Question

Nick Fitzgerald holds a​ well-diversified portfolio of​ high-quality, large-cap stocks. The current value of​ Fitzgerald's portfolio is $ 745,000​, 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 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 2150 ​that's trading at ​$76.00​, and​ (2) a​ six-month put with a strike price of 2,075 ​that's quoted at ​$57.50.

a. How many​ S&P 500 puts would Nick have to buy to protect his ​$745,000 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.

a. The number of​ S&P 500 puts Fitzgerald would have to buy to protect his ​$745,000 stock portfolio is ………… put options.  ​(Round up to the nearest whole​ number.)

To buy the necessary number of 2,150 ​puts, it would cost him ​$ …………... ​(Round to the nearest​ cent.)

To buy the necessary number of 2, 075 ​puts, it would cost him ​$....................... ​(Round to the nearest​ cent.)

b. If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by

20​% over the next six​ months, the net profit​ (or loss) Fitzgerald will earn​ (or sustain) from the hedge using 2,150 puts is ​$................................ ​ (Round to the nearest cent. Enter a positive number for a profit and a negative number for a​ loss.)

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by 20​% over the next six​ months, the net profit​ (or loss) Fitzgerald will earn​ (or sustain) from the hedge using

2,075 puts is ​$.................................. ​(Round to the nearest cent. Enter a positive number for a profit and a negative number for a​ loss.)

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by only 10​% over the next six​ months, the net profit​ (or loss) Fitzgerald will earn​ (or sustain) from the hedge using 2,150 puts is ​$................................. ​(Round to the nearest cent. Enter a positive number for a profit and a negative number for a​ loss.)

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by only 10​% over the next six​ months, the net profit​ (or loss) Fitzgerald will earn​ (or sustain) from the hedge using 2,075 puts is ​$................................... ​(Round to the nearest cent. Enter a positive number for a profit and a negative number for a​ loss.)

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio go up by 15​%

over the next six​ months, the net profit​ (or loss) Fitzgerald will earn​ (or sustain) from the hedge using 2,150 puts is ​$............................... ​(Round to the nearest cent. Enter a positive number for a profit and a negative number for a​ loss.)

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio go up by 15​% over the next six​ months, the net profit​ (or loss) Fitzgerald will earn​ (or sustain) from the hedge using

2,075 puts is ​$...................................... ​(Round to the nearest cent. Enter a positive number for a profit and a negative number for a​ loss.)

c. Do you think Fitzgerald should set up the put hedge​ and, if​ so, using which put​ option? ​(Select from the​ drop-down menus.)

Fitzgerald would certainly be better off with a put option hedge if the market …………. From the above​ analysis, the put option with a 2,150 strike price provides a better hedge when the market ………...​, while the put option with a 2,075strike price provides a better hedge when the market ………………. .

d. The number of DJIA puts Fitzgerald would have to buy to protect his ​$745,000

stock portfolio is…………………… put options.  ​(Round up to the nearest whole​ number.)

To buy the necessary number of DJIA​ puts, it would cost him ​$........................... ​(Round to the nearest​ cent.)

If both the market​ (as measured by the​ DJIA) and the Fitzgerald portfolio fall by 20​% over the next six​ months, the net profit​ (or loss) will Fitzgerald earn​ (or sustain) from the hedge using DJIA puts is ​$............................ ​(Round to the nearest cent. Enter a positive number for a profit and a negative number for a​ loss.)

Fitzgerald would be better off with the ……………..….. put options.  ​(Select from the​ drop-down menu.)

Answer 1

a. The number of​ S&P 500 puts Fitzgerald would have to buy to protect his ​$745,000 stock portfolio:

=745000/2150=338.6364

Rounded to nearest whole number =339

The number of​ S&P 500 puts Fitzgerald would have to buy to protect his ​$745,000 stock portfolio is 339  put options.

To buy the necessary number of 2,150 ​puts, it would cost him ​$76.00*339=$25,764.00

To buy the necessary number of 2, 075 ​puts, it would cost him ​$57.50*339=$19,492.50

b. (i)If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by

20​% over the next six​ months:

Value of Portfolio=745000*(1-0.2)=$596,000

Loss from Portfolio =745000-596000=$149,000

Value of S&P=2200*(1-0.2)=1760

Payoff from Put option =339*(2150-1760)=$132,210

Cost of Put Option=$25764

Net Loss=(149000-132210)+25764=$42,554

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by

20​% over the next six​ months, the net ( loss) Fitzgerald will sustain from the hedge using 2,150 puts is( ​-$.42,554)

Put option with Strike=2075

Payoff from Put option =339*(2075-1760)=$106785

Cost of Put Option=$19,492.50

Net Loss=(149000-106785)+19492.50=$61,707.50

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by 20​% over the next six​ months, the net  loss Fitzgerald will sustain from the hedge using

2,075 puts is (-​$61,707.50)

(ii)If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by

10​% over the next six​ months:

Value of Portfolio=745000*(1-0.1)=$670,500

Loss from Portfolio =745000-670500=$74,500

Value of S&P=2200*(1-0.1)=1980

Payoff from Put option =339*(2150-1980)=$57,630

Cost of Put Option=$25764

Net Loss=(74500-57630)+25764=$42,634

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by

10​% over the next six​ months, the net ( loss) Fitzgerald will sustain from the hedge using 2,150 puts is( ​-$.42,634)

Put option with Strike=2075

Payoff from Put option =339*(2075-1980)=$32,205

Cost of Put Option=$19,492.50

Net Loss=(74500-32205)+19492.50=$61,787.50

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio fall by 10​% over the next six​ months, the net  loss Fitzgerald will sustain from the hedge using

2,075 puts is (-​$61,787.50)

(iii)If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio go up by 15​%

over the next six​ months:

Value of Portfolio=745000*(1+0.15)=$856,750

Gain from Portfolio =856750-745000=$111750

Value of S&P=2200*(1+0.15)=2530

Payoff from Put option =$0

Cost of Put Option=$25764

Net Gain=111750-25764=$85,986

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio go up  by

15​% over the next six​ months, the net PROFIT Fitzgerald will Earn from the hedge using 2,150 puts is

$85,986

Put option with Strike=2075

Payoff from Put option =$0

Cost of Put Option=$19,492.50

Net Gain=111750-19492.50=$92,257.50

If both the market​ (as measured by the​ S&P 500) and the Fitzgerald portfolio go up  by 15​% over the next six​ months, the net PROFIT  Fitzgerald will EARN from the hedge using

2,075 puts is $92,257.50