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	9.35%		15%		0.7
B	12.65		15		1.3
C	14.85		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.)

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

     %

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. What would you expect the standard deviation of Fund P to be?
   1. Less than 15%
   2. Greater than 15%
   3. Equal to 15%

Answer 1

Answer : (a.) Calculation of Market Risk Premium :

As the market is in equilibrium which means that Expected Return on Stock is equal to Required Return

taking Stock A as Base,

Required Return = Risk Free Rate + (Beta * Market Risk Premium)

9.35% = 5.5% + (0.7 * Market Risk Premium)

9.35% - 5.5% = 0.7 * Market Risk Premium

==> Market Risk Premium = 3.85% / 0.7

= 5.5%

(b.) Calculation of Beta of Fund P

Portfolio Beta = Sum of (Beta * Weight of Beta)

= (0.7 * 1/3) + (1.3 * 1/3) + (1.7 * 1/3)

= 1.23

(c.) Calculation of Required Return of Fund P

Required Return = 5.5% + (1.23333 * 5.5%)

= 12.28%

(d.) Correct Option is less than 15%

Reason :

As the portfolio are not perfectly correlated .Therefore , there will be benefit of diversifiaction of risk when the portfolio are not perfectly correlated .Therefore as the result of diversification , The expected Standard deviation will be less than 15%.