Nick Fitzgerald holds a well-diversified portfolio of high-quality, large-cap stocks. The current value of Fitzgerald's portfolio is $ 735 comma 000$735,000, 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 any of 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 comma 2002,200 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 comma 1502,150 that's trading at $76.0076.00, and (2) a six-month put with a strike price of 2 comma 0752,075 that's quoted at $58.0058.00. a. How many S&P 500 puts would Nick have to buy to protect his $735 comma 000735,000 stock portfolio? How much would it cost him to buy the necessary number of puts with a $2 comma 1502,150 strike price? How much would it cost to buy the puts with a $2 comma 0752,075 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 1515% over the next six months. What if the market and Nick's portfolio fall by only 55%? What if they go up by 1515%? c. Do you think Nick should set up the put hedge and, if so, using which put option? Explain. d. Finally, assume that the DJIA is currently at 17 comma 55017,550 and that a six-month put option on the Dow is available with a strike price of 174174, and is currently trading at $8.008.00. How many of these puts would Nick have to buy to protect his portfolio, and what would they cost? Would Nick be better off with the Dow options or the S&P 2 comma 1502,150 puts? Briefly explain. a. The number of S&P 500 puts Fitzgerald would have to buy to protect his $735 comma 000735,000 stock portfolio is 33 put options.(Round up to the nearest whole number.) To buy the necessary number of 2 comma 1502,150 puts, it would cost him $3040030400. (Round to the nearest cent.) To buy the necessary number of 2 comma 0752,075 puts, it would cost him $2320023200. (Round to the nearest cent.) b. If both the market (as measured by the S&P 500) and the Fitzgerald portfolio fall by 1515% over the next six months, the net profit (or loss) Fitzgerald will earn (or sustain) from the hedge using 2 comma 1502,150 puts is $nothing. (Round to the nearest cent. Enter a positive number for a profit and a negative number for a loss.)