P. F. Chang holds a well-diversified portfolio of high-quality, large-cap stocks. The current value of Chang’s portfolio is $735,000, but he is concerned that the market is heading for a big fall (perhaps as much as 20%) over the next 3 to 6 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 1,470 and among the many put options available on this index are two that have caught his eye: (1) a 6-month put with a strike price of 1,450 that’s trading at $26, and (2) a 6-month put with a strike price of 1,390 that’s quoted at $4.50.
a. How many S&P 500 puts would Chang have to buy to protect his $735,000 stock portfolio? How much would it cost him to buy the necessary number of 1,450 puts?
How much would it cost to buy the 1,390 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 6 months. What if the market and the Chang portfolio fall by only 5%? What if they go up by 10%?
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 14,550 and that a 6-month put option on the Dow is available with a strike of 144, and is currently trading at $2.50. 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 1,450 puts? Briefly explain.