Stocks A and B have the following probability distributions of expected future r
ID: 2785240 • Letter: S
Question
Stocks A and B have the following probability distributions of expected future returns:
Calculate the expected rate of return, rB, for Stock B (rA = 15.70%.) Do not round intermediate calculations. Round your answer to two decimal places.
%
Calculate the standard deviation of expected returns, A, for Stock A (B = 22.45%.) 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?
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.
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.
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.
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.
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.
Probability A B 0.1 (11%) (28%) 0.2 3 0 0.3 16 22 0.2 23 28 0.2 34 50Explanation / Answer
a.
Expected rate of return is the weighted average of individual returns
Stock B, expected return = 0.1-0.28 + 0.2*0 + 0.3*0.22 + 0.2*0.28 + 0.2*0.5 = 0.1940 = 19.40%
b.
Standard deviaiton is the square root of sum of squared deviations from the mean times the probability:
Stock A, std dev = [0.1*(0.157-0.11)^2 + 0.2*(0.157-0.03)^2 + 0.3*(0.157-0.16)^2 + 0.2*(0.157-0.23)^2 + 0.2*(0.157-0.34)^2]^(1/2) = 13.46%
c.
Coefficient of variation = standard deviation/expected return
Stock B = 22.45%/19.4% = 1.16
d.
Option A
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.