S&P 500 is now at 2,100. Ignore interest rate (assume

S&P 500 is now at 2,100. Ignore interest rate (assume everything is given in PV terms). Suppose you own a $20M portfolio with a beta of 0.9. S&P 500 is expected to drop by 3% (or by 33 points, 3% ·1,100 = 33). Futures on S&P500 have a multiplier 250.

A. Should you long or short futures on S&P500 to hedge your portfolio?
B. If S&P500 drops by 33 points, what is the dollar change in the portfolio value?
C. If S&P500 drops by 33 points, what is the dollar change in the value of one futures contract (with a multiplier 250)? [Note the sign of the delta depends on whether the contract is longed or shorted. Be careful.]
D. What is the delta of your portfolio?
E. What is the delta of one futures contract?
F. How many futures contracts should you take a position in to hedge away the risk of S&P500 dropping?
G. Your answer to “f” would change if the S&P500 index were expected to drop by 5%. (True / False)