Question

Answer the question parts (a) and (b), and show all your work briefly:

a) You manage an equity fund with an expected risk premium of 10.2% and a standard deviation of 16%. The rate on Treasury bills is 4%. Your client chooses to invest $40,000 of her portfolio in your equity fund and $60,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client's portfolio?

b) Hakim purchased a stock one year ago at a price of $32 a share. In the past year, he has received four quarterly dividends of $0.75 each. Today he sold the stock for $38 a share. How much is his capital gain?

Answer 1

Expected return on equity is computed as shown below:

= risk free rate + risk premium

= 0.04 + 0.102

= 14.2% or 0.142

Expected return of portfolio is computed as follows:

= risk free rate x weight in treasury bills + return on equity x weight in equity

= 0.04 x $ 60,000 / ($ 60,000 + $ 40,000) + 0.142 x $ 40,000 / ($ 60,000 + $ 40,000)

= 0.04 x 0.60 + 0.142 x 0.40

= 8.08%

Standard deviation of portfolio is computed as shown below:

= Weight of equity fund in the portfolio x standard deviation

= 0.40 x 0.16

= 6.4%

b. The capital gain is computed as shown below:

= Selling price per share - purchase price per share

= $ 38 - $ 32

= $ 6

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