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sults in a value-weighted portfolio, which, for example, invests a proportion in GM stock that
equals the ratio of GM™s market value to the market value of all listed stocks.
Such strategies are called indexing. The investor chooses a portfolio with all the stocks in
a broad market index such as the Standard & Poor™s 500 index. The rate of return on the port-
folio then replicates the return on the index. Indexing has become an extremely popular strat-
egy for passive investors. We call the capital allocation line provided by one-month T-bills
capital market and a broad index of common stocks the capital market line (CML). That is, a passive strat-
line egy based on stocks and bills generates an investment opportunity set that is represented by
the CML.
The capital allocation
line using the market
index portfolio as the
Historical Evidence on the Capital Market Line
risky asset.

Can we use past data to help forecast the risk-return trade-off offered by the CML? The notion
that one can use historical returns to forecast the future seems straightforward but actually is
somewhat problematic. On one hand, you wish to use all available data to obtain a large sam-
ple. But when using long time series, old data may no longer be representative of future cir-
cumstances. Another reason for weeding out subperiods is that some past events simply may
be too improbable to be given equal weight with results from other periods. Do the data we
have pose this problem?
Table 5.5 breaks the 76-year period, 1926“2001 into four subperiods and shows the risk
premium, standard deviation, and reward-to-variability ratio for each subperiod. That ratio is
Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition

Triumph of the Optimists
As a whole, the last 7 decades have been very kind Table 5.1 would seem to indicate. First, results from the
to U.S. equity investors. Stock investments have out- first 25 years of the last century (which included the
performed investments in safe Treasury bills by more first World War) were less favorable to stocks. Second,
than 8% per year. The real rate of return averaged U.S. returns have been better than that of most other
more than 9%, implying an expected doubling of countries, and so a more representative value for the
the real value of the investment portfolio about every historical risk premium may be lower than the U.S. ex-
8 years! perience. Finally, the sample that is amenable to his-
Is this experience representative? A new book by torical analysis suffers from a self-selection problem.
three professors at the London Business School, Elroy Only those markets that have survived to be studied
Dimson, Paul Marsh, and Mike Staunton, extends the can be included in the analysis. This leaves out coun-
U.S. evidence to other countries and to longer time tries such as Russia or China, whose markets were shut
periods. Their conclusion is given in the book™s title, down during communist rule, and whose results if
Triumph of the Optimists*: in every country in their included would surely bring down the average perfor-
study (which included markets in North America, Eu- mance of equity investments. Nevertheless, there is
rope, Asia, and Africa), the investment optimists”those powerful evidence of a risk premium that shows its
who bet on the economy by investing in stocks rather force everywhere the authors looked.
than bonds or bills”were vindicated. Over the long
haul, stocks beat bonds everywhere. *Elroy Dimson, Paul Marsh, Mike Staunton, Triumph of the Optimists:
On the other hand, the equity risk premium is prob- 101 Years of Global Investment Returns. Princeton University Press,
ably not as large as the post-1926 evidence from Princeton, N.J.: 2002.

the slope of the CML based on the subperiod data. Indeed, the differences across subperiods
are quite striking.
The most plausible explanation for the variation in subperiod returns is based on the
observation that the standard deviation of returns is quite large in all subperiods. If we take
the 76-year standard deviation of 20.3% as representative and assume that returns in one year
are nearly uncorrelated with those in other years (the evidence suggests that any correlation
across years is small), then the standard deviation of our estimate of the mean return in any of
our 19-year subperiods will be 20.3/ 19 4.7% , which is fairly large. This means that in
approximately one out of three cases, a 19-year average will deviate by 4.7% or more from the
true mean. Applying this insight to the data in Table 5.5 tells us that we cannot reject with any
confidence the possibility that the true mean is similar in all subperiods! In other words, the
“noise” in the data is so large that we simply cannot make reliable inferences from average re-
turns in any subperiod. The variation in returns across subperiods may simply reflect statisti-
cal variation, and we have to reconcile ourselves to the fact that the market return and the
reward-to-variability ratio for passive (as well as active!) strategies is simply very hard to
The instability of average excess return on stocks over the 19-year subperiods in Table 5.5
also calls into question the precision of the 76-year average excess return (8.64%) as an esti-
mate of the risk premium on stocks looking into the future. In fact, there has been consider-
able recent debate among financial economists about the “true” equity risk premium, with an
emerging consensus that the historical average is an unrealistically high estimate of the future
risk premium. This argument is based on several factors: the use of longer time periods in

Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition

158 Part TWO Portfolio Theory

which equity returns are examined; a broad range of countries rather than just the U.S. in
which excess returns are computed (Dimson, Marsh, and Staunton, 2001); direct surveys of
financial executives about their expectations for stock market returns (Graham and Harvey,
2001); and inferences from stock market data about investor expectations (Jagannathan,
McGrattan, and Scherbina, 2000; Fama and French, 2002). The nearby box discusses some of
this evidence.

