commercial paper) that are listed in Appendix B.2·6. We will just use the
term cash, because it is shorter. We have already talked at length about bonds and their many
di¬erent varieties. Stocks are often further categorized into a few hundred large-¬rm stocks
that are quite visible, liquid and trade very frequently, and mostly make up the popular S&P500
index; and a few thousand small-¬rm stocks that trade less frequently.
You should not take any of these categories too literally, because each of them is quite diverse.
Categories hide a lot of
variation. They are only For example, we already know that bonds may include anything from Treasury bonds, corporate
broadly indicative.
bonds, municipal bonds, foreign bonds, to even more exotic instruments. Nevertheless, these
categories can be useful in giving a broad perspective”because most, though not all, bonds
behave more like other bonds than they behave like stocks. The same holds true for stocks
and cash”most, but not all stocks behave more like other stocks, and most, but not all money
market instruments behave more like other money market instruments. So let us begin our
examination of investments by looking at the historical performances of these asset categories.


11·1.A. Graphical Representation of Historical Stock Market Returns

We begin with Figure 11.1, which shows the year-by-year rates of return of the S&P500. It
The time series diagram.
represents the performance of the 500 largest ¬rms in the U.S. stock market. Looking at the
data, you would have earned 2.3% in 1970, 13.5% in 1971, and so on. The table in Figure 11.1
allows you to compute the average rate of return over all 35 years as 12.3% per annum”also
marked by the red triangle in the graph on the left side, and in the table at the end of the data.
Figures 11.2 and 11.3 take the same data as Figure 11.1, but present it di¬erently. The density
The histogram shows
how spread out returns function”a smooth version of a histogram”in Figure 11.2 is based on the number of returns
are.
that fall within a range. For example, the table in Figure 11.1 shows that only 1971, 1979, 1982,
1988, and 1992 had rates of return between 10% and 20%. In this period, the most frequent
return range was between 20% and 30%, but there were also a good number of returns below
10%”and even two years in which you would have lost more than 20% of your money (1974
and 2002). The density function makes it easy to see how spread out returns are.
¬le=invmotive.tex: RP
273
Section 11·1. Stocks, Bonds, and Cash, 1970“2004.




Figure 11.1. The Time Series of Rates of Returns on the S&P500, 1970“2004

+2.3% +29.6% ’2.2% ’5.7%
1970 1980 1990 2000
+13.5% ’2.3% +21.9% ’12.8%
1971 1981 1991 2001
+21.7% +18.2% +15.3% ’21.9%
1972 1982 1992 2002
’16.5% +23.0% +9.8% +26.4%
1973 1983 1993 2003
’25.4% +4.6% +0.5% +9.0%
1974 1984 1994 2004
+37.7% +30.8% +38.0%
1975 1985 1995 Average 12.3%
+22.6% +23.9% +23.4%
1976 1986 1996 Std Dev 16.7%
’5.9% +0.5% +31.6%
1977 1987 1997
+7.8% +18.8% +25.3%
1978 1988 1998
+18.0% +30.1% +21.4%
1979 1989 1999
0.8
0.6
0.4
0.2
S&P500

0.0
’0.4 ’0.2




1970 1975 1980 1985 1990 1995 2000 2005

year

The graph is a representation of the data below.
¬le=invmotive.tex: LP
274 Chapter 11. A First Look at Investments.




Figure 11.2. Density Function of S&P500 Rates of Return, 1970“2004
2.0
1.5
Density

1.0
0.5
0.0




’0.4 ’0.2 0.0 0.2 0.4 0.6 0.8

S&P500

< ’20% ’20%, ’10% ’10%, 0% 0%-10% 10%-20% 20%-30% 30% ’ 40% > 40%
Return Range
Number of Years 2 2 4 7 5 10 5 0


The graph and table are just di¬erent representations of the data in Figure 11.1.
¬le=invmotive.tex: RP
275
Section 11·1. Stocks, Bonds, and Cash, 1970“2004.




Figure 11.3. Cumulative Rates of Return For the S&P500, 1970“2004
500.0
50.0
S&P500

5.0
0.5
0.1




1970 1975 1980 1985 1990 1995 2000 2005

year

1970 $1.02 1980 $2.31 1990 $8.43 2000 $42.06
1971 $1.16 1981 $2.25 1991 $10.28 2001 $36.68
1972 $1.41 1982 $2.66 1992 $11.85 2002 $28.64
1973 $1.18 1983 $3.27 1993 $13.02 2003 $36.19
1974 $0.88 1984 $3.43 1994 $13.08 2004 $39.45
1975 $1.21 1985 $4.48 1995 $18.06
1976 $1.49 1986 $5.55 1996 $22.28
1977 $1.40 1987 $5.58 1997 $29.31
1978 $1.51 1988 $6.63 1998 $36.74
1979 $1.78 1989 $8.62 1999 $44.62

The graph and table are just di¬erent representations of the data in Figure 11.1.
¬le=invmotive.tex: LP
276 Chapter 11. A First Look at Investments.

The cumulative return graph in Figure 11.3 o¬ers yet another perspective. It plots the cumu-
The cumulative rate of
return graph shows how lated annual returns (on a logarithmic scale). For example, by the end of 1973, the compound
long-run investments
return of $1 invested in 1970 would have been
would have fared.


· (1 + 2.3%) · (1 + 13.5%) · (1 + 21.7%) · (1 ’ 16.5%) ≈ $1.18
$1
(11.1)
I1970 · (1 + r1970 ) · (1 + r1971 ) · (1 + r1972 ) · (1 + r1973 ) .

