Points Problem

A fund manager has a portfolio worth $$50$ million with a beta of $0\mathrm{.}87.$ The 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. The current index level is $2,670,$ one contract is on $250$ times

the index, the risk$-$free rate is $2\mathrm{.}50\%$ per annum, and the dividend yield on the index is $2\%.$ The current

three$-$month futures price is $2,677.$

What position should the fund manager take to hedge exposure to the market over the next two months?

Calculate the effect of your strategy on the fund manager's returns if the level of the market in two

months is $2,500,2,600,2,700,$ and $2,800.$ Assume that the one$-$month futures price is $0\mathrm{.}25\%$ higher

than the index level at this time.

Percentage that the futures price $is$ higher than the index level $0\mathrm{.}25\%$

Hint: Multiply $($Number of controcts$)$x$($Dlfference between futures price when entering the contract and the futures price in twa months$)x($Multiplier on the lindex$)$

Hint: Percentage change in the level of the index over two months

Hint: Percentage change in the level of the index over two months plus dividend yield over two months

Hint: Percentage change in the level of the index $($inolading dividend yjeld$)$ over two months minus the risk$-$free rate over two months

Hint: Multiply the excess return on the index $($including dividend yield$]$ by the ponfolio beto

Hint: Excess retum on the $($unitedged$)$ portfolio over two months plus the risk$-$free rate over two months

Hint: Use the original value of the $($uninedged$)$ portfolio and the associated expected return over two months