A fund manager manager is concerned about the performance of the market over the next two months and plans to use three$-$month futures contracts on a well$-$diversified index to hedge its risk. Additional information is as follows:

The portfolio is worth $$50$ million beta with beta of $0\mathrm{.}87.$

The current level of the index is $1250,$ and one contract is on $250$ times the index.

The risk$-$free rate is $6\%$ per annum.

The dividend yield on the index is $3\%$ per annum.

The current $3-$month futures price is $1259.$

a$)$ What position should the fund manager take to eliminate all exposure to the market over the next two months?

A: Short $138$ contracts.

b$)$ Calculate the effect of your strategy on the fund manager$$s returns if the market index in two months $($at expiration of hedge$)$ is $1,000,1,100,1,200,1,300,$ and $1,400.($Assume that the corresponding one$-$month futures prices are as calculated in your spreadsheet.$)$

A: To do this last problem, we will recreate the spreadsheet from class that traced out these hedge positions, answering the following questions for each outcome. Please review the detailed slide from class that explains these calculations, and you should practice at least one of these rows by hand!

What is the cash flow associated with futures position?

What is the percent return on the market index $($including dividends$)?$

What is the predicted return on the equity portfolio, as forecasted by the CAPM?

What is the cash flow on the equity portfolio?

What is the cash flow on the hedged equity portfolio $($i$.$e$.,$ CF on futures position plus CF on equity portfolio$)?$