Principles of Managerial Finance

CHAPTER 5 Risk and Return 223

TABLE 5.5 The Calculation of the Standard Deviation

of the Returns for Assets A and Ba

ikj k kjk (kjk)^2 Prj (kjk)^2 Prj

Asset A

1 13% 15% 2% 4% .25 1%

215 15 0 0 .50 0

317 15 2 4 .25 (^1) 

3
j 1
(kjk)^2 Prj2%
kA

3
j 1
(kjk

)^2 Prj

2% 1

.

4

1

%
Asset B
1 7% 15% 8% 64% .25 16%
215 15 0 0 .50 0
3 23 15 8 64 .25 (^1)  (^6) 

3
j 1
(kjk)^2 Prj32%
kB
3
j 1
(kjk)^2 Prj^32 %^5

.

6

6

%
aCalculations in this table are made in percentage form rather than decimal form—e.g., 13%
rather than 0.13. As a result, some of the intermediate computations may appear to be incon-
sistent with those that would result from using decimal form. Regardless, the resulting stan-
dard deviations are correct and identical to those that would result from using decimal rather
than percentage form.
TABLE 5.6 Historical Returns and Standard
Deviations for Selected Security
Investments (1926–2000)
Investment Average annual return Standard deviation
Large-company stocks 13.0% 20.2%
Small-company stocks 17.3 33.4
Long-term corporate bonds 6.0 8.7
Long-term government bonds 5.7 9.4
U.S. Treasury bills 3.9 3.2
Inflation 3.2% 4.4%
Source: Stocks, Bonds, Bills, and Inflation, 2001 Yearbook(Chicago: Ibbotson Associates,
Inc., 2001).
tionship between risk and return. That relationship reflects risk aversionby mar-
ket participants, who require higher returns as compensation for greater risk. The
historical data in Table 5.6 clearly show that during the 1926–2000 period,
investors were rewarded with higher returns on higher-risk investments.