$[5$ points$]$ Suppose the S&P $500$ currently has a level of $875$ and one contract is $$250$ S&P$.$

The continuously compounded return on a $1-$year T$-$bill is $4\mathrm{.}75\%.$ You wish to hedge an

$$800,000$ portfolio that has a beta of $1\mathrm{.}1$ and a correlation of $1\mathrm{.}0$ with the S&P $500.$

i$.$ What is the $1-$year futures price for the S&P $500$ assuming no dividends?

$[1$ point$]$

$800000250$

ii$.$ How many S&P $500$ futures contracts should you short to hedge your portfolio?

$[2$ points$]$

iii. What return do you expect on the hedged portfolio? Why? $[2$ points$]$