Fundamentals of Financial Management (Concise 6th Edition)

Chapter 8 Risk and Rates of Return 253

As the discussion in Chapter 6 implied, the required return for any stock can be
found as follows:

Required return on a stock " Risk-free return $ Premium for the stock’s risk

Here the risk-free return includes a premium for expected in! ation; and if we
assume that the stocks under consideration have similar maturities and liquidity,
the required return on Stock L can be found using the Security Market Line (SML)
equation:

Requir ed return
on Stock L

(^) " Risk -free
return
(^) $
(
Mark et risk
premium
)
(
Stock L’s
beta
)
rL " rRF $ (rM # rRF)bL 8-7
" rRF $ (RPM)bL
" 6% $ (11% # 6%)(0.5)
" 6% $ 2.5%
" 8.5%
Stock H had bH $ 2.0, so its required rate of return is 16%:
rH " 6% $ (5%)2.0 " 16%
An average stock, with b = 1.0, would have a required return of 11%, the same as
the market return:
rA " 6% $ (5%)1.0 " 11% " rM
The SML equation is plotted in Figure 8-8 using the data shown below the
graph on Stocks L, A, and H and assuming that rRF $ 6% and rM $ 11%. Note the
following points:

1. Required rates of return are shown on the vertical axis, while risk as measured
   by beta is shown on the horizontal axis. This graph is quite different from the
   one shown in Figure 8-7, where we calculated betas. In the earlier graph, the
   returns on individual stocks were plotted on the vertical axis and returns on
   the market index were shown on the horizontal axis. The betas found in Fig-
   ure 8-7 were then plotted as points on the horizontal axis of Figure 8-8.


2. Riskless securities have bi $ 0; so the return on the riskless asset, rRF $ 6.0%, is
   shown as the vertical axis intercept in Figure 8-8.


3. The slope of the SML in Figure 8-8 can be found using the rise-over-run proce-
   dure. When beta goes from 0 to 1.0, the required return goes from 6% to 11%,
   or 5%; so the slope is 5%/1.0 $ 5%. Thus, a 1-unit increase in beta causes a 5%
   increase in the required rate of return.


4. The slope of the SML re! ects the degree of risk aversion in the economy—the
   greater the average investor’s risk aversion, (a) the steeper the slope of the line
   and (b) the greater the risk premium for all stocks—hence, the higher the
   required rate of return on all stocks.

Both the SML and a company’s position on it change over time due to changes in
interest rates, investors’ risk aversion, and individual companies’ betas. Such
changes are discussed in the following sections.

8-4a The Impact of Expected Inflation

As we discussed in Chapter 6, interest amounts to “rent” on borrowed money, or
the price of money. Thus, rRF is the price of money to a riskless borrower. We also

Security Market Line

(SML) Equation

An equation that shows

the relationship between

risk as measured by beta

and the required rates of

return on individual

securities.

Security Market Line

(SML) Equation

An equation that shows

the relationship between

risk as measured by beta

and the required rates of

return on individual

securities.