Question

Problem 8-13

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 9.05 % 14 % 0.7

B 11.22 14 1.2

C 12.96 14 1.6

Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 6%, and the market is in equilibrium. (That is, required returns equal expected returns.)

a. What is the market risk premium (rM - rRF)? 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 14%, equal to 14%, or greater than 14%?

I. less than 14%

II. greater than 14%

III. equal to 14%

Answer 1

a

Using stock A data

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

9.05 = 6 + 0.7 * (Market risk premium%)

Market risk premium% = 4.36

b

Weight of Stock A = 0.3333

Weight of Stock B = 0.3333

Weight of Stock C = 0.3333

Beta of Portfolio = Weight of Stock A*Beta of Stock A+Weight of Stock B*Beta of Stock B+Weight of Stock C*Beta of Stock C

Beta of Portfolio = 0.7*0.3333+1.2*0.3333+1.6*0.3333

Beta of Portfolio = 1.1666

c

As std dev for all stock is 14% and they are not perfectly correlated std dev of portfolio will be less than 14%