using the formula below, assume you have a $500 million equity portfolio with a beta of 1.2 to the S&P 500. You want to raise the beta of the portfolio to 1.8 by using futures. You choose to use S&P 500 index futures when the index is at 3000. (That means each contract represents $750,000 of index exposure or 3000 * 250 multiplier). How many future contracts would you use and will you be long or short:

a. Long 800 contracts

b. Long 400 contracts

c. Short 400 contracts

d. Short 333 contracts