P. F. Chang holds a well-diversified portfolio of high-quality, large-cap stocks. The current value of Chang's portfolio is

$ 735 comma 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

1 comma 470

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

1 comma 450

that's trading at

27.00

,

and (2) a six-month put with a strike price of

1 comma 390

that's quoted at

3.00

.

a. How many S&P 500 puts would Chang have to buy to protect his

$735 comma 000

stock portfolio? How much would it cost him to buy the necessary number of

1 comma 450

puts? How much would it cost to buy the

1 comma 390

puts?

b. Now, considering the performance of both the put options and the Chang portfolio, determine how much net profit (or loss) Chang will earn from each of these put hedges if both the market (as measured by the S&P 500) and the Chang portfolio fall by

15

%

over the next six months. What if the market and the Chang portfolio fall by only

5

%?

What if they go up by

15

%?

c. Do you think Chang should set up the put hedge and, if so, using which put option? Explain.

d. Finally, assume that the DJIA is currently at

14 comma 550

and that a six-month put option on the Dow is available with a strike price of

144

,

and is currently trading at

2.00

.

How many of these puts would Chang have to buy to protect his portfolio, and what would they cost? Would Chang be better off with the Dow options or the S&P

1 comma 450

puts? Briefly explain.