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
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 permissi
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 pe
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 vari
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
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
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.
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
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 i
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
incre
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
Tr
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
Investme
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
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
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
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 co
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 wo
$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
h
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 Indus
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
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 sto
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
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 ris
= 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) an
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 gol
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 marke
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
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 mil
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-fre