The cumulative return perspective illustrates geometric returns, which adjust for the fact that
a return of ’50% followed by +100% is a net zero return, even though the average rate of these
two returns would be a +25%. The geometric rate of return is always lower than the arithmetic
rate of return. For example, our 18% compound rate of return corresponds to a 4.2% annualized
rate, which is lower than the 5.25% arithmetic average rate of return from 1970 to 2003. The
graph shows that an investment in the stock market of $1 at the start of 1970 would have
ended up as $39.70 at the end of 2004”of course, ignoring all taxes.


11·1.B. Comparative Investment Performance

What does history tell us about rate-of-return patterns on our three major investment categories”
Explore the complex
¬gure ¬rst. Stare at it. stocks, bonds, and cash? We can ¬nd out by plotting exactly the same graphs as those in
Figures 11.1“11.3. Figure 11.4 repeats them for a set of historical investment choices all on
the same scale. It displays a lot of information about the performance of these investments.
Do not expect to understand everything at ¬rst glance: you need to stare at the elements of
Figure 11.4 for a while to comprehend them.
¬le=invmotive.tex: RP
277
Section 11·1. Stocks, Bonds, and Cash, 1970“2004.

You have already seen the ¬rst row”investments in “cash.” Only the scale is di¬erent to make The ¬rst row is again
“cash.”
direct comparison to the other investments in the graphs below easier. Note how tight the
distribution of cash returns is around its 7% mean.
The second row describes investments in 20-year Treasury bonds. The graph in column 3 The second row,
long-term bonds, offered
shows that the bars are now sometimes slightly negative (years in which you would have earned
more reward, but was
a negative rate of return), but there are also years in which you would have done much better. more risky, too.
This is why the histogram is much wider for 20-year bonds than it is for cash securities, and
this is why the risk was 12% per year”although the average rate of return was a higher 10% per
year. By 2004, your $1 invested in 1970 would have become $19.29.
The third row describes an investment in an “index fund” that holds stocks to replicate the The third row, stocks
overall, offered even
rate of return on the S&P500 index. Sometimes, this is colloquially called “stocks” or “the stock
more reward, but was
market,” though it is really only “large stocks.” Large stocks would have been even more risky even more risky.
(with a mean rate of return of 12% per year and a risk of 17% per year), but your $1 invested in
1970 would have been worth $39.45 in 2004.
Let us see how some individual stock investments would have di¬ered from just the broad Individual stocks can
offer more reward, or be
category “stocks.” The remaining four rows represent the rates of returns for four stalwarts:
even more risky.
Coca Cola [KO], PepsiCo [PEP], Sony [SNE], and United Airlines [UAL]. The histograms are all
over the place: investing in a single stock would have been a rather risky venture, even for
these household names. Indeed, we could not even plot the ¬nal year for UAL in the right-most
cumulative return graph, because UAL stock investors lost all invested money in the 2003
bankruptcy, which on the logarithmic scale would have been minus in¬nity.

Side Note: The compound in¬‚ation rate from 1970 to 2002 was 5.0. (Put di¬erently, $1 in 1970 purchased as
much as $5.04 did in 2003.) Therefore, the $9.69 end result in cash would have been worth $9.69/$5.04 ≈ 1.92
in 1970-in¬‚ation-adjusted dollars. Over 30 years, you would have only doubled your real purchasing power.
You can easily compute equivalent real returns for the other investment opportunities.
Furthermore, the di¬erence between $39 in stocks and $9.69 in cash or $19.29 in bonds is an understatement
for you. Interest was taxable each year, while the capital gain in stocks was not (the dividend gain would have
been taxable). Very roughly, a highly taxed investor would have ended up with about $5 in “cash,” $13 in bonds,
and $33 in stocks. Therefore, in real and after-tax terms, from 1970 to 2004, a highly taxed investor would
have ended up just about even if invested in “cash,” doubled or tripled if invested in bonds, and quintupled if
invested in stocks. This was a great 30 years for stocks!


From 1926 to 2002, the annual risk and reward of some large asset-class investments were
Side Note:
approximately as follows:


“Reward” “Risk”
E (˜) Sdv (˜)
r r
Asset Class
Short-Term U.S. Government Treasury Bills 4% 3%
Long-Term U.S. Government Treasury Bonds 5%+ 9%+
Long-Term Corporate Bonds 6% 9%
Large Firm Stocks 10% 20%
Small Firm Stocks 15% 30%


(In¬‚ation was about 3% per year.)
(Source: Ibbotson Associates, and others.)
278
Figure 11.4. Comparative Investment Performance, 1970“2004



Description Density Function Rates of Return Compound Return


’1 0 1 2 3 1970 1975 1980 1985 1990 1995 2000 2005 1970 1975 1980 1985 1990 1995 2000 2005

“Cash” (Federal Funds Rate)




+300%
Mean (Reward): 6.8%/yr




$100
Std.Dev. (Risk): 3.4%/yr
$1 in Jan 1970 would have




$10
+100%
become $9.69 in 2004
Correl w/ S&P500: ’2.8%




$1
0
Beta w/ S&P500: ’0.0




’100%




$0.1




¬le=invmotive.tex: LP
“Bonds” (20-Year Treasury)




+300%
Mean (Reward): 9.4%/yr




$100
Std.Dev. (Risk): 11.8%/yr
$1 in Jan 1970 would have




$10
+100%
become $19.29 in 2004
Correl w/ S&P500: +25%




$1
0



Beta w/ S&P500: +0.2




Chapter 11. A First Look at Investments.
’100%




$0.1
“Stock Market” (S&P500)
+300%




Mean (Reward): 12.4%/yr




$100
Std.Dev. (Risk): 16.7%/yr
$1 in Jan 1970 would have




$10
+100%




become $39.45 in 2004
Correl w/ S&P500: +100%




$1
0




Beta w/ S&P500: +1.0
’100%




$0.1
Section 11·1. Stocks, Bonds, and Cash, 1970“2004.
+300%
CocaCola (KO)




