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	8.78%		14%		0.8
B	10.83		14		1.3
C	12.47		14		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.)

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 14%, equal to 14%, or greater than 14%?
   
   1. Less than 14%
   2. Greater than 14%
   3. Equal to 14%

Answer 1

a

Using stock A values

As per CAPM

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

8.78 = 5.5 + 0.8 * (Market risk premium%)

Market risk premium% = 4.1

b

Weight of A = 0.3333

Weight of B = 0.3333

Weight of C = 0.3333

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

Beta of Fund = 0.8*0.3333+1.3*0.3333+1.7*0.3333

Beta of Fund = 1.27

c

Weight of A = 0.3333

Weight of B = 0.3333

Weight of C = 0.3333

Return of Fund = Weight of A*Return of A+Weight of B*Return of B+Weight of C*Return of C

Return of Fund = 8.78*0.3333+10.83*0.3333+12.47*0.3333

Return of Fund = 10.69

d

As stocks are not perfectly correlated and as they have same std dev of 14%, due to diversification effect, std dev of portfolio should be lower than 14%