Suppose profits or losses on stock investments are taxed at a rate of 30%. [Assume that increases in the value of a stock are taxed at a rate of 30% in that year whether or not the stock is actually solddo not worry about the intricacies of how U.S. tax law actually works.Similarly, a decline in the value of your stock position reduces your taxes in that year by 30% of the loss.]For simplicity, assume that gains or losses onfuturespositions are not taxed at all.Also, assume that the stock pays no dividends.You want to price a one-year maturity S&P 500 futures contract in this tax environment.

1. If you buy the stock index today for S0and the index sells for S1at the end of the year, what is the net-of-tax value of your stock investment?
2. How many futures contracts would you enter to hedge that net-of-tax value?[For simplicity, assume that each futures contract is on "one unit" of the index.]
3. What is the zero-cost, hedged portfolio that you would use to derive spot-futures parity in this setting? For each unit of the index that you hold, specify how many positions you would take the S&P futures contract, and in borrowing or lending.Hint: look back at your answer to part (b).
4. Assume that interest paid or received on T-bills also faces a tax rate of 30%. Find the parity value for the forward price.
5. How does the parity price you derived compare to the "usual" parity value?

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NetofTax Value of Stock Investment Scenario 1 Stock price increases S1 S0 Gain on investment S1 S0 T... View the full answer