question #1 please show all of the work.Fundamentals of Futures and Options Markets, Eight Edition by John C. Hull is the book we use

\fQuestion 1 Which contract provides the best hedge? If I employ the minimum-variance hedging strategy, then the best hedge corresponds to using the futures contract with the highest R2 . Therefore, the contract that gives me the best hedge is the futures contract on NASDAQ 100. How many contracts do I need to hedge the position? Let h denote the minimum-variance hedge ratio. The value of h is the regression coefficient of the change in my portfolio value versus change in the NASDAQ 100 futures. Therefore: h = 0.980 (1) Let N denote the optimal NASDAQ 100 futures contracts, Qportfolio denote the value of the stock portfolio being hedged and Qfutures denote the size of one futures contract. The value of Qfutures is: Qfutures = Price Multiplier = 4, 034.50 $100 = $403, 450 (2) Therefore the value of N is: N = h Qportfolio 0.98 $20 million = = 48.58 Qfutures $403, 450 (3) In summary, I need to short 49 NASDAQ 100 futures contracts. What side of the market do I need to hedge? I am currently long on my underlying stock portfolio. Therefore, to hedge, I need to go short on the NASDAQ 100 futures. After 2 Months The value of the stock portfolio at the time of sale is: Valuestock portfolio = $20 million (1 5%) = $19 million (4) Thus, the loss from the stock portfolio is: Loss = $20 million $19 million = $1 million (5) The quoted value of the futures contract is: Valuefutures = 49 contracts 3, 830 $100 = $18, 767, 000 (6) Therefore, the profit from the short position in the 49 futures contracts is: Profit = [49 contracts 4, 034.50 $100] $18, 767, 000 = $1, 002, 050 (7) The net profit from the hedged position is: Net Profit = $1, 002, 050 $1, 000, 000 = $2, 050 1 (8)