A portfolio manager in charge of a portfolio worth $$10$ million is concerned that themarket might decline rapidly during the next six months and would like to useoptions on the S&P $100$ to provide protection against the portfolio falling below $$9\mathrm{.}5$million. The S&P $100$ index is currently standing at $500$ and each contract is on $100$times the index. lf the portfolio has a beta of $0\mathrm{.}5$ and the interest rate is $10\%,$ howmany put options and what strike price should be purchased?