You have estimated the following probability distributions of expected future re

Question

You have estimated the following probability distributions of expected future returns for Stocks X and Y:

Stock X                                   Stock Y

Probability       Return                         Probability       Return

.1                     -10%                            .2                     2%

.2                     10                                .2                     7

.4                     15                                .3                     12

.2                     20                                .2                     15

.1                     40                                .1                     16

a. What is the expected rate of return for Stock X? Stock Y?

b. What is the standard deviation of expected returns for Stock X? For Stock Y?

c. Which stock would you consider to be riskier? Why?

Explanation / Answer

X Y Prob Return (x) Prob Return (y) 0.1 -10% 0.2 2% 0.2 10% 0.2 7% 0.4 15% 0.3 12% 0.2 20% 0.2 15% 0.1 40% 0.1 16% Expected rate of return 15.000% 10.000% Prob {x-E(x)}^2 Prob {y-E(y)}^2 0.1 6.25% 0.2 0.64% 0.2 0.25% 0.2 0.09% 0.4 0.00% 0.3 0.04% 0.2 0.25% 0.2 0.25% 0.1 6.25% 0.1 0.36% Standard deviation = sqrt(Expected value of (Ex - x)^2)) 11.62% 4.94% Stock X is riskier since its std dev is higher (answer c)

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