Question

Consider the following information for three stocks, 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 8.28 % 16 % 0.8 B 9.51 16 1.1 C 11.56 16 1.6 Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 5%, and the market is in equilibrium. (That is, required returns equal expected returns.) The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below. Open spreadsheet What is the market risk premium (rM - rRF)

Answer 1

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%.