Principles of Managerial Finance

CHAPTER 5 Risk and Return 225

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EXAMPLE When the standard deviations (from Table 5.5) and the expected returns (from

Table 5.4) for assets A and B are substituted into Equation 5.4, the coefficients of

variation for A and B are 0.094 (1.41% 15%) and 0.377 (5.66% 15%),

respectively. Asset B has the higher coefficient of variation and is therefore more

risky than asset A—which we already know from the standard deviation.

(Because both assets have the same expected return, the coefficient of variation

has not provided any new information.)

The real utility of the coefficient of variation comes in comparing the risks of

assets that have differentexpected returns.

EXAMPLE A firm wants to select the less risky of two alternative assets—X and Y. The

expected return, standard deviation, and coefficient of variation for each of these

assets’ returns are

Judging solely on the basis of their standard deviations, the firm would prefer

asset X, which has a lower standard deviation than asset Y (9% versus 10%).

However, management would be making a serious error in choosing asset X over

asset Y, because the dispersion—the risk—of the asset, as reflected in the coeffi-

cient of variation, is lower for Y (0.50) than for X (0.75). Clearly, using the coef-

ficient of variation to compare asset risk is effective because it also considers the

relative size, or expected return, of the assets.

Review Questions

5–4 Explain how the rangeis used in sensitivity analysis.

5–5 What does a plot of the probability distributionof outcomes show a deci-

sion maker about an asset’s risk?

5–6 What relationship exists between the size of the standard deviationand

the degree of asset risk?

5–7 When is the coefficient of variationpreferred over the standard deviation

for comparing asset risk?

5.3 Risk of a Portfolio

In real-world situations, the risk of any single investment would not be viewed

independently of other assets. (We did so for teaching purposes.) New invest-

ments must be considered in light of their impact on the risk and return of the

Statistics Asset X Asset Y

(1) Expected return 12% 20%

(2) Standard deviation 9%a 10%

(3) Coefficient of variation [(2) (1)] 0.75 0.50a

aPreferred asset using the given risk measure.