A trader owns $1000$ shares of IBM stock. The trader also has $$10,000$ in cash. Consider the following two strategies that the trader can follow.

Strategy $1$: The trader holds the position of $1000$ shares for one year, and invests $10,000$ cash in a risk free bond for an annual return of $5\%.$

Strategy $2$: The trader buys $1000$ put options on IBM with strike price $x=60$ that expire in one year. The price of each call option is $p=5.$ The trader then holds $1000$ IBM shares and invests the remaining cash in the risk free bond for an annual return of $5\%.$

For what values of IBM share price $S_T$ in one year at the expiration date, does Strategy $2$ prove to be the better one?

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