Consider the following information for stocks A, B and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is each of the correlation coefficients is between 0 and 1). Fund P has one-third of its funds invested in each of the three stocks and the risk-free rate is 5.5%.

Stock

Expected Return

Standard Deviation

Beta

A

9.55%

15%

0.9

B

10.45%

15%

1.1

C

12.70%

15%

1.6

a. What is the market risk premium?

b. What is the beta of Fund P?

c. What is the required return of Fund P?

d. Would you expect the standard deviation of Fund P to be less than 15%, equal to 15% or greater than 15%? Explain.

Part a: The market risk premium is $ 4.50

Part b: The beta of fund P is 1.20

Part c: The required return of fund P is 10.9%

Part d: The value of standard deviation of P is equal to 15% for the correlation coefficients equal to 1 and less than 15%  for all other values of correlation coefficient.

Explanation:

Part a:

As the given value of expected rate of return is

Expected Return = Risk-free rate of return + Beta x Risk premium

From the data

Expected return for A is 9.55%, Risk free rate of return is given as 5.5%, Beta for A is 0.9 so

9.55% = 5.5% + .9 x Risk premium

Risk Premium = (9.55 - 5.50) / 0.9 = $ 4.50

Hence, the market risk premium is $ 4.50

Part b:

For the fund P, Beta is given as the average of the three individual Betas as  

Average of beta =(Beta1+Beta2+Beta3)/3

                            =( 0.9 +1.1 + 1.6) / 3 = 1.20

Hence,the beta of fund P is 1.20

Part c:

The Required Return is given as

Required Return = Risk-free rate of return + Beta x Risk premium

Required Return = 5.5 + 1.20 x 4.50

Required return = 10.9 %

Hence, the required return of fund P is 10.9%

Part d:

If the correlation coefficient of portfolio is 1

In this situation unsystematic risk can not be diversified.So, The standard deviation of the fund P is equal to 15%.

If the correlation coefficient of portfolio shall be in the  range of 0 to 1.

In this situation unsystematic risk can be little bit diversified.So, The standard deviation of the fund P should be less than 15%.