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

(^446) © The McGraw−Hill
Companies, 2002
Calculating the Variance
To calculate the variances of the returns on our two stocks, we first determine the
squared deviations from the expected return. We then multiply each possible squared
deviation by its probability. We add these up, and the result is the variance. The standard
deviation, as always, is the square root of the variance.
To illustrate, let us return to the Stock U we originally discussed, which has an ex-
pected return of E(RU) 20%. In a given year, it will actually return either 30 percent
or 10 percent. The possible deviations are thus 30%
20% 10% and 10%
20% 

10%. In this case, the variance is:
Variance ^2 .50 (10%)^2 .50 (
10%)^2 .01
The standard deviation is the square root of this:
Standard deviation .10 10%
Table 13.4 summarizes these calculations for both stocks. Notice that Stock L has a
much larger variance.
When we put the expected return and variability information for our two stocks to-
gether, we have:
Stock L Stock U
Expected return, E(R) 25% 20%
Variance, 2 .2025 .0100
Standard deviation, 45% 10%
.01
418 PART FIVE Risk and Return

TABLE 13.3

Calculation of Expected

Return

Stock L Stock U

(3) (5)

(2) Rate of Rate of

(1) Probability Return (4) Return (6)

State of of State of if State Product if State Product

Economy Economy Occurs (2) (3) Occurs (2) (5)

Recession .80 
.20 
.16 .30 .24

Boom .20 .70 .14 .10 .02

E(RL) 
2% E(RU) 26%

percent return in 80 percent of the years and a 10 percent return in 20 percent of the years.

To calculate the expected return, we again just multiply the possibilities by the probabilities

and add up the results:

E(RU) .80 30% .20 10% 26%

Table 13.3 summarizes the calculations for both stocks. Notice that the expected return on L

is 
2 percent.

The risk premium for Stock U is 26% 
10% 16% in this case. The risk premium for

Stock L is negative:
2% 
10% 
12%. This is a little odd, but, for reasons we discuss

later, it is not impossible.