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Futures price on the three-month maturity

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Reference no: EM133111902

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.

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

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

-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?

-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).

-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.

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

-What is the beta of the hedged portfolio? What is the alpha of the hedged portfolio?

Reference no: EM133111902

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