Expected returns Stocks A and B have the following probability distributions of
ID: 2780441 • Letter: E
Question
Expected returns
Stocks A and B have the following probability distributions of expected future returns:
Calculate the expected rate of return, rB, for Stock B (rA = 14.00%.) Do not round intermediate calculations. Round your answer to two decimal places.
_______%
Calculate the standard deviation of expected returns, A, for Stock A (B = 23.05%.) Do not round intermediate calculations. Round your answer to two decimal places.
______%
Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.________%
Is it possible that most investors might regard Stock B as being less risky than Stock A?
a.If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
b.If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
c.If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
d.If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
e.If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
Probability A B 0.1 -13% -40% 0.2 2 0 0.3 11 19 0.2 18 28 0.2 40 42Explanation / Answer
a.
Expected return is the weighted average of individual returns
Expected return of stock B = 0.1*-0.4+ 0.2*0+ 0.3*0.19+ 0.2*0.28+ 0.2*0.42 = 0.1570 = 15.70%
b.
Standard deviation is the square root of sum of squared deviations from the mean times the probability
Std dev = [0.1*(0.14-(-0.13))^2 + 0.2*(0.14-0.02)^2 + 0.3*(0.14-0.11)^2 + 0.2*(0.14-0.18)^2 + 0.2*(0.14-0.40)^2]^(1/2) = 0.1558 = 15.58%
c.
Coefficient of variation = Std dev / mean = 23.05%/15.70% = 1.47
d.
Option e - If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
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