Question

Assume that you are the portfolio manager of the BG Fund, a $3.5 million hedge fund that contains the following stocks. The market risk premium is 6.00% and the risk-free rate is 5.5%. What rate of return should investors expect (and require) on this fund?

                        Stock                           Amount($)                              Beta

                        A                                 1,100,000                                1.15

                        B                                 700,000                                   0.60

                        C                                 850,000                                   1.50

                        D                                 850,000                                   0.85

                        Total                            $3,500,000

		10.56%
		10.83%
		11.81%
		12.15%
		12.31%

Answer 1

From the given investment, first calculating weight of each asset,

Weight of stock A Wa = Investment in A/Total investment = 1100000/3500000 = 0.3143

Weight of Stock B Wb = Investment in B/Total investment = 700000/3500000 = 0.2

Weight of Stock C Wc = Investment in C/Total investment = 850000/3500000 = 0.2429

Weight of Stock D Wd = Investment in D/Total investment = 850000/3500000 = 0.2429

Beta of stock A, Ba = 1.15

Beta of stock B, Bb = 0.6

Beta of stock C, Bc = 1.5

Beta of stock D, Bd = 0.85

So, Beta of portfolio is weighted average beta of its assets

=> Beta of portfolio = Wa*Ba + Wb*Bb + Wc*Bc + Wd*Bd = 0.3143*1.15+0.2*0.6+0.2429*1.5+0.2429*0.85 = 1.0521

Using CAPM, expected return on a portfolio is Rf + Beta*MRP

=> Expected return on portfolio = 5.5 + 1.0521*6 = 11.81%

Option C is correct.