Nick Fitzgerald holds a well-diversified portfolio of high-quality, large-cap stocks. The current value of Fitzgerald's portfolio is $732,000, 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 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 2854 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 $2800 that's trading at $77.50, and (2) a six-month put with a strike price of $2725 that's quoted at $59.50.

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 price of 255, and is currently trading at $8.03. 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 2800 puts? Briefly explain.

$732,000/25509 ~28 put options

255*100*28=22,484

If the market drops by 20%, then hedging using DJIA put with a strike price of 255:

Net Profit= $732,000*(20%)+120,114.40 = -$26,285.60

Please show math on how to find 120,114.40