Question

1. Assume that you are the portfolio manager of the SF Fund, a $3 million hedge fund that contains the following stocks. The required rate of return on the market is 12.00% and the risk-free rate is 4.00%. What rate of return should investors expect (and require) on this fund?

                        Stock                           Amount                                   Beta
                        A                                 $1,075,000                              1.20
                        B                                      675,000                              0.50
                        C                                      750,000                              1.40
                        D                                      500,000                              0.75
                        Total                            $3,000,000

A.10.56%

B.10.83%

C.11.11%

D.11.38%

E.12.14%

2. DVC stock has a required return of 25%. The expected market return is 15% and the risk-free rate is 5%. What is the beta of the DVC stock?

A.1

B.1.5

C.2

D.2.5

E.3

Answer 1

QUESTION-1

Step-1, The Beta of the portfolio

Stocks	Amount invested ($)	Weight to total value [Amount invested / Total value]	Beta of the stock	Overall Beta [Beta of the stock x Weight to total value]
A	1,075,000	0.3583	1.20	0.4300
B	675,000	0.2250	0.50	0.1125
C	750,000	0.2500	1.40	0.3500
D	500,000	0.1667	0.75	0.1250
TOTAL	3,000,000			1.0175

Step-2, The fund's required rate of return

As per Capital Asset Pricing Model [CAPM], the Required Rate of Return is calculated by using the following equation

Required Rate of Return = Risk-free Rate + Beta(Market Rate of Return – Risk-free Rate)

= Rf + B[Rm – Rf]

= 4.00% + 1.0175[12.00%- 4.00%]

= 4.00% + [1.0175 x 8.00%]

= 4.00% + 8.14%

= 12.14%

The Funds expected rate of return is (E). 12.14%%

QUESTION-2

As per Capital Asset Pricing Model [CAPM], the Required Rate of Return is calculated by using the following equation

Required Rate of Return = Risk-free Rate + Beta(Market Rate of Return – Risk-free Rate)

25.00% = 5.00% + Beta(15.00%- 5.00%)

25.00% - 5.00% = Beta(15.00%- 5.00%)

20.00% = Beta x 10.00%

Beta = 20.00% / 10.00%

Beta = 2.00

Therefore, the beta of the DVC stock is (c). 2