4. You are managing a portfolio of $1,500,000, with a beta of 1. For the long-term you are bullish, but you think the market may fall over the next month. The market index is currently at a level of 3,000 but you anticipate it to drop to 2,700 over the upcoming month. You are considering hedging this risk in the futures market.

a. If the anticipated drop materializes, what is the expected return (loss) on your portfolio? What is the dollar amount of your expected loss? b. If the anticipated drop materializes, by how much does the value of a futures position on the S&P change? (The futures contract calls for delivery of $250 times the value of the index) c. Given your answers to parts (a) and (b), how many futures contracts are needed to hedge the market risk in your portfolio? Will the hedge consist of a long or a short position? d. (*) How would your answer to part (c) change if you wanted to hedge not the entirety of the market risk, but rather only reduce it by half? (i.e. maintain a beta of 0.5 rather than 0)