Question

CAPM, PORTFOLIO RISK, AND RETURN

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	10.10%		16%		0.9
B	11.01		16		1.1
C	13.28		16		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.)

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 16%, equal to 16%, or greater than 16%?
   
   1. Less than 16%
   2. Greater than 16%
   3. Equal to 16%
   
   

Answer 1

a

Using stock A data

As per CAPM

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

10.1 = 6 + 0.9 * (Market risk premium%)

Market risk premium% = 4.56

b

Weight of A = 0.3333

Weight of B = 0.3333

Weight of C = 0.3333

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

Beta of Portfolio = 0.9*0.3333+1.1*0.3333+1.6*0.3333

Beta of Portfolio = 1.20

c

Weight of A = 0.3333

Weight of B = 0.3333

Weight of C = 0.3333

Expected return of Portfolio = Weight of A*Expected return of A+Weight of B*Expected return of B+Weight of C*Expected return of C

Expected return of Portfolio = 10.1*0.3333+11.01*0.3333+13.28*0.3333

Expected return of Portfolio = 11.46

d

Less than 16% as std dev of all stocks are 16% and they are not perfectly correlated