A company has a $36 million portfolio with a beta of 1.2. The S&P index is currently standing at 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.)
(i) Eliminate all systematic risk in the portfolio?
(ii) Reduce the beta to 0.9?
(iii) Increase beta to 1.8?
Need to know how the calculations are done step by step.