It is July $16.$ A company has a portfolio of stocks worth $$50$ million. The beta of the portfolio is $1\mathrm{.}3.$ The company would like to use the December futures contract on a stock index to change the beta of the portfolio to $0\mathrm{.}7$ during the period July $16$ to November $16.$ The index futures price is $2,500,$ and each contract is on $$250$ times the index.

$($a$)$ What position should the company take?

ANSWER:

$($b$)$ Suppose that the company changes its mind and decides to increase the beta of the portfolio from $1\mathrm{.}3$ to $1\mathrm{.}7.$ What position in futures contracts should it take?