Nick Fitzgerald holds a well-diversified portfolio of high-quality large-cap stocks.
The current value of Fitzgerald’s portfolio is $825,000, 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 longterm 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 $77, and 

(2) A six-month put with a strike price of 2,725 that’s quoted at $56.
a. How many S&P 500 puts would Nick have to buy to protect his $825,000 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 up by 10%?

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 25,509 and that a six-month put option on the Dow is available with a strike of 255, and is currently trading at $8.08. 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 2,800 puts? Briefly explain.