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

© The McGraw−Hill^447

Companies, 2002

Stock L has a higher expected return, but U has less risk. You could get a 70 percent re-
turn on your investment in L, but you could also lose 20 percent. Notice that an invest-
ment in U will always pay at least 10 percent.
Which of these two stocks should you buy? We can’t really say; it depends on your
personal preferences. We can be reasonably sure that some investors would prefer L to
U and some would prefer U to L.
You’ve probably noticed that the way we have calculated expected returns and vari-
ances here is somewhat different from the way we did it in the last chapter. The reason
is that in Chapter 12, we were examining actual historical returns, so we estimated the
average return and the variance based on some actual events. Here, we have projected
futurereturns and their associated probabilities, so this is the information with which we
must work.

CHAPTER 13 Return, Risk, and the Security Market Line 419

TABLE 13.4

Calculation of Variance

(2) (3) (4)

(1) Probability Return Deviation Squared Return (5)

State of of State from Expected Deviation from Product

Economy of Economy Return Expected Return (2) (4)

Stock L

Recession .50 
.20 
.25 
.45 
.45^2 .2025 .10125

Boom .50 .70 
.25  .45 .45^2 .2025 .10125

(^2) L.2025
Stock U
Recession .50 .30
.20  .10 .10^2 .01 .005
Boom .50 .10
.20 
.10
.10^2 .01 .005
(^2) U.010
More Unequal Probabilities
Going back to Example 13.1, what are the variances on the two stocks once we have unequal
probabilities? The standard deviations?
We can summarize the needed calculations as follows:
Based on these calculations, the standard deviation for L is (^) L.36 36%. The
standard deviation for U is much smaller, (^) U.0064 .08 or 8%.
.1296
EXAMPLE 13.2
(2) (3) (4)
(1) Probability Return Deviation Squared Return (5)
State of of State from Expected Deviation from Product
Economy of Economy Return Expected Return (2) (4)
Stock L
Recession .80
.20
(
.02) 
.18 .0324 .02592
Boom .20 .70
(
.02)  .72 .5184 .10368
(^2) L.12960
Stock U
Recession .80 .30
.26  .04 .0016 .00128
Boom .20 .10
.26 
.16 .0256 .00512
(^2) U.00640