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 8.50% 14% 0.7 B 10.50 14 1.1 C 12.50 14 1.5 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.) 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. % Would you expect the standard deviation of Fund P to be less than 14%, equal to 14%, or greater than 14%? Less than 14% Greater than 14% Equal to 14%

Answer 1

Hii,

So first let

Re = Expected Rate of return

Rf= Risk free rate of return

B = beta

Rm= Market return

(i) First of all we shall calculate Beta of portfolio which will be weighted average beta of individual stocks.

So Beta of fund P = 1/3*(0.7)+1/3*(1.1)+1/3*(1.5)

= 1.10

(ii) Market risk premium (Rm - Rf)

We know that, Re = Rf + B(Rm - Rf) as per capital asset pricing model (CAPM)

We can use any of the stock i.e. Stock A, B or C's data. So we use here stock A's data, we get,

8.5 = 5+ 0.7(Rm - 5)

8.5 = 5 + 0.7 Rm - 3.5

8.5-5+3.5 = 0.7Rm

Rm = 10%

(iii) Required return of fund P:

Using CAPM again,

Re = Rf + B(Rm - Rf)

Re = 5 + 1.10(10-5)

Re = 10.5%