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#1
01-17-2018, 11:09 PM
 SweepingRocks Member SOA Join Date: Jun 2017 College: Bentley University Posts: 53
Stupid question on caps

So I have the ASM manual and for some reason I just cannot understand the reasoning behind how they're calculating the profit from caps. Here's a question I'm having particular trouble understanding:

A trader shorts one share of a stock index for 50 and buys a 60-strike European call option on that stock that expires in 2 years for 10. Assume the annual effective risk-free interest rate is 3%.
The stock index increases to 75 after 2 years.
Calculate the profit on your combined position and determine an alternative name for this combined position.

So I know that it's a cap, because you're shorting a stock and your buying a call option. What I can't wrap my mind around is the profit. The book states that the profit is 50(1.03^2)-60 from the short sale and -10(1.03^2) from the call, or -17.56.

Now I might be very stupid, but why in the world would you subtract 60 from 50(1.03^2)?? Isn't 60 just the strike price? Why would that play a role in the profit? And wouldn't the trader make a profit of 75-60-10(1.03^2) on the call option alone? If someone could please help my lost soul, I'd be grateful.
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#2
01-17-2018, 11:42 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,225

Assume that the trader covers the short position by exercising the call for 60. Alternatively he covers by buying the share for 75 offset with a payoff of 15 from the call.
#3
01-17-2018, 11:45 PM
 ARodOmaha Member SOA Join Date: May 2016 Location: Omaha, NE Studying for MFE College: University of Nebraska (alma mater) Favorite beer: Captain Morgan Posts: 155

Quote:
 Originally Posted by SweepingRocks So I have the ASM manual and for some reason I just cannot understand the reasoning behind how they're calculating the profit from caps. Here's a question I'm having particular trouble understanding: A trader shorts one share of a stock index for 50 and buys a 60-strike European call option on that stock that expires in 2 years for 10. Assume the annual effective risk-free interest rate is 3%. The stock index increases to 75 after 2 years. Calculate the profit on your combined position and determine an alternative name for this combined position. So I know that it's a cap, because you're shorting a stock and your buying a call option. What I can't wrap my mind around is the profit. The book states that the profit is 50(1.03^2)-60 from the short sale and -10(1.03^2) from the call, or -17.56. Now I might be very stupid, but why in the world would you subtract 60 from 50(1.03^2)?? Isn't 60 just the strike price? Why would that play a role in the profit? And wouldn't the trader make a profit of 75-60-10(1.03^2) on the call option alone? If someone could please help my lost soul, I'd be grateful.
First and foremost, note that the answers are the same either way.

Abe combined +75 with -75 and his explanation was confusing. But here is the SOA version of the answer (taken from introductory derivatives question #13):

Buying a call in conjunction with a short position is a form of insurance called a cap. Answers (A) and (B) are incorrect because a floor is the purchase of a put to insure against a long position. Answer (E) is incorrect because writing a covered call is the sale of a call along with a long position in the stock, so that the investor is selling rather than buying insurance. The profit is the payoff at time 2 less the future value of the initial cost. The stock payoff is –75 and the option payoff is 75 – 60 = 15 for a total of –60. The future value of the initial cost is (–50 + 10)(1.03)(1.03) = –42.44. the profit is –60 – (–42.44) = –17.56.
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#4
01-18-2018, 12:13 AM
 SweepingRocks Member SOA Join Date: Jun 2017 College: Bentley University Posts: 53

Quote:
 Originally Posted by Academic Actuary Assume that the trader covers the short position by exercising the call for 60. Alternatively he covers by buying the share for 75 offset with a payoff of 15 from the call.
Quote:
 Originally Posted by ARodOmaha First and foremost, note that the answers are the same either way. Abe combined +75 with -75 and his explanation was confusing. But here is the SOA version of the answer (taken from introductory derivatives question #13): Buying a call in conjunction with a short position is a form of insurance called a cap. Answers (A) and (B) are incorrect because a floor is the purchase of a put to insure against a long position. Answer (E) is incorrect because writing a covered call is the sale of a call along with a long position in the stock, so that the investor is selling rather than buying insurance. The profit is the payoff at time 2 less the future value of the initial cost. The stock payoff is –75 and the option payoff is 75 – 60 = 15 for a total of –60. The future value of the initial cost is (–50 + 10)(1.03)(1.03) = –42.44. the profit is –60 – (–42.44) = –17.56.

Okay so I think I understand everything except for the stock payoff being -75. Are we assuming he buys the stock back that he originally sold? I apologize if this is a stupid question.
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#5
01-18-2018, 12:18 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,225

When you calculate profit or loss you generally assume you close all open positions which would require buying back the shorted (borrowed) stock to repay the loan .