A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on the S&P index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to achieve the following? (Indicate the number of contracts that should be traded and whether the position is long or short.)
a. Eliminate all systematic risk in the portfolio
b. Reduce the beta to 0.9
c. Increase beta to 1.8