$100
Mean (Reward): 16.3%/yr




$10
Std.Dev. (Risk): 28.5%/yr




+100%
$1 in Jan 1970 would have




$1
become $63.71 in 2004




0
Correl w/ S&P500: +63%




’100%




$0.1
Beta w/ S&P500: +1.0




+300%
PepsiCo (PEP)




$100
Mean (Reward): 17.6%/yr




$10
Std.Dev. (Risk): 25.5%/yr




+100%
$1 in Jan 1970 would have




$1
become $128.78 in 2004




0
Correl w/ S&P500: +59%




’100%




$0.1
Beta w/ S&P500: +0.9




+300%




¬le=invmotive.tex: RP
Sony (SNE)




$100
Mean (Reward): 22.3%/yr




$10
Std.Dev. (Risk): 66.9%/yr




+100%
$1 in Jan 1970 would have




$1
become $29.94 in 2004




0
Correl w/ S&P500: +37%




’100%




$0.1
Beta w/ S&P500: +1.5




+300%
United (UAL)




$100
Mean (Reward): 4.7%/yr




$10
Std.Dev. (Risk): 51.x%/yr
+100%




$1 in Jan 1970 would have




$1
become $0.00 in 2004
0




Correl w/ S&P500: +57%
’100%




$0.1
Beta w/ S&P500: +1.7 ’1 0 1 2 3 1970 1975 1980 1985 1990 1995 2000 2005 1970 1975 1980 1985 1990 1995 2000 2005




Description Density Function Time Series Compound Return




279
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280 Chapter 11. A First Look at Investments.

11·1.C. Comovement, Beta, and Correlation

Figure 11.5 highlights the rates of return on the S&P500 and one speci¬c stock, Coca-Cola (KO).
What is the correlation
mentioned in the ¬gure? The top row redraws the graphs for these two investments from the third column in Figure 11.4.
Do you notice a correlation between these two rates of return? Are the years in which one is
positive (or above its mean) more likely to also see the other be positive (or above its mean),
and vice-versa? It does seem that way. For example, the worst rates of return for both are 1974.
Similarly, 1973, 2000, and 2001 were bad years for investors in either the S&P500 or Coca-Cola.
In contrast, 1989 and 1975 were good years for both. The correlation is not perfect: in 1979,
the S&P500 had a good year, but Coca-Cola had a bad one. It is very common for all sorts of
investments to move together with the stock market: in years of malaise, almost everything
tends to be in malaise. In years of exuberance, almost everything tends to be exuberant.
This comovement of investments is very important if you do not like risk. An investment that
Why do we care about
comovement? increases in value whenever the rest of your portfolio decreases in value is practically like
“insurance” that pays o¬ when you need it most. You might buy into such an investment even
if it o¬ers only a very low expected rate of return. In contrast, you might not like an investment
that does very badly whenever the rest of the portfolio also does badly. To be included in your
portfolio, such an investment would have to o¬er a very high expected rate of return.
How can we measure the extent to which securities covary with others? For example, you might
Quantifying
comovement”Market- want to know how Coca-Cola performs if your current portfolio is the S&P500 (a common stand-
beta, the best-¬t
in for the market portfolio). Will Coca-Cola also go down if the market goes down (and make
line.
a bad situation worse), or will it go up and thereby serve as useful insurance? How can you
quantify such comovement? Graphically, you can plot the two return series against one another,
as is done in the lower plot in Figure 11.5. The graph also shows the best line between the two
series. This line has a slope of 1.07 and is called the market-beta of Coca-Cola™s stock. This
market-beta is an important measure of comovement for an investor who owns the market
portfolio. Loosely speaking, if a stock has a very steep positive slope, say +3, then if the
market and our portfolio drops by 10%, this stock would be expected to drop by 30%”it would
make a bad situation worse. In contrast, if a stock has a very negative slope, say ’1, then if the
market drops by 10%, this investment would “rescue” us, earning a positive 10% rate of return.
It would act like insurance.
Another common measure of comovement is the correlation. A correlation of 100% indicates
Market-beta, the best-¬t
line, is related to that two variables always perfectly move together; a correlation of 0% indicates that two vari-
correlation, too.
ables move about independently; and a correlation of ’100% indicates that two variables always
perfectly move in opposite directions. (A correlation can never exceed +100% or ’100%.) In
this case, the correlation is +63%. Slope and correlation are very similar measures”in fact, a
positive correlation implies a positive beta and vice-versa. Of course, beta and correlation are
only measures of average comovement: even for positive beta investments, there are individual
years in which the investment and stock market do not move together. We already mentioned
1979 and 2000 as examples in which Coca-Cola and the S&P500 went their di¬erent ways. Neg-
ative betas are rare. There are only a very few investment categories that are generally thought
to be negatively correlated with the market”principally gold and other precious metals.
Solve Now!
Q 11.1 What can you see in a time-series graph that is lost in a histogram?

Q 11.2 What can you see in a histogram that is more di¬cult to see in the time-series graph?

Q 11.3 What can you see in a cumulative return graph that is di¬cult to see in the time-series
graph?

Q 11.4 How do you graph a “market-beta”? What should be on the X-axis, what should be on
the Y-axis? What is an individual data point?

Q 11.5 What is the market beta of the market?
¬le=invmotive.tex: RP
281
Section 11·1. Stocks, Bonds, and Cash, 1970“2004.




