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	8.08	%	16	%	0.7
B	10.28		16		1.2
C	11.60		16		1.5

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.) The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

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

Solution :-

Under market equilibrium, Expected rate of return = required rate of return.

Hence, for Stock A

E(R) = Rf + beta * ( Rm - Rf )

8.08% = 5.0% + 0.7 * ( Rm - Rf )

3.08% = 0.7 * ( Rm - Rf )

Rm - Rf = 0.044 = 4.4%

Market Risk Premium = 4.4%

(b)

Beta of the fund

Beta of a fund P is the weighted average of each stock's beta

Weight in each stock = 0.3333

Beta = ( 0.3333 * 0.7 ) + ( 0.3333 * 1.2 ) + ( 0.3333 * 1.5 )

Beta = 1.133

Beta of the Fund P = 1.133

(c)

Required rate of return under market equilibrium, according to CAPM model

Required rate of return =

Rf + Beta * ( Rm - Rf )

= 5.0% + 1.1333 * 4.4%

= 9.987%

(D)

As the Coefficient of Correlation is less than 1 , So Unsystematic Risk Can be Diversified

Therefore Standard Deviation of the fund will be Less than 16%

Therefore Option A is Correct

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