132 CHAPTER 3 Risk and ReturnrMrequired rate of return on a portfolio consisting
of all stocks, which is called the market portfolio.
rMis also the required rate of return on an aver-
age (bA1.0) stock.
RPM(rMrRF) risk premium on “the market,” and also on an
average (b 1.0) stock. This is the additional
return over the risk-free rate required to com-
pensate an average investor for assuming an aver-
age amount of risk. Average risk means a stock
whose bibA1.0.
RPi(rMrRF)bi(RPM)birisk premium on the ith stock. The stock’s risk
premium will be less than, equal to, or greater
than the premium on an average stock, RPM, de-
pending on whether its beta is less than, equal to,
or greater than 1.0. If bi bA 1.0, then
RPiRPM.The market risk premium, RPM, shows the premium investors require for bear-
ing the risk of an average stock, and it depends on the degree of risk aversion that
investors on average have.^13 Let us assume that at the current time, Treasury bonds
yield rRF6% and an average share of stock has a required return of rM11%.
Therefore, the market risk premium is 5 percent:
RPMrMrRF11% 6% 5%.
It follows that if one stock were twice as risky as another, its risk premium would be
twice as high, while if its risk were only half as much, its risk premium would be half as
large. Further, we can measure a stock’s relative riskiness by its beta coefficient.
Therefore, the risk premium for the ith stock is:
Risk premium for Stock i RPi(RPM)bi (3-8)
If we know the market risk premium, RPM, and the stock’s risk as measured by its beta
coefficient, bi, we can find the stock’s risk premium as the product (RPM)bi. For exam-
ple, if bi0.5 and RPM5%, then RPiis 2.5 percent:
RPi(5%)(0.5)
2.5%.
As the discussion in Chapter 1 implied, the required return for any investment can
be expressed in general terms as
Required return Risk-free return Premium for risk.
Here the risk-free return includes a premium for expected inflation, and we assume
that the assets under consideration have similar maturities and liquidity. Under these
conditions, the relationship between the required return and risk is called the
Security Market Line (SML)(^13) It should be noted that the risk premium of an average stock, rMrRF, cannot be measured with great
precision because it is impossible to obtain precise values for the expected future return on the market, rM.
However, empirical studies suggest that where long-term U.S. Treasury bonds are used to measure rRFand
where rMis an estimate of the expected (not historical) return on the S&P 500 Industrial Stocks, the market
risk premium varies somewhat from year to year, and it has generally ranged from 4 to 6 percent during the
last 20 years.