Suppose profits or losses on stock investments are taxed at a rate of 30%. [Assume that increases
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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.
- 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?
- 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.]
- 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).
- Assume that interest paid or received on T-bills also faces a tax rate of 30%. Find the parity value for the forward price.
- How does the parity price you derived compare to the "usual" parity value?
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