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You have a diversified portfolio of U.S equities. Your portfolio has a value of $10 million, and a beta of 1.5. Its volatility is 25% per annum, while the volatility of the S&P 500 index is 20% per annum. The current level of the index is 4,450. You would like to hedge you portfolio and have decided to hedge using S&P 500 futures contracts that expires in three months. This futures contract is trading at 4,463 and the value of the contract is $250 times the index. The average dividend yield on the index is 2% per annum and the risk free rate is currently at 1.5% per annum. All rates are continuously compounded.
a.Is this futures contract fairly priced?
b. if not, design the arbitrage strategy to profit from this mispricing. Show all your positions and cash flows in a table, as in the lectures
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