An investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor uses the 3-months Mini S&P 500 futures contract to hedge. The index is currently 1,500 and one contract is for delivery of $50 times the index.

a. If the beta of the stock is 1.3, what is the optimal hedging strategy for the investor?

b. If the risk free interest rate is 1% per month, find the approximate value of the investors position (stock and futures) after 1 month if the index is 1,200.