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	8.92	%	16	%	0.8
B	10.39		16		1.1
C	12.84		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.

a. What is the market risk premium (r_M - r_RF)? Round your answer to two decimal places.

b. What is the beta of Fund P? Do not round intermediate calculations. Round your answer to two decimal places.

c. What is the required return of Fund P? Do not round intermediate calculations. Round your answer to two decimal places.

d. Would you expect the standard deviation of Fund P to be less than 16%, equal to 16%, or greater than 16%?

less than 16%

greater than 16%

equal to 16%

Answer 1

a. Given that the Risk Free Rate = 5%,

Using CAPM on Stock A,
Re = Rf + Beta x (Market Risk Premium)
8.92% = 5% + 0.8 x (Market Risk Premium)
Hence, Market Risk Premium = 3.92%/0.8 = 4.9%

b. Since Fund P has invested equal proportion in each of the three stocks, its beta would be the weighted average of the stock beta i.e.
1/3 x 0.8 + 1/3 x 1.1 + 1/3 x 1.6 = 1.17

c. Using CAPM of the Fund,
Rp = 5% + 1.17 x 4.9% = 10.73%

d. I would expect the standard deviation to be less than because there is no direct correlation between the stocks.