Complete question:
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.
Answer:
1. $4.50
2. 1.2
3. 10.9
4. <15%
Explanation:
a) Computation of the market risk premium.We have,
Accounting to CAPM model.We have,
Expected Return = Risk-free rate of return + Beta x Risk premium
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
(b) Computation of the beta of Fund P.We have,
Average of beta = ( 0.9 +1.1 + 1.6) / 3 = 1.20
Hence,the beta of fund P is 1.20
(c) Computation of the required return of Fund P.We have,
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%
(d) If the correlation coefficient of 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 portfolio shall be 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%.
