Principles of Managerial Finance

coefficient of variation (CV)
A measure of relative dispersion
that is useful in comparing the
risks of assets with differing
expected returns.

224 PART 2 Important Financial Concepts

95%

99%

0

Return (%)

Probability Density

–3σk –2σk –1σk k +1σk +2σk +3σk

68%

FIGURE 5.4

Bell-Shaped Curve
Normal probability distribu-
tion, with ranges

11. Tables of values indicating the probabilities associated with various deviations from the expected value of a nor-
    mal distribution can be found in any basic statistics text. These values can be used to establish confidence limits and
    make inferences about possible outcomes. Such applications can be found in most basic statistics and upper-level
    managerial finance textbooks.

normal probability distribution
A symmetrical probability distri-
bution whose shape resembles a
“bell-shaped” curve.

Normal Distribution A normal probability distribution,depicted in Figure

5.4, always resembles a “bell-shaped” curve. It is symmetrical: From the peak of

the graph, the curve’s extensions are mirror images (reflections) of each other.

The symmetry of the curve means that half the probability is associated with the

values to the left of the peak and half with the values to the right. As noted on the

figure, for normal probability distributions, 68 percent of the possible outcomes

will lie between 1 standard deviation from the expected value, 95 percent of all

outcomes will lie between 2 standard deviations from the expected value, and

99 percent of all outcomes will lie between 3 standard deviations from the

expected value.^11

EXAMPLE If we assume that the probability distribution of returns for the Norman Company

is normal, 68% of the possible outcomes would have a return ranging between

13.59 and 16.41% for asset A and between 9.34 and 20.66% for asset B; 95% of

the possible return outcomes would range between 12.18 and 17.82% for asset A

and between 3.68 and 26.32% for asset B; and 99% of the possible return outcomes

would range between 10.77 and 19.23% for asset A and between 1.98 and

31.98% for asset B. The greater risk of asset B is clearly reflected in its much wider

range of possible returns for each level of confidence (68%, 95%, etc.).

Coefficient of Variation

The coefficient of variation,CV,is a measure of relative dispersion that is useful

in comparing the risks of assets with differing expected returns. Equation 5.4

gives the expression for the coefficient of variation:

CV (5.4)

The higher the coefficient of variation, the greater the risk.

k



k