Question

Suppose you are the money manager of a $4 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta
A $ 400,000 1.50
B 600,000 (0.50)
C 1,000,000 1.25
D 2,000,000 0.75

Answer 1

Calculating the weights of each individual stock:

Stock-A = $400,000 / $4,000,000

Stock-A = 0.1 or 10%

Stock-B = $600,000/ $4,000,000

Stock-B = 0.15 or 15%

Stock-C = $1,000,000 / $4,000,000

Stock-C = 0.25 or 25%

Stock-D = $2,000,000 / $4,000,000

Stock-D = 0.5 or 50%

Calculating the portfolio beta:

Portfolio beta = W1 × Beta of stock-A + W2 × Beta of stock-B + W3 × Beta of stock-C + W4 × Beta of stock-D

Portfolio beta = 0.1 × 1.50 + 0.15 × (0.50) + 0.25 × 1.25 + 0.5 × 0.75

Portfolio beta = 0.15 - 0.075 + 0.3125 + 0.375

Portfolio beta = 0.7625

Now, calculating the required rate of return:

E(Rp) = Rf + [Rm - Rf] × portfolio beta

E(Rp) = 0.06 + [0.14-0.06] × 0.7625

E(Rp) = 0.06 + 0.061

E(Rp) = 0.121 or 12.1%