# Question

You hold an $ 8 million stock portfolio with a beta of 1.0. You believe that the risk- adjusted abnormal return on the portfolio (the alpha) over the next three months is 2 percent. The S& P/ TSX 60 index currently is at 800 and the risk- free rate is 1 percent per quarter.

a. What will be the futures price on the three- month maturity S& P/ TSX 60 futures contract?

b. How many S& P/ TSX 60 futures contracts are needed to hedge the stock portfolio?

c. What will be the profit on that futures position in three months as a function of the value of the S& P/ TSX 60 index on the maturity date?

d. If the alpha of the portfolio is 2 percent, show that the expected rate of return (in decimal form) on the portfolio as a function of the market return is rp = .03 + 1.0 × (rM -.01).

e. Let ST be the value of the index in three months. Then ST/ S0 = ST/ 800 = 1 + rM. (We are ignoring dividends here to keep things simple.) Substitute this expression in the equation for the portfolio return, rp, and calculate the expected value of the hedged (stock- plus- futures) portfolio in three months as a function of the value of the index.

f. Show that the hedged portfolio provides an expected rate of return of 3 percent over the next three months.

g. What is the beta of the hedged portfolio? What is the alpha of the hedged portfolio?

a. What will be the futures price on the three- month maturity S& P/ TSX 60 futures contract?

b. How many S& P/ TSX 60 futures contracts are needed to hedge the stock portfolio?

c. What will be the profit on that futures position in three months as a function of the value of the S& P/ TSX 60 index on the maturity date?

d. If the alpha of the portfolio is 2 percent, show that the expected rate of return (in decimal form) on the portfolio as a function of the market return is rp = .03 + 1.0 × (rM -.01).

e. Let ST be the value of the index in three months. Then ST/ S0 = ST/ 800 = 1 + rM. (We are ignoring dividends here to keep things simple.) Substitute this expression in the equation for the portfolio return, rp, and calculate the expected value of the hedged (stock- plus- futures) portfolio in three months as a function of the value of the index.

f. Show that the hedged portfolio provides an expected rate of return of 3 percent over the next three months.

g. What is the beta of the hedged portfolio? What is the alpha of the hedged portfolio?

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