A manager would like to protect a $$1,000,000$ portfolio from

any decline below $$800,000$ in the next three months before

transaction costs and premiums. The risk free rate is $4\%.$

The beta of the portfolio is $2.$ The stock index is at $250.$

Three$-$month puts on the index are available with

Exercise Price: $220225230,$ and $235$

Premium: $$1247$

What is the best strategy$($lowest cost$)$ the manager could use to

achieve his$/$her goal if the future index level is expected to

be: $215220225$ or $230?$ Justify your answer.