13 Nick Fitzgerald holds a well-diversified portfolio of high-quality, large-cap stocks.

P14.13 Nick Fitzgerald holds a​ well-diversified portfolio of​ high-quality, large-cap stocks. The current value of​ Fitzgerald's portfolio is $ 750,000​, but he is concerned that the market is heading for a big-fall all ​ (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 2,200 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 2,150 ​that's trading at ​$75.00 ​, and​ (2) a​ six-month put with a strike price of 2,075 ​that's quoted at ​$57.00.

a. How many​ S&P 500 puts would Nick have to buy to protect his ​$750,000 stock​ portfolio? How much would it cost him to buy the necessary number of puts with a ​$2,150 strike​ price? How much would it cost to buy the puts with a ​$2,075 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 20​% over the next six months. What if the market and​ Nick's portfolio-fall by only 10​%?

What if they go up by 15​%?

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 17,550 and that a​ six-month put option on the Dow is available with a strike price of 174​, and is currently trading at ​$7.75. 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 2,150 ​puts? Briefly explain.