Stock X and Y have the following probability distributions of expected future re

Question

Stock X and Y have the following probability distributions of expected future returns.
Probability                X                    Y

0.1                          (10%)          (35%)

0.2                             2               0    

0.4                            12              20  

0.2                            20              25

0.1                            38              45

a) Calculate the expected rate of return, rˆY, for Stock Y (rˆX=12%).

b) Calculate the standard deviation of expected returns, X, for Stock X ( Y=20.35%). Now calculate the coefficient of variation for Stock Y. Is it possible that most investors will regard Stock Y as being less risky than Stock X ? Explain.

Explanation / Answer

a.

Expected Rate of Return Y = Probability * Future expected returns of stock Y

Expected Rate of Return Y = 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%) =14%

b.X^2 =[ E(r)X -E(r)Y]^2 * probability

X^2 = (-10% - 12%)^2(0.1) + (2% - 12%)^2(0.2) + (12% - 12%)^2(0.4)+ (20% - 12%)^2(0.2) + (38% - 12%)^2(0.1) = 148.8%.

X = 12.20%

CVX = X/R X = 12.20%/12% = 1.02, while

CVY = 20.35%/14% = 1.45.

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

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