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  #1  
Old 01-17-2018, 11:09 PM
SweepingRocks SweepingRocks is offline
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Default 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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Old 01-17-2018, 11:42 PM
Academic Actuary Academic Actuary is online now
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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.
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  #3  
Old 01-17-2018, 11:45 PM
ARodOmaha ARodOmaha is offline
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Quote:
Originally Posted by SweepingRocks View Post
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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Old 01-18-2018, 12:13 AM
SweepingRocks SweepingRocks is offline
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Originally Posted by Academic Actuary View Post
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 View Post
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  
Old 01-18-2018, 12:18 AM
Academic Actuary Academic Actuary is online now
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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 .
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