252 Part 3 Financial Assets
returns, analysts often look to historical data to estimate the market risk premium.
Historical data suggest that the market risk premium varies somewhat from year
to year due to changes in investors’ risk aversion but that it has generally ranged
from 4% to 8%.
While historical estimates might be a good starting point for estimating the
market risk premium, those estimates would be misleading if investors’ attitudes
toward risk changed considerably over time. (See “Estimating the Market Risk
Premium” box above.) Indeed, many analysts have argued that the market risk
premium has fallen in recent years. If this claim is correct, the market risk pre-
mium is considerably lower than one based on historical data.
The risk premium on individual stocks varies in a systematic manner from the
market risk premium. For example, if one stock is twice as risky as another stock
as measured by their beta coef" cients, its risk premium should be twice as high.
Therefore, if we know the market risk premium, RPM, and the stock’s beta, bi, we
can " nd its risk premium as the product (RPM)bi. For example, if beta for Stock L $
0.5 and RPM $ 5%, RPL will be 2.5%:8-6 Risk premium for Stock L " RPi " (RPM)bi
" (5%)(0.5)
" 2.5%The Capital Asset Pricing Model (CAPM) is more than a theory
describing the trade-o" between risk and return—it is also
widely used in practice. As we will see later, investors use the
CAPM to determine the discount rate for valuing stocks and
corporate managers use it to estimate the cost of equity
capital.
The market risk premium is a key component of the
CAPM, and it should be the di" erence between the expected
future return on the overall stock market and the expected
future return on a riskless investment. However, we cannot
obtain investors’ expectations; instead, academicians and
practitioners often use a historical risk premium as a proxy
for the expected risk premium. The historical premium is
found by taking the di" erence between the actual return on
the overall stock market and the risk-free rate during a num-
ber of di" erent years and then averaging the annual results.
Morningstar (through its recent purchase of Ibbotson Asso-
ciates) may provide the most comprehensive estimates of
historical risk premiums. It reports that the annual premiums
have averaged 7.1% over the past 82 years.
However, there are three potential problems with his-
torical risk premiums. First, what is the proper number of
years over which to compute the average? Morningstar goes
back to 1926, when good data # rst became available; but
that is an arbitrary choice, and the starting and ending points
make a major di" erence in the calculated premium.Second, historical premiums are likely to be misleading at
times when the market risk premium is changing. To illustrate,
the stock market was very strong from 1995 through 1999, in
part because investors were becoming less risk-averse, which
means that they applied a lower risk premium when they valued
stocks. The strong market resulted in stock returns of about
30% per year; and when bond yields were subtracted from the
high stock returns, the calculated risk premiums averaged
22.3% a year. When those high numbers were added to data
from prior years, they caused the long-run historical risk pre-
mium as reported by Morningstar to increase. Thus, a declin-
ing “true” risk premium led to very high stock returns, which,
in turn, led to an increase in the calculated historical risk pre-
mium. That’s a worrisome result, to say the least.
The third concern is that historical estimates may be
biased upward because they include only the returns of # rms
that have survived—they do not re% ect the losses incurred
on investments in failed # rms. Stephen Brown, William
Goetzmann, and Stephen Ross discussed the implications of
this “survivorship bias” in a 1995 Journal of Finance article.
Putting these ideas into practice, Tim Koller, Marc Goedhart,
and David Wessels recently suggested that survivorship bias
increases historical returns by 1% to 2% a year. Therefore,
they suggest that practitioners subtract 1% to 2% from the
historical estimates to obtain the risk premium used in the
CAPM.Sources: Stocks, Bonds, Bills, and In! ation: (Valuation Edition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008); Stephen J. Brown, William N.
Goetzmann, and Stephen A. Ross, “Survival,” Journal of Finance, Vol. 50, no. 3 (July 1995), pp. 853–873; and Tim Koller, Marc Goedhart, and
David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th edition (New York: McKinsey & Company, 2005).ESTIMATING THE MARKET RISK PREMIUM