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.)

Stock Expected Return Standard Deviation Beta

A 8.62% 15% 0.7

B 11.29 15 1.3

C 13.07 15 1.7

Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)

What is the market risk premium (rM - rRF)? Round your answer to two decimal places.

___%

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

___

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

___%

Answer 1

1) As per CAPM, expected return can be computed as -

Expected return = Risk free rate + Beta x Market risk premium

Now, we use the value of expected return of any stock and input in the above formula as risk free rate and market risk premium would be the same for all.

8.62% = 5.5% + 0.7 x Market risk premium

or, 3.12% = 0.7 x Market risk premium

pr, Market risk premium = 3.12% / 0.7 = 4.4571428571% or 4.46%

2) Beta of portfolio = Beta_A x Weight_A + Beta_B x Weight_B + Beta_C x Weight_C

Weight of each stock in the portfolio is one third or 1/ 3.

Beta of portfolio = (0.7 x 1 / 3) + (1.3 x 1/ 3) + (1.7 x 1/ 3) = 1.233333333 or 1.23

3) Required return of Fund P = 5.5% + 1.233333333 x 4.4571428571% = 10.99714% or 11.00% (or try 10.99%)