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.) Stock Expected Return Standard Deviation Beta
A 8.50% 16% 0.8
B 9.50 16 1.2
C 10.50 16 1.6

Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 6.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)

Required:
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.

a. $2.5

b. 1.20

c. 9.5%  

Explanation:

We can calculate the market risk premium and the required return according to the CAPM model by using the simple expected return formula given below. Average beta can be calculated by dividing the sum of all beta with the number of betas

(a) Computation of the market risk premium

According to the CAPM model

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

8.50 = 6.5 + 0.8(Risk premium )

Risk Premium = (8.50 - 6.5) / 0.8

Risk Premium = $2.5

(b) Computation of the beta of Fund P.We have,

Average of beta = ( 0.8 + 1.2 + 1.6) / 3

Average of beta = 1.20

(c) Computation of the required return of Fund P

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

Required Return = 6.5 + 1.20 (2.50 )

Required return = 9.5%  

(d) If the correlation coefficient of the portfolio shall be 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 the portfolio shall be a range of 0 to 1. In this situation, unsystematic risk can be a little bit diversified. So, The standard deviation of the fund P should be less than 15%.

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