Chapter 8 Risk and Rates of Return 2518-4 THE RELATIONSHIP BETWEEN RISK AND
RATES OF RETURN
The preceding section demonstrated that under the CAPM theory, beta is the most
appropriate measure of a stock’s relevant risk. The next issue is this: For a given
level of risk as measured by beta, what rate of return is required to compensate
investors for bearing that risk? To begin, let us de" ne the following terms:
rˆi $ expected rate of return on the ith stock.
ri $ required rate of return on the ith stock. Note that if rˆi is less than ri, the typi-
cal investor will not purchase this stock or will sell it if he or she owns it.
If rˆi is greater than ri, the investor will purchase the stock because it looks
like a bargain. Investors will be indifferent if rˆi $ ri. Buying and selling by
investors tends to force the expected return to equal the required return,
although the two can differ from time to time before the adjustment is
completed.- r $ realized, after-the-fact return. A person obviously does not know r– at the
time he or she is considering the purchase of a stock.
rRF $ risk-free rate of return. In this context, rRF is generally measured by the
return on U.S. Treasury securities. Some analysts recommend that short-
term T-bills be used; others recommend long-term T-bonds. We gener-
ally use T-bonds because their maturity is closer to the average investor’s
holding period of stocks.
bi $ beta coef" cient of the ith stock. The beta of an average stock is bA $ 1.0.
rM $ required rate of return on a portfolio consisting of all stocks, which is
called the market portfolio. rM is also the required rate of return on an aver-
age (bA $ 1.0) stock.
RPM $ (rM – rRF) $ risk premium on “the market” and the premium on an aver-
age stock. This is the additional return over the risk-free rate required to
compensate an average investor for assuming an average amount of
risk. Average risk means a stock where bi $ bA $ 1.0.
RPi $ (rM – rRF)bi $ (RPM)bi $ risk premium on the ith stock. A stock’s risk
premium will be less than, equal to, or greater than the premium on an
average stock, RPM, depending on whether its beta is less than, equal to,
or greater than 1.0. If bi $ bA $ 1.0, then RPi $ RPM.
The market risk premium, RPM, shows the premium that investors require for
bearing the risk of an average stock. The size of this premium depends on how
risky investors think the stock market is and on their degree of risk aversion. Let
us assume that at the current time, Treasury bonds yield rRF $ 6% and an average
share of stock has a required rate of return of rM $ 11%. Therefore, the market risk
premium is 5%, calculated as follows:
RPM " rM # rRF " 11% # 6% " 5%
It should be noted that the risk premium of an average stock, rM! rRF , is actually
hard to measure because it is impossible to obtain a precise estimate of the expected
future return of the market, rM.^22 Given the dif" culty of estimating future market
Market Risk Premium,
RPM
The additional return over
the risk-free rate needed to
compensate investors for
assuming an average
amount of risk.Market Risk Premium,
RPM
The additional return over
the risk-free rate needed to
compensate investors for
assuming an average
amount of risk.(^22) This concept, as well as other aspects of the CAPM, is discussed in more detail in Chapter 3 of Eugene F.
Brigham and Philip R. Daves, Intermediate Financial Management, 9th ed., (Mason, OH: Thomson/South-Western,
2007). That chapter also discusses the assumptions embodied in the CAPM framework. Some of those
assumptions are unrealistic; and because of this, the theory does not hold exactly.