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	8.01	%	15	%	0.7
B	10.16		15		1.2
C	11.88		15		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.)

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

%

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

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

%

4. Would you expect the standard deviation of Fund P to be less than 15%, equal to 15%, or greater than 15%?
   1. less than 15%
   2. greater than 15%
   3. equal to 15%

_____IIIIII

Answer 1

a

Using Stock A Data

As per CAPM

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

8.01 = 5 + 0.7 * (Market risk premium%)

Market risk premium% = 4.3

Weight of Stock A = 0.3333

Weight of Stock B = 0.3333

Weight of Stock C = 0.3333

Beta of Fund P = 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 Fund P = 0.7*0.3333+1.2*0.3333+1.6*0.3333

Beta P = 1.17

c

Weight of Stock A = 0.3333

Weight of Stock B = 0.3333

Weight of Stock C = 0.3333

Expected return of Fund P = Weight of Stock A*Expected return of Stock A+Weight of Stock B*Expected return of Stock B+Weight of Stock B*Expected return of Stock C

Expected return of Fund P = 8.01*0.3333+10.16*0.3333+11.88*0.3333

Expected return of Fund P = 10.02%

d

As std dev of all stocks is equal to 15% and the are not perfectly correlated the std dev of Fund P will be less than 15%