A friend of yours owns 75,000 shares of Merck. The current price of the stock is $102.26, the S\&P 500 index is at 4,172.47 and the current June futures contract is 4192. (as of Oct, 31, 2023 , The companies beta is 0.38 (according to Google finance. You can always double check the beta with your own calculations). Your friend likes the stock as an investment because of its management and other attributes but is concerned that over the next few months the market may not perform well because of inflation (due to say, higher gas prices). The friend hears you took a financial engineering class and asks for your help (a) Would you recommend to short or long futures contract? Explain (b) Find the number of futures contract that are needed to hedge the Merck stock. Explain how the hedge affects the risk of this asset. (c) Suppose that by mid-January, the S\&P 500 index settles at a level of 4,101.5 while the Merck stock has increased to $105.25. What would be the total gain (loss) of a hedged position in this case if in January the futures contract is for 1545 ? (d) Suppose that your friend only wants to take the beta down to 0.15, find the number of futures contract that are needed to hedge the Merck stock (e) Suppose that your friend in fact thinks the market will do well and wants to take the beta up to 1, find the number of futures contract that are needed to hedge the Merck stock