Figure 11.5. Rate of Returns on The S&P500 and Coca-Cola (KO)
0.6




0.6
Coca’Cola (KO)
0.2




0.2
s&p500
’0.2




’0.2
’0.6




’0.6




1970 1980 1990 2000 1970 1980 1990 2000
Year Year


d  
d  
d
‚ ©
 
0.8




1989
1991
0.6




1982 1975
1971 1995
1996
0.4




1985
1986
Coca’Cola (KO)




1997
1972
1978 1988
1990 1984
0.2




2003
1994
1981
1970 1993 1992 1983 1980
2000 1987
0.0




1998
1976
1977
2002
1999
1973
’0.2




2004 1979
2001
’0.6




1974

’0.2 ’0.1 0.0 0.1 0.2 0.3 0.4

s&p500
The lower graph combines the information from the two upper graphs. The stock market rate of return is on the
X-axis, the Coca-Cola rate of return is on the Y -axis. The ¬gure shows that in years when the stock market did well,
Coca-Cola tended to do well, too, and vice-versa. This can be seen in the slope of the best ¬tting line, which is called
the market-beta of Coca-Cola and which will play an important role.
¬le=invmotive.tex: LP
282 Chapter 11. A First Look at Investments.

11·2. Visible and General Historical Stock Regularities

What can you learn from these graphs? Actually, almost everything that there is to learn about
The main empirical
regularities. investments”and I will explain these facts in great detail soon.

• The history indicates that stocks o¬ered higher average rates of return than bonds, which
in turn o¬ered higher average rates of return than “cash.” However, keep in mind that
this was only on average. In any given year, the relationship might have been reversed.
For example in 2002, stock investors lost 22% of their wealth, while cash investors gained
about 1.7%.

• Although stocks did well (on average), you could have lost your shirt investing in them,
especially if you had bet on just one individual stock. For example, if you had invested $1
into United Airlines in 1970, you would have had only 22 cents left in 2002”and nothing
the following year.

• Cash was the safest investment”its distribution is tightly centered around its mean, so
there were no years with negative returns. Bonds were riskier. Stocks were riskier, yet.
(Sometimes, stocks are called “noisy,” because it is really di¬cult to predict what they
will turn out to o¬er.)

• There was some sort of relationship between risk and reward: the riskiest investments
tended to have higher mean rates of return.
(However, the risk has to be looked at “in context.” Thus, please do not overread the
simple relationship between the mean and the standard deviation here.)

• Large portfolios consisting of many stocks tended to have less risk than individual stocks.
The S&P500 fund had a risk of 17%, much less than the risk of most individual stocks.
(This is due to diversi¬cation.)

• A positive average rate of return usually, but not always, translates into a positive com-
pound holding rate of return. United Airlines had a positive average rate of return, despite
having lost all investors™ money.
(You already know why: A stock that doubles and then halves has rates of return of +100%
and “50%. It would have earned you a 0% total compound rate of return. But the average
rate of return would have been positive, [100% + (’50%)]/2 = +25%.)

• Stocks tend to move together. For example, if you look at 2001“2002, not only did the
S&P500 go down, but the individual stocks also tended to go down. In 1998, on the other
hand, most tended to go up (or at least not down much). The mid-1990s were good to
all stocks. And so on. In contrast, money market returns had little to do with the stock
market. Long-term bonds were in between.
On annual frequency, the correlation between cash and the stock market (the S&P500) was
about zero; between long-term bond returns and stock market around 30%; and between
our individual stocks and the stock market around 40% to 70%. The fact that investment
rates of return tend to move together will be important. It will be the foundation for the
market-beta, a measure of risk that we shall propose in Chapter 13.
¬le=invmotive.tex: RP
283
Section 11·3. History or Opportunities?.

11·3. History or Opportunities?

Ultimately, ¬nance is not interested in history for its own sake. We want to know more about History is only useful
over longer horizons,
the future, and history is useful primarily because it is our best available indicator of the
not over just a few years.
future. But which history? One year? Thirty years? One hundred years? Trust me when
I state that if we had drawn the graphs beginning in 1926 instead of 1970, our conclusions
would have all remained the same. However, if we had started in 2001, what would we have
seen? Two awful years for stock investors. We know intuitively that this would not have been
a representative sample period. To make any sensible inferences about what is going on in the
¬nancial markets, we need many years of history, not just one, two, or three”and certainly not
the 6-week investment performance touted by some funds or friends (who also often display
remarkable selective memory!). The ¬‚ip side of this argument is that we cannot reliably say
what the rate of return will be over one year. We will be better in forecasting the average annual
rate of return over 5 to 10 years than over 1 year. Any single year will be very noisy.
Instead of relying on just one year, relying on statistics computed over many years is much Still, history can be
rather misleading. The
better. However, although 20 to 30 years of performance is the minimum number necessary to
Nikkei is a good example.
learn something about return patterns, this is still not su¬cient. Again, we are really interested
in what will happen in the next 5 to 10 years, not what did happen in the last 5 to 10 years. Yes,
the historical performance can help us judge, but you should not trust it blindly. For example,
an investor in UAL in 2000 might have guessed that the average rate of return for UAL would
have been positive”and would have been sorely disappointed. Investors in the Japanese stock
market in 1990 had seen the Nikkei-225 stock market index rise from 10,000 to 40,000”a four
fold increase in just four years”a 40% rate of return every year. If they had believed history,
they would have expected 40, 000 · (1 + 40%)13 ≈ 3.2 million by the end of 2002. Instead, the
Nikkei had fallen below 8,000 in April 2003, and has only recently recovered to 12,000. History
would have been a terrible guide.
Nevertheless, despite the intrinsic hazards in using historical information in forecasting stock But, we do not have
much choice other than
market returns, having historical data is a great advantage. It is a rich source of forecasting
to use some history.
power, so, like everyone else, we will use historical statistics. Yet we must also be careful in not
overinterpreting them. For example, if we see crazily high or crazily low past historical rates
of return, we should try to exercise additional caution.
Fortunately for us, though, it turns out that correlations and risk (explained in the following Historical risk and betas
are better predictors of
chapters) tend to be more stable than historical mean rates of return. So, even though we do
the future risk and
not believe that a $1 investment in PepsiCo will return $100 in 30 years, or that PepsiCo will betas.
return 18% next year, or that PepsiCo has an expected rate of return of 18% over the long run,
we can believe that PepsiCo has a risk of around 25% to 30% per year, and that its correlation
with the S&P500 is around 60%.
To learn investments, we shall pretend that we know the statistical distributions from which Presume we know today
the expected statistics
future investment returns will be drawn. That is, we assume that we know the future expected
for the future, although
rates of return, their standard deviations, correlations, etc., but we do not know the actual we do not know future
draws. For example, we assume that we may know that the lotto combination “5,10,12,33,34,38” realized statistics.
has an expected investment rate of return of “5 cents, but we do not know whether this combi-
nation will win the jackpot. Usually, historical statistics will be our guide to future statistics.