Costs and Benefits of Passive Investing
How reasonable is it for an investor to pursue a passive strategy? We cannot answer such a
question definitively without comparing passive strategy results to the costs and benefits ac-
cruing to an active portfolio strategy. Some issues are worth considering, however.
First, the alternative active strategy entails costs. Whether you choose to invest your own
valuable time to acquire the information needed to generate an optimal active portfolio of
risky assets or whether you delegate the task to a professional who will charge a fee, con-
structing an active portfolio is more expensive than constructing a passive one. The passive
portfolio requires only small commissions on purchases of U.S. T-bills (or zero commissions
if you purchase bills directly from the government) and management fees to a mutual fund
company that offers a market index fund to the public. An index fund has the lowest operating
expenses of all mutual stock funds because it requires minimal effort.
A second argument supporting a passive strategy is the free-rider benefit. If you assume
there are many active, knowledgeable investors who quickly bid up prices of undervalued as-
sets and offer down overvalued assets (by selling), you have to conclude that most of the time
most assets will be fairly priced. Therefore, a well-diversified portfolio of common stock will
be a reasonably fair buy, and the passive strategy may not be inferior to that of the average ac-
tive investor. We will expand on this insight and provide a more comprehensive analysis of the
relative success of passive strategies in Chapter 8.
To summarize, a passive strategy involves investment in two passive portfolios: virtually
risk-free short-term T-bills (or a money market fund) and a fund of common stocks that mim-
ics a broad market index. Recall that the capital allocation line representing such a strategy is
called the capital market line. Using Table 5.5, we see that using 1926 to 2001 data, the pas-
sive risky portfolio has offered an average excess return of 8.6% with a standard deviation of
20.7%, resulting in a reward-to-variability ratio of 0.42.

SUMMARY • Investors face a trade-off between risk and expected return. Historical data confirm our
intuition that assets with low degrees of risk provide lower returns on average than do
those of higher risk.
• Shifting funds from the risky portfolio to the risk-free asset is the simplest way to reduce

risk. Another method involves diversification of the risky portfolio. We take up
diversification in later chapters.
• U.S. T-bills provide a perfectly risk-free asset in nominal terms only. Nevertheless, the
standard deviation of real rates on short-term T-bills is small compared to that of assets
such as long-term bonds and common stocks, so for the purpose of our analysis, we
consider T-bills the risk-free asset. Besides T-bills, money market funds hold short-term,
safe obligations such as commercial paper and CDs. These entail some default risk but
relatively little compared to most other risky assets. For convenience, we often refer to
money market funds as risk-free assets.
• A risky investment portfolio (referred to here as the risky asset) can be characterized by its
reward-to-variability ratio. This ratio is the slope of the capital allocation line (CAL), the
Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition

5 Risk and Return: Past and Prologue

line connecting the risk-free asset to the risky asset. All combinations of the risky and risk-
free asset lie on this line. Investors would prefer a steeper sloping CAL, because that
means higher expected returns for any level of risk. If the borrowing rate is greater than
the lending rate, the CAL will be “kinked” at the point corresponding to an investment of
100% of the complete portfolio in the risky asset.
• An investor™s preferred choice among the portfolios on the capital allocation line will
depend on risk aversion. Risk-averse investors will weight their complete portfolios more
heavily toward Treasury bills. Risk-tolerant investors will hold higher proportions of their
complete portfolios in the risky asset.
• The capital market line is the capital allocation line that results from using a passive
investment strategy that treats a market index portfolio, such as the Standard &
Poor™s 500, as the risky asset. Passive strategies are low-cost ways of obtaining
well-diversified portfolios with performance that will reflect that of the broad stock

arithmetic average, 133 expected return, 136 reward-to-variability
asset allocation, 148 geometric average, 133 ratio, 152
capital allocation line, 152 holding-period return, 132 risk aversion, 138
capital market line, 156 inflation rate, 147 risk-free rate, 137
complete portfolio, 149 nominal interest rate, 147 risk premium, 137
dollar-weighted average passive strategy, 156 scenario analysis, 136
return, 134 probability distribution, 136 standard deviation, 136
excess return, 138 real interest rate, 147 variance, 136

1. A portfolio of nondividend-paying stocks earned a geometric mean return of
5.0% between January 1, 1996, and December 31, 2002. The arithmetic mean
return for the same period was 6.0 %. If the market value of the portfolio at the
beginning of 1996 was $100,000, what was the market value of the portfolio at
the end of 2002?
2. Which of the following statements about the standard deviation is/are true? A standard
i. Is the square root of the variance.
ii. Is denominated in the same units as the original data.
iii. Can be a positive or a negative number.
3. Which of the following statements reflects the importance of the asset allocation
decision to the investment process? The asset allocation decision:
a. Helps the investor decide on realistic investment goals.
b. Identifies the specific securities to include in a portfolio.
c. Determines most of the portfolio™s returns and volatility over time.

d. Creates a standard by which to establish an appropriate investment time
4. Look at Table 5.2 in the text. Suppose you now revise your expectations regarding the
stock market as follows:

State of the
Economy Probability HPR
Boom 0.3 44%
Normal growth 0.4 14
Recession 0.3 16
Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition

160 Part TWO Portfolio Theory

Use Equations 5.3“5.5 to compute the mean and standard deviation of the HPR on
stocks. Compare your revised parameters with the ones in the text.
5. The stock of Business Adventures sells for $40 a share. Its likely dividend payout
and end-of-year price depend on the state of the economy by the end of the year as

Dividend Stock Price
Boom $2.00 $50
Normal economy 1.00 43
Recession .50 34

a. Calculate the expected holding-period return and standard deviation of the holding-
period return. All three scenarios are equally likely.
b. Calculate the expected return and standard deviation of a portfolio invested
half in Business Adventures and half in Treasury bills. The return on bills
is 4%.
Use the following data in answering questions 6, 7, and 8.

Utility Formula Data

Expected Standard
Investment Return E(r) Deviation
1 .12 .30
2 .15 .50
3 .21 .16
4 .24 .21

U E(r) 1
„2A where A 4

6. Based on the utility formula above, which investment would you select if you were risk
averse with A 4?
a. 1
b. 2
c. 3
d. 4
7. Based on the utility formula above, which investment would you select if you were risk


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