1. Use the following table to answer parts A and B. The risk-free rate is 4%, th

Question

1. Use the following table to answer parts A and B. The risk-free rate is 4%, the return on the market index is forecast at 14% with a standard deviation of 9%.

A) Use CAPM to calculate the expected/fair return and the alpha for each stock.

B) Would you recommend either of these stocks to an investor with a well-diversified portfolio? Explain.

2. Assume you buy a $1,000 face value bond with 7 years until maturity, a coupon rate of 5% paid semiannually, and a yield to maturity of 8%.

A) What is the price of this bond?

B) Assume that the yield to maturity falls to 7% after one year, and the investor decides to sell the bond. What would be the holding period return for the investor?

Explanation / Answer

1) a) Using CAPM, Expected Return E(R) = Rf + beta x (Rm - Rf)

For Mercury, E(R) = 4% + 2.5 x (14% - 4%) = 29%

For Electric, E(R) = 4% + 0.8 x (14% - 4%) = 12%

b) Mercury offers lower forecasted returns given the risk, while Electric offers higher forecasted returns given the beta. Alpha for Mercury = 20% - 29% = -9%, Alpha for Electric = 13% - 12% = 1%

2) Bond Price can be calculated using PV function

N = 7 x 2 = 14, PMT = 5% x 1000 / 2 = 25, FV = 1000, I/Y = 8%/2 = 4% => Compute PV = $841.55

After a year, bond price is

N = 6 x 2 = 12, PMT = 25, FV = 1000, I/Y = 7%/2 => Compute PV = $903.37

Holding Period Return = (903.37 + 25 x 2) / 841.55 - 1 = 13.29%

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