lot of potentially relevant information. If you are in the business of
throwing grenades, you need some measure of the variation around
the average fuse time.5 Similarly, if you are in the business of
investing in securities, you need some measure of how
0
5
10
15
20
25
Source: Stocks, Bonds, Bills and Inflation 1999 Yearbook, 1999
Ibbotson Associates, Inc. Based on copyrighted works by Ibbotson and
Sinquefield. All Rights Reserved. Used with permission.
Introduction to Risk, Return, and the Opportunity C
9 Lets confirm this. Suppose you invest $7,500 in autos and $2,500 in
gold. If the recession hits, the rate of return on autos will be 8
percent, and the value of the auto investment will fall by 8 percent to
$6,900. The rate of return on gold will be 20
We can calculate variance by weighting each squared deviation by the
probability and then summing the results. Table 9.3 confirms that this
method gives the same answer.
Self-Test 3 Calculate the variance and standard deviation of this
second coin-tossing
the other hand, are two industries with less than average macro
exposures: Food companies. Companies selling staples, such as
breakfast cereal, flour, and dog food, find that demand for their
products is relatively stable in good times and bad. Electric u
and an ice cream shop. By diversifying your investment across the two
businesses you make an average level of profit come rain or shine.
ASSET VERSUS PORTFOLIO RISK The history of returns on
different asset classes provides compelling evidence of a riskre
and received a higherthan-expected return. By averaging the returns
across both the rough years and the smooth, we should get a fair idea
of the typical return that investors might justifiably expect. While
common stocks have offered the highest average r
project. Micro risks wash out in diversified portfolios. Company
managers may worry about both macro and micro risks, but only the
former affect the cost of capital.
334 SECTION THREE
Summary
How can one estimate the opportunity cost of capital for an ave
the average performance of investors in the 500 firms. Only a small
proportion of the 9,000 or so publicly traded companies are
represented in the S&P 500. However, these firms are among the
largest in the country and they account for roughly 70 percent o
calculated. Suppose that you are offered the chance to play the
following game. You start by investing $100. Then two coins are
flipped. For each head that comes up your starting balance will be
increased by 20 percent, and for each tail that comes up you
Self-Test 2 Here are the average rates of return for the postwar period
19501998:
Stocks 14.7% Treasury bonds 6.4 Treasury bills 5.2
What were the risk premium on stocks and the maturity premium on
Treasury bonds for this period?
USING HISTORICAL EVIDENCE
Other Investment Criteria Internal Rate of Return
A Closer Look at the Rate of Return Rule
Calculating the Rate of Return for Long-Lived Projects
A Word of Caution
Payback
Book Rate of Return
Investment Criteria When Projects Interact Mutually Exclusive
P
FIGURE 3.17 The variability of a portfolio with equal holdings in
Merck and Ford Motor would have been only 70 percent of the
variability of the individual stocks.
20 15 10 5 0 5 10 15 20 25 30 Merck return, percent 25 30
1 4 7 10 13 16 19 22 25 28 31 34
standard deviations look high to you? They should. Remember that the
market portfolios standard deviation was about 20 percent over the
entire 19261998 period. Of our individual stocks only Exxon had a
standard deviation of less than 20 percent. Most stoc
7. CAPM and Expected Return. If the risk-free rate is 6 percent and
the expected rate of return on the market portfolio is 14 percent, is a
security with a beta of 1.25 and an expected rate of return of 16
percent overpriced or underpriced? 8. Using Beta.
Long-term Treasury bonds
Treasury bills
Common stocks (S&P 500)
10,000.0
1,000.0
100.0
10.0
1.0
0.1
Source: Stocks, Bonds, Bills and Inflation 1999 Yearbook, 1999
Ibbotson Associates, Inc. Based on copyrighted works by Ibbotson and
Sinquefield. All Rights
Stock Standard Deviation, % Biogen 46.6 Compaq 46.7 Delta Airlines
26.9 Exxon 16.0 Ford Motor Co. 24.9 MCI WorldCom 34.4 Merck
24.5 Microsoft 34.0 PepsiCo 26.5 Xerox 27.3
326 SECTION THREE
simply the average of the three possible outcomes.8 For the auto s
about the same as that of Merck. Again you can see that in about a
third of the cases the return differed from the average by more than
one standard deviation. An investment in either Merck or Ford would
have been very variable. But the fortunes of the tw
$400,000 1 = $400,000 .935 = $373,832 1.07 Therefore, at an
interest rate of 7 percent, the present value of the $400,000 payoff
from the office building is $373,832. Lets assume that as soon as you
have purchased the land and laid out the money for const
a. What was the risk premium on the S&P 500 in each year? b. What
was the average risk premium? c. What was the standard deviation of
the risk premium?
10. Market Indexes. In 1990, the Dow Jones Industrial Average was at
a level of about 2,600. In early 2
investors might reasonably expect from investments in different types
of securities and of the risks that they face. Let us look, therefore, at
the risks and returns that investors have experienced in the past.
314 SECTION THREE
MARKET INDEXES Investors c
Therefore, Table 3.13 lists the annual standard deviations for our
three portfolios of securities over the period 19261998. As expected,
Treasury bills were the least variable security, and common stocks
were the most variable. Treasury bonds hold the mid
deviation is 10.6 percent. Well compare that portfolio to a partially
diversified one, invested 75 percent in autos and 25 percent in gold.
For example, if you have a $10,000 portfolio, you could put $7,500 in
autos and $2,500 in gold. First, we need to c
Even if you hold a well-diversified portfolio, you will not eliminate all
risk. You will still be exposed to macroeconomic changes that affect
most stocks and the overall stock market. These macro risks combine
to create market riskthat is, the risk that
= interest rate on Treasury bills (1999) + normal risk premium = 4.8 +
9.4 = 14.2%
The expected return on an investment provides compensation to
investors both for waiting (the time value of money) and for worrying
(the risk of the particular asset).
3Thi
The variance is
[.3 (8 5)2] + [.4 (5 5)2] + [.3 (18 5)2] = 101.4 The standard
deviation is 101.4 = 10.07 percent, which is lower than the value
assuming equal probabilities of each scenario. 5 The gold mining
stocks returns are more highly correlated with
Investors demand higher expected rates of return from stocks with
returns that are very sensitive to fluctuations in the stock market.
2. Diversifiable Risk. In light of what youve learned about market
versus diversifiable (unique) risks, explain why an i
Treasury bonds issued by the U.S. government and maturing in about
20 years. 3. A portfolio of stocks of the 500 large firms that make up
the Standard & Poors Composite Index. These portfolios are not
equally risky. Treasury bills are about as safe an inv
30. Leverage and Portfolio Risk.Footnote 4 in the material asks you to
consider a borrow-andinvest strategy in which you use $1 million of
your own money and borrow another $1 million to invest $2 million in
a market index fund. If the risk-free interest
deviation of the market portfolios return is 20 percent. e. What is the
expected rate of return on each stock? Use the capital asset pricing
model with a market risk premium of 8 percent. The risk-free rate of
interest is 4 percent.
10. Calculating Beta.