Side Note: For the most part, we will work with historical statistics as if they were our expected statistics.
So, we will try to slip in “unnoticed” that the historical statistical outcomes tell us something about the future
expected statistical outcomes. After the sermon about how historical statistics need not be perfectly indicative
of the future statistics, you should realize that equating the two will be a big and not necessarily innocuous
jump. Fortunately, as we have already mentioned, historical betas and risks are pretty indicative of future betas
and risks. Unfortunately, historical expected rates of return are not too indicative of future expected rates of
return. Know what you can and what you cannot trust.
¬le=invmotive.tex: LP
284 Chapter 11. A First Look at Investments.

Solve Now!
Q 11.6 Rank the following asset categories in terms of risk and reward: money-market, long-
term bonds, the stock market, and a typical individual stock.


Q 11.7 Is the average individual stock safer or riskier than the stock market?


Q 11.8 Is it possible for an investment to have a positive average rate of return, but still lose you
every penny?




11·4. Eggs and Baskets

Although the goal of this part of the book is to develop investments in a technical manner,
The basic investment
choices. we can explain the intuition with a parable about Easter eggs”a variation of the folk wisdom
“Don™t put all your eggs in one basket.” Assume that you are an Easter-egg-seller and that you
have to stock the baskets that you will be carrying to the market tomorrow. Your problem is
that you do not know which color eggs will be the most sought after. Say that you can guess
that the color that will most likely sell is blue (or colors close to blue)”but you really will not
know until you start selling the eggs at the market.


11·4.A. The Overall Basket

The ¬rst question is, what strategies can you pursue?
Strategies”go for the
highest expected rate of
return, go for the safest
• You can paint all your eggs blue. This strategy is the equivalent of purchasing just the
strategy, or choose a
little of each. investments that have the highest possible expected rate of return. It will work great if
you guess right, and this guess is the single most likely outcome”but it also has a very
high chance of leaving you entirely destitute. It is a high-risk strategy.

• You can play it safe and not paint your eggs. Uncolored eggs can always be sold for
food, so you assume practically no risk. This strategy is the equivalent of purchasing the
very lowest-risk investments that also have the very lowest expected rates of return”like
Treasury bills. You e¬ectively give up on trying to obtain a high expected rate of return
in exchange for more safety. It is a very low-risk strategy.

• You can stock your baskets with eggs of many colors”a strategy called diversi¬cation.
You will not sell all eggs, but you will likely sell a good number. This strategy is the equiv-
alent of purchasing many di¬erent stocks (or a mutual fund that holds many di¬erent
stocks), where some investments will lose and others will gain. Relative to bringing only
blue eggs, you are giving up some expected value today, but you are gaining some extra
security, because you will not likely run into a situation where you cannot sell any eggs.
The more varied the colors that you choose, the safer will be your basket. But you will
not want all colors in equal proportions. You will want to tilt the color mix towards
blue, because you believe blue o¬ers the highest expected rates of return. Moreover, this
basket will probably be similar to the baskets that other smart egg-sellers will choose. In
the ¬nancial markets, this basket is probably close to something like the market portfolio,
which has eggs of all sorts of di¬erent colors. Some colors in the market portfolio are
relatively more prominent than others. The market portfolio will have relatively more
“blue eggs,” because they have the highest expected rate of return. Relative to bringing
only blue eggs, this strategy is not as high mean, but it is also not as high risk. Relative
to bringing only unpainted eggs, it is a higher mean strategy but also with higher risk.
¬le=invmotive.tex: RP
285
Section 11·4. Eggs and Baskets.

11·4.B. The Marginal Risk Contribution

A very important question is “How much are you willing to pay to have, say, one more yellow You might choose some
yellow eggs, even though
egg in your basket?” If you believe blue eggs o¬er the highest expected rates of return, would
they are not great
you even bring any yellow eggs? Yes! Even if you do not believe that yellow is likely to sell investments in
tomorrow, a yellow egg will likely sell precisely when most of your blue eggs won™t sell. Yellow themselves.
provides you with the equivalent of “insurance””it pays o¬ when the rest of your portfolio is
losing. Therefore, you may very well be willing to bring some yellow eggs, and even though you
expect to make a loss on them”of course, within reasonable bounds. You may be prepared to
lose 5 cents on each yellow egg you bring, but you would not be prepared to lose $100.
In sum, yellow eggs are valuable to you because they are di¬erent from the rest of your portfolio. Yellow is valuable,
because it is different.
What matters is the insurance that yellow pay o¬ when your blue investments do not.
Perhaps the most important aspect is that you realize that it is not the own risk of each egg The risk of yellow eggs is
irrelevant. What matters
color itself that is important, but the overall basket risk and each color™s contribution thereto.
is risk of the overall
In fact, you already know that you may even expect to lose money on yellow eggs (just as basket. Yellow eggs help
you may expect to lose money on your homeowner™s insurance). This again emphasizes that because they are
different. If you bought
having yellow eggs as insurance is useful only because most of your eggs are not yellow. The
too many yellow eggs,
risk contribution of yellow thus inevitably must depend on all the other eggs in your portfolios. they would no longer be
different from the rest
Of course, it would make no sense to bring only yellow eggs”in this case, you would not only
of your portfolio!
expect to lose 5 cents per egg, you would also most likely always lose these 5 cents and on
all your eggs. In the ¬nancial market, the degree to which one stock investment is similar to
others in your portfolio will be measured by the aforementioned beta”and if your portfolio is
the market portfolio, then it is called the market beta. You will be willing to hold some stocks
in the market portfolio that have a low expected rate of return because they are di¬erent from
the rest of your portfolio”but only some, and only if their expected rate of return is not too
low.
In sum, when you look at your ¬nal basket, you should consider each egg along two dimensions” Assets matter on the
margin on two
how does it contribute to your overall expected rate of return (what is its own expected rate of
dimensions: expected
return?), and how does it contribute to your overall portfolio risk (how does its return covary return and risk
with that of your overall basket?). In a good portfolio, you will try to earn a high expected rate contribution.
of return with low risk, which you accomplish by having a balanced mix of all kinds of eggs”a
balance that evaluates each egg by its expected rate of return versus its uniqueness in your
basket.


