Nick Fitzgerald holds a well-diversified portfolio of high-quality, large-cap stocks. The current value of Fitzgerald's portfolio is $815,000, but he is concerned that the market is heading for a big fall (perhaps as much as 20%) over the next three to six months. He doesn't want to sell all his stocks because he feels they all have good long-term potential and should perform nicely once stock prices have bottomed out. As a result, he's thinking about using index options to hedge his portfolio. Assume that the S&P 500 currently stands at 2,854 and among the many put options available on this index are two that have caught his eye: (1) a six-month put with a strike price of 2,800 that's trading at $75.50, and (2) a six-month put with a strike price of 2,725 that's quoted at $58.50. a. How many S&P 500 puts would Nick have to buy to protect his $815,000 stock portfolio? How much would it cost him to buy the necessary number of puts with a $2,800 strike price? How much would it cost to buy the puts with a $2,725 strike price? b. Now, considering the performance of both the put options and Nick's portfolio, determine how much net profit (or loss) Nick will earn from each of these put hedges if both the market (as measured by the S&P 500) and Nick's portfolio fall by 15% over the next six months. What if the market and Nick's portfolio fall by only 5%? What if they go