EXPECTED RETURNS Stocks A and B have the following probability distributions of

Question

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

Probability                          A                             B

0.2                                          (15%)                    (30%)

0.2                                          4                              0

0.3                                          11                           21

0.2                                          24                           27

0.1                                          33                           36

a. Calculate the expected rate of return, rB, for Stock B (rA = 9.20%.) Do not round intermediate calculations. Round your answer to two decimal places.

b. Calculate the standard deviation of expected returns, A, for Stock A (B = 22.39%.) Do not round intermediate calculations. Round your answer to two decimal places.

c. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

d. Is it possible that most investors might regard Stock B as being less risky than Stock A?

I. 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.

II. 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.

III. 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.

IV. 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.

V. 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.

Explanation / Answer

a.

Expected return is the weighted average of individual returns

Expected return of stock B = 0.2*-0.3+ 0.2*0+ 0.3*0.21+ 0.2*0.27+ 0.1*0.36= 0.0930 = 9.30%

b.

Standard deviation is the square root of sum of squared deviations from the mean times the probability

Std dev = [0.2*(0.092-(-0.15))^2 + 0.2*(0.092-0.04)^2 + 0.3*(0.092-0.11)^2 + 0.2*(0.092-0.24)^2 + 0.1*(0.092-0.33)^2]^(1/2) = 0.1497 = 14.97%

c.

Coefficient of variation = Std dev / mean = 22.39%/9.3% = 2.41

d.

Option IV - 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.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.