11·4.C. The Market Equilibrium

Assume now that you own one factory among many that is selling a particular type of colored If everyone is willing to
pay more for unique
egg to many smart egg traders. It would make sense for you to assume that your egg traders
eggs, then unique eggs
are smart, that they like to buy eggs in colors that have high expected rates of return, but will sell for higher prices
that they also like to buy some eggs that are di¬erent and unique. In other words, you should and therefore earn a
lower expected rate of
assume that your traders do the same optimal basket stocking calculations that we have just
return.
gone through. You can even work out how much smart egg traders would be willing to pay for
eggs of your factory™s color. If your egg color is very di¬erent from those of the other eggs in
traders™ baskets, you can charge more for your eggs than if your eggs are very much like the rest
of their eggs. In equilibrium, there should be a relationship”the most unusual-colored eggs
should command higher prices and thereby earn egg traders lower expected rates of return,
but egg traders still like them because of the insurance such eggs o¬er them, within reasonable
bounds, of course.
For stocks, this model is called the CAPM. It says that stocks that earn high rates of returns when For stocks, this model is
called the CAPM.
the (market) portfolio of other stocks does poorly are more desirable, therefore priced higher,
and therefore o¬er a lower expected rate of return. And this is what we are ultimately really
after. As corporate executives, we want to know how our investors are valuing our projects.
If our projects earn our investors money when the rests of their portfolio are doing poorly,
then our investors will want us to take these projects on their behalves even if our projects
have a (reasonably mildly) low expected rate of return. In ¬nance-speak, we should use a lower
¬le=invmotive.tex: LP
286 Chapter 11. A First Look at Investments.

cost of capital for these projects, because they have lower market-betas”market-beta being a
measure of the similarities of our projects™ rates of return with those of other investments in
the market. The CAPM gives us the precise formula that relates the market beta to the cost
of capital, because it presumes that it can work out exactly what smart egg traders (market
investors) like and dislike.




11·5. Summary

The chapter covered the following major points:

• Figure 11.4 showed an analysis of historical rate of return patterns of stocks, bonds, and
cash investments.

“ Stocks, on average, had higher average rates of return than bonds, which in turn had
higher average rates of return than cash investments.
“ Individual stocks were most risky. Large stock market portfolios had lower risk than
individual stock holdings. Bonds had lower risk yet, and cash was least risky.

• Stocks (and many other investments) tended to correlate: when the stock market overall
had a good year, most stocks also had a good year.

• Historical data can help us in predicting the future. It is especially useful and reliable in
predicting future risk and correlation.

• Investments revolves around the following concepts:

1. Investors can reduce their overall portfolio risk by diversifying”holding many dif-
ferent types of investments.
2. An individual investment is more desirable if it has a higher expected rate of return,
and if it has a lower correlation with the investor™s overall portfolio.
3. The CAPM is a model that corporations can use to assess the value of their projects
to their investors. It assumes that all investors follow smart investment rules, which
allows the CAPM to relate the expected rate of return of each investment to the
correlation of each investment with an investors™ portfolios.
CHAPTER 12
Securities and Portfolios

Applications
last ¬le change: Feb 10, 2006 (19:13h)

last major edit: Jul 2004




This chapter appears in the Survey text only.


This chapter ¬rst explains where stocks come from and where they are traded. It then explains
the process of going long (buying an asset to speculate that it will go up) and going short (selling
an asset to speculate that it will go down). Finally, it explains portfolios and indexes.




287
¬le=secp¬os-g.tex: LP
288 Chapter 12. Securities and Portfolios.

12·1. Some Background Information About Equities Market
Microstructure

The topic of investments traditionally focuses on equities (stocks) more than on other instru-
ments. The main reasons may be that data on stocks are relatively easy to come by and that
stocks are simply more interesting from a corporate perspective than many other ¬nancial in-
struments (e.g., foreign government bonds). So it makes sense to describe a few institutional
details as to how investors and stocks “connect””exchange cash for claims.


