Modern Portfolio Managers $($MPM$)$ hold a $8\mathrm{.}0$ million dollar portfolio of stocks with a

beta of $\mathrm{.}65$ measured with respect to the S&P $500$ index. The current value of a futures

contract on the index is $1045.2.$ The multiplier on the futures equals $$250.$ If MPM wishes

to increase its systematic risk in its portfolio to $85,$ how many contracts must it buy or sell?

Sell $6\mathrm{.}1232$

Buy $6\mathrm{.}1232$

Sell $0\mathrm{.}10452$

Buy $26\mathrm{.}13$

Buy $26\mathrm{.}024$