On April 1, an investor holds 40,300 shares of a certain stock. The market price is $25 per share. The investor is interested in completely hedging against movements in the market over the next month and decides to use the June Mini S&P 500 futures contract. The index is currently 4,000 and one contract is for delivery of $50 times the index. The beta of the stock is 1.9. What strategy should the investor follow?

b. Now after a month the investor wishes to partially unwind their hedge to a target beta of 1.2. Using your answer from part a, what strategy should the investor follow? They still hold 40,300 shares and the market price is now $27 per share. The June Mini S&P Futures index is still at 4,000 and one contract for delivery is of $50 times the index. What will be the residual remaining position in their futures contracts ?