Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

V. Risk and Return 13. Return, Risk, and the

Security Market Line

(^462) © The McGraw−Hill
Companies, 2002
suppose that the risk-free rate is Rf8%. Notice that a risk-free asset, by definition, has
no systematic risk (or unsystematic risk), so a risk-free asset has a beta of zero.
Beta and the Risk Premium
Consider a portfolio made up of Asset A and a risk-free asset. We can calculate some
different possible portfolio expected returns and betas by varying the percentages in-
vested in these two assets. For example, if 25 percent of the portfolio is invested in As-
set A, then the expected return is:
E(RP) .25 E(RA) (1
.25) Rf
.25 20% .75 8%
11%
Similarly, the beta on the portfolio, (^) P, would be:
(^) P.25 
A(1
.25)  0
.25 1.6
.40
Notice that, because the weights have to add up to 1, the percentage invested in the risk-
free asset is equal to 1 minus the percentage invested in Asset A.
One thing that you might wonder about is whether or not it is possible for the per-
centage invested in Asset A to exceed 100 percent. The answer is yes. This can happen
if the investor borrows at the risk-free rate. For example, suppose an investor has $100
and borrows an additional $50 at 8 percent, the risk-free rate. The total investment in
Asset A would be $150, or 150 percent of the investor’s wealth. The expected return in
this case would be:
E(RP) 1.50 E(RA) (1
1.50) Rf
1.50 20%
.50 8%
26%
The beta on the portfolio would be:
(^) P1.50 
A(1
1.50)  0
1.50 1.6
2.4
We can calculate some other possibilities, as follows:
In Figure 13.2A, these portfolio expected returns are plotted against the portfolio betas.
Notice that all the combinations fall on a straight line.
Percentage of Portfolio Portfolio Portfolio
in Asset A Expected Return Beta
0% 8% .0
25 11 .4
50 14 .8
75 17 1.2
100 20 1.6
125 23 2.0
150 26 2.4
434 PART FIVE Risk and Return