Suppose the manager of a $100 million stock portfolio (with a beta of 1.2 and a dividend yield of 1.00% p a) wants to hedge using the March 2019 S&P 500 futures. The March 2019 contract expires in 4 months.On the previous day, the S&P 500 index closed at 2720, and the March 2019 S&P 500 futures closed at 2730. Contract size for S&PS00 futures is 250 times. 4months later, the S&P 500 index fals by 5% from 2720 to 2584 (3 points) 4. a. What is the notional dollar price of one contract? How would the manager hedge her stock portfolio (Buy or sell index futures)? What is the number of contracts needed to hedge? b. c. What is the 4-month return on the portfolio? How much is the gain/loss on the stock portfolio? How much dividend does the manager receive in the 4 month period? (Hint: Dividend yield is given on an annualized basis.) d. Assume that the futures contracts were closed out on expiration day, what is the gain/loss on the futures contracts? e. f. What is the total profit for the manager