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	8.65%		16%		0.7
B	10.45		16		1.1
C	12.25		16		1.5

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 16%
   2. Greater than 16%
   3. Equal to 16%

Answer 1

Stock	Expected Return	Standard Deviation	Beta
A	9%	16%	0.70
B	10%	16%	1.10
C	12%	16%	1.50

Weight of each stock in Fund P is 1/3.

Risk Free Rate = 5.5%

Answer 1)

Expected Return = Risk Free Rate + Beta * (Expected Market Return - Risk Free Rate)

.09 = .055 + .7*(Expected Market Return -.055)

3.5% = .70 * Expected Market Return - 3.85%

7.35% = .70 * Expected Market Return

Expected Market Return = 10.50%

Market Risk Premium = (Expected Market Return - Risk Free Rate)

Market Risk Premium = (.105-.055) = 5.0%

Answer 2)

Beta of Fund P = (Beta of A * Weight of A) + (Beta of B * Weight of B) + (Beta of C * Weight of C)

Beta of Fund P = (.70*.33) + (1.1 * .33) + (1.5*.33)

Beta of Fund P = .233 + .366 + .5

Beta of Fund P = 1.10

Answer 3)

Required Return of Fund P = (Required Return of A * Weight of A) + (Required Return of B * Weight of B) + (Required Return of C * Weight of C)

Required Return of Fund P = (.09*.33) + (.1*.33) + (.12*.33)

Required Return of Fund P = . 0283 + .0348 + .0408

Required Return of Fund P = 10.45%

Answer 4) Option a) Standard Deviation of Fund P will be less than 16%

This is because as more stocks are added in portfolio, the risk gets diversified. As a result , the risk (Standard Deviation) gets reduced.

Option B) is incorrect as standard deviation of portfolio will not be greater than 16% as correlation helps the stock to reduce the standard deviation of portfolio. Also, a single stock will have more standard deviation than the portfolio of equally weighted stocks.

Option C) is incorrect as standard deviation of portfolio will not be equal to 16% as correlation helps the stock to reduce the standard deviation of portfolio