12·1.A. Brokers

Most individuals place their orders to buy or sell stocks with a retail broker, such as Ameritrade
Brokers execute and
keep track (a “deep-discount broker”), Charles Schwab (a discount broker), or Merrill Lynch (a full service
broker). Investors can place either market orders, which ask for execution at the current price,
or limit orders, which ask for execution if the price is above or below a limit that the investor
can specify. (There are also many other types of orders, e.g., stop-loss orders [which instruct a
broker to sell a security if it has lost a certain amount of money], GTC [good-to-cancel orders],
and ¬ll-or-kill orders.) The ¬rst function of retail brokers is to execute these trades. They
usually do so by routing investors™ orders to a centralized trading location (e.g., a particular
stock exchange), the choice of which is typically at the retail broker™s discretion, as is the
particular agent (e.g., ¬‚oor broker) engaged to execute the trade. The second function of retail
brokers is to keep track of investors™ holdings, to facilitate purchasing on margin (whereby
investors can borrow money to purchase stock, allowing them to purchase more securities
than they could a¬ord on a purely cash basis), and to facilitate selling securities “short,” which
allows investors to speculate that a stock will go down.
Many larger investors, such as funds (described in Section 12·3.B), break these two functions
Prime Brokers break the
two main functions apart: the investor can employ its own traders, while the broker takes care only of the book-
apart. They leave
keeping of the investor™s portfolio, margin provision and the shorting provisions. Such limited
execution to others.
brokers are called prime brokers.

Side Note: Discount brokers may charge only $10 or so per trade, but they often receive kickback payments
from the market-maker [see below] to which they route your order. This is called “payment for order ¬‚ow.”
The market-maker in turn recoups this payment to the broker by executing your trade at a price that is less
favorable. Although the purpose of such an arrangement seems deceptive, the evidence suggests that discount
brokers are still often cheaper in facilitating investor trades”especially small investor trades”even after taking
this hidden payment into account. They just are not as (relatively) cheap as they want to make you believe.




12·1.B. Exchanges and Non-Exchanges

Exchanges are centralized trading locations where ¬nancial securities are traded. The two most
The standard process.
important stock exchanges in the United States are the New York Stock Exchange (NYSE) and
Nasdaq (originally an acronym for “National Association of Securities Dealers Automated Quo-
tation” System). The NYSE is an auction market, in which one designated specialist (assigned
for each stock) manages the auction process by trading with individual ¬‚oor brokers. The spe-
cialist is often a monopolist. In contrast to this human process in one physical location on Wall
Street, Nasdaq is a purely electronic exchange without specialists. (For security reasons, its
location”well, the location of its computer systems”is secret!) For each Nasdaq stock, there
is at least one market-maker, who has agreed to continuously stand by to o¬er to buy or sell
shares, thereby creating a liquid and immediate market for the general public. Most Nasdaq
stocks have multiple market-makers, drawn from a pool of about 500 trading ¬rms (such as J.P.
Morgan or ETrade), which compete to o¬er the best price. Market-makers have one advantage
over the general public: they can see the limit order book, which contains as-yet-unexecuted
orders from investors to purchase or sell if the stock price changes”giving them a good idea
at which price a lot of buying or selling activity will happen. The NYSE is the older exchange,
and for historical reasons, controls considerably more trading than Nasdaq, especially when it
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Section 12·1. Some Background Information About Equities Market Microstructure.

comes to “blue chip” stocks. (“Blue chip” now means “well established and serious”; ironically,
the term itself came from poker, where the highest-denomination chips were blue.) Nasdaq
tends to trade smaller and high-technology ¬rms.
Continuous trading”trading at any moment an investor wants to execute”relies on the pres- Auctions have lower
execution costs, but also
ence of the standby intermediaries (specialists or market-makers), who are willing to absorb
lower execution speed.
shares when no one else is available. This is risky business, and thus any intermediary must
earn a good rate of return to be willing to do so. To avoid this cost, some countries have orga-
nized their exchanges into non-continuous auction systems, which match buy and sell orders
a couple of times each day. The disadvantage is that you cannot execute orders immediately
but have to delay until a whole range of buy orders and sell orders have accumulated. The ad-
vantage is that this eliminates the risk that an (expensive) intermediary would otherwise have
to bear. Thus, auctions generally o¬er lower trading costs but slower execution.
Even in the United States, innovation and change are everywhere. For example, electronic com- New Alternative Trading
Institutions: ECNs and
munications networks (ECNs) have recently made big inroads into the trading business, replac-
more.
ing exchanges especially for large institutional trades. (They can trade the same stocks that
exchanges are trading, and compete with exchanges in terms of cost and speed of execution.)
An ECN cuts out the specialist, allowing investors to post price-contingent orders themselves.
ECNs may specialize in lower execution costs, more broker kickbacks (see the sidenote below),
or faster execution. The biggest ECNs are Archipelago and Instinet. An even more interesting
method to buy and trade stocks are crossing systems, such as ITG POSIT. ITG focuses pri-
marily on matching large institutional trades with one another in an auction-like manner. If no
match on the other side is found, the order may simply not be executed. But if a match is made,
by cutting out the specialist or market-maker, the execution is a lot cheaper than it would have
been on an exchange. Recently, even more novel trading places have sprung up. For example,
Liquidnet uses peer-to-peer networking”like the original Napster”to match buyers and sell-
ers in real-time. ECNs or electronic limit order books are now the dominant trading systems
for equities worldwide, with only the U.S. exchange ¬‚oors as holdouts. Such mechanisms are
also used to trade futures, derivatives, currencies, and even some bonds.
There are many other ¬nancial markets, too. There are ¬nancial exchanges handling stock Other markets,
especially OTC.
options, commodities, insurance contracts, etc. A fascinating segment are the over-the-counter
(OTC) markets. Over-the-counter means “call around, usually to a set of traders well-known to
trade in the asset, until you ¬nd someone willing to buy or sell at a price you like.” Though
undergoing rapid institutional change, most bond transactions are still OTC. Although OTC
markets handle signi¬cantly more bond trading in terms of transaction dollar amounts than
exchanges, their transaction costs are prohibitively high for retail investors”if you call without
knowing the market in great detail, the person on the other end of the line will be happy to quote
you a shamelessly high price, hoping that you do not know any better alternatives. The NASD
(National Association of Securities Dealers) also operates a semi-OTC market for the stocks
of smaller ¬rms, the pink sheets. Foreign securities trade on their local national exchanges,
but the costs for U.S. retail investors are again often too high to make direct participation
worthwhile.


