CP

108 CHAPTER 3 Risk and Return

the riskiness of the stock. To calculate the standard deviation, we proceed as shown in

Table 3-3, taking the following steps:

1. Calculate the expected rate of return:

For Martin, we previously found r ˆ
15%.

2. Subtract the expected rate of return (r) from each possible outcome (rˆ i) to obtain a
   set of deviations aboutr as shown in Column 1 of Table 3-3:ˆ
   Deviationi
   rir.ˆ

Expected rate of return
ˆr
(^) a
n
i
1
Piri.
FIGURE 3-2 Continuous Probability Distributions of Martin Products’
and U.S. Water’s Rates of Return
Probability Density
U.S. Water
Martin Products
–70 0 15 100
Expected
Rate of Return
Rate of Return
(%)
Note: The assumptions regarding the probabilities of various outcomes have been changed from those in Figure
3-1. There the probability of obtaining exactly 15 percent was 40 percent; here it is much smallerbecause there are
many possible outcomes instead of just three. With continuous distributions, it is more appropriate to ask what the
probability is of obtaining at least some specified rate of return than to ask what the probability is of obtaining ex-
actly that rate. This topic is covered in detail in statistics courses.
TABLE 3-3 Calculating Martin Products’ Standard Deviation
riˆr(rir)ˆ^2 (riˆr)^2 Pi
(1) (2) (3)
100  15
85 7,225 (7,225)(0.3)
2,167.5
15  15
0 0 (0)(0.4)
0.0
 70  15
 85 7,225 (7,225)(0.3)
2,167.5
Variance
^2
4,335.0
Standard deviation

2 ^2
2 4,335
65.84%.

106 Risk and Return