Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

V. Risk and Return 12. Some Lessons from

Capital Market History

(^426) © The McGraw−Hill
Companies, 2002
deviation. If we were examining projected future returns, then the procedure would be
different. We describe this procedure in the next chapter.
To illustrate how we calculate the historical variance, suppose a particular investment
had returns of 10 percent, 12 percent, 3 percent, and
9 percent over the last four years.
The average return is (.10 .12 .03
.09)/4 4%. Notice that the return is never
actually equal to 4 percent. Instead, the first return deviates from the average by .10

.04 .06, the second return deviates from the average by .12
.04 .08, and so on.
To compute the variance, we square each of these deviations, add them up, and divide
the result by the number of returns less 1, or 3 in this case. Most of this information is
summarized in the table below.
In the first column, we write down the four actual returns. In the third column, we cal-
culate the difference between the actual returns and the average by subtracting out
CHAPTER 12 Some Lessons from Capital Market History 397

FIGURE 12.9

16

14

12

10

8

6

4

2

0

Number

of years

Return (%)

–80 –70– 60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 70 80 90

11

2

4

13

11

13

12

13

3

2

Source: © Stocks, Bonds, Bills, and Inflation 2001 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G.

Ibbotson and Rex A. Sinquefield). All rights reserved.

Frequency Distribution of Returns on Large-Company Stocks: 1926–2000

For an easy-to-

read review of basic

stats, check out

http://www.robertniles.com/

stats.

(1) (2) (3) (4)

Actual Average Deviation Squared

Return Return (1) 
(2) Deviation

.10 .04 .06 .0036

.12 .04 .08 .0064

.03 .04 
.01 .0001


.09 .04 
.13 .0169

Totals .16 .00 .0270