12·1.C. How Securities Appear and Disappear

Most publicly traded equities appear on public exchanges through initial public o¬erings Firms ¬rst sell shares in
IPOs.
(IPOs), whereby a privately traded company ¬rst sells shares to ordinary investors. IPOs are usu-
ally executed by underwriters (investment bankers such as Goldman Sachs or Merrill Lynch),
which are familiar with the complex legal and regulatory process and which have easy access
to an investor client base to buy the newly issued shares. Shares in IPOs are typically sold at a
¬xed price”and for about 10% below the price at which they are likely to trade on the ¬rst day
of after-market open trading. (Many IPO shares are allocated to the brokerage ¬rm™s favorite
customers, and can be an important source of pro¬t.)
¬le=secp¬os-g.tex: LP
290 Chapter 12. Securities and Portfolios.

Usually, about a third of the company is sold in the IPO, and the typical IPO o¬ers shares worth
Money ¬‚ows into the
¬nancial markets between $20 million and $100 million, although some are much larger (e.g., privatizations,
through IPOs and SEOs.
like British Telecom). About two-thirds of all such IPO companies never amount to much or
even die within a couple of years, but the remaining third soon thereafter o¬er more shares
in seasoned equity o¬erings (SEO). These days, however, much expansion in the number of
shares in publicly traded companies, especially large companies, comes not from seasoned
equity o¬erings, but from employee stock option plans, which eventually become unrestricted
publicly traded shares.
In 1933/1934, Congress established the SEC through the Securities Exchange Acts. It further
Publicly traded
companies must report regulated investment advisors through the Investment Advisors Act of 1940. (The details of
¬nancials, and restrict
these acts can be obtained at the SEC website.) Today, publicly traded companies must regularly
insider trading.
report their ¬nancials and other information to the SEC, and their executives have ¬duciary
obligations to their shareholders. Generally, the SEC prohibits insider trading on unreleased
speci¬c information, although more general trading by insiders is legal (and seems to be done
fairly pro¬tably by these insiders).
Capital ¬‚ows out of the ¬nancial markets in a number of ways”through dividends and share
Money ¬‚ows out from
the ¬nancial markets in repurchases, or more dramatically, through delistings and bankruptcies. Many companies pay
dividends and share
some of their earnings in dividends to investors. Dividends, of course, do not fall like manna
repurchases.
from heaven. For example, a ¬rm worth $100,000 may pay $1,000, and would therefore be
worth $99,000 after the dividend distribution. If you own a share of $100, you would own
(roughly) $99 in stock and $1 in dividends after the payment”still $100 in total, no better
or worse. (If you have to pay some taxes on dividend receipts, you might come out for the
worse.) Alternatively, ¬rms may reduce their outstanding shares by paying out earnings in
share repurchases. For example, the ¬rm may dedicate the $1,000 to share repurchases, and
you could ask the ¬rm to dedicate $100 thereof to repurchasing your share. But even if you hold
onto your share, you have not lost anything. Previously, you owned $100/$100, 000 = 0.1% of
a $100,000 company, for a net of $100. Now, you will own $100/$99, 000 = 1.0101% of a
$99,000 company”multiply this to ¬nd that your share is still worth $100. In either case, the
value of outstanding public equity in the ¬rm has shrunk from $100,000 to $99,000. We shall
discuss dividends and share repurchases in Part IV.
Firms can shrink more drastically, too: some ¬rms voluntarily liquidate, determining that they
Shares can also shrink
out of the ¬nancial can pay their shareholders more if they sell their assets and return the money to them. This
markets in bankruptcies,
is rare, because managers usually like to keep their jobs”even if continuation of the company
liquidations, and
is not in the interest of shareholders. More commonly, ¬rms make bad investments, and fall
delistings.
in value to the point where they are delisted from the exchange and/or go into bankruptcy.
Fortunately, investors enjoy limited liability, which means that they can at most lose their
investments and do not have to pay for any further sins of management.




Anecdote: Trading Volume in the Tech Bubble
During the Tech bubble of 1999 and 2000, IPO underpricing reached one-day returns of 65% on average. Getting
an IPO share allocation was like getting free money. Of course, ordinary investors rarely received any such share
allocations”only the underwriter™s favorite clients did. This later sparked a number of lawsuits, one of which
revealed that Credit Suisse First Boston (CSFB) allocated shares of IPOs to more than 100 customers who, in
return for IPO allocations, funneled between 33 and 65 percent of their IPO pro¬ts back to CSFB in the form of
excessive trading of other stocks (like Compaq and Disney) at in¬‚ated trading commissions.
How important was this “kickback” activity? In the aggregate, in 1999 and 2000, underwriters left about $66
billion on the table for their ¬rst-day IPO buyers. If investors rebated 20 percent back to underwriters in the
form of extra commissions, this would amount to $13 billion in excessive underwriter pro¬ts. At an average
commission of 10 cents per share, this would require 130 billion shares traded, or an average of 250 million
shares per trading day. This ¬gure suggests that kickback portfolio churning may have accounted for as much
as 10 percent of all shares traded.
Source: Ritter-Welch (2002).
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291
Section 12·2. Equities Transaction Costs.

Solve Now!
Q 12.1 What are the two main functions of brokerage ¬rms?


Q 12.2 How does a prime broker di¬er from a retail broker?


Q 12.3 What is a specialist? What is a market-maker? When trading, what advantage do the
two have over you?


Q 12.4 Describe some alternatives to the main exchanges.


Q 12.5 Describe some mechanisms by which more shares appear and disappear in the market.

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