# Actuarial Discussion Forum - Professional Discussions for Professional Actuaries

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1. ## payoff error

I'm going over one of my practice exams and I think there may be a mistake in the way the question was written.

It asks for the portfolio that produces the given payoff diagram. The correct answer is "A short put with exercise price of 50 plus long call with exercise price 150." My answer was "A short put with exercise price 150 plus long call with exercise price 50."

Don't both of those produce the same payoff diagram?

______/
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2. Your's also looks like this:

____________/
/

But, are there numbers in the payoff graph? Because, take for example a spot price of 200. his answer, you would have 0 payoff from the put and 50 payoff from the call, so you get 50.

for a spot price of 200, and your answer, you'd get payoff from put, 0, payoff from call, 150.

So while it makes the same shape, I think the lines are steeper and such in different areas, maybe making the answer wrong?

3. Actually, if you compute the payoff for different levels, you get the follow:

stock price....Profit from short 150 put......Profit from long 50 call......Total
0 ........................... -150 ............................. 0....................... -150
50........................... -100 .............................. 0 .................... -100
75............................. -75 ...............................25................. ...... -50
100.............................-50...............................50............... ..........0
125.............................-25...............................75............... ..........50
150................................0.............. .................100.......................100
200............................... 0................................150.............. .......150

If you graph the stock price vs the Total, your graph actually looks like a long foward. The answer in the book is correct.

4. Ok so I can see why his answer is wrong now. However, I don't think that those values make a long forward. I mean, when I'm graphing them out, I get the portion between stock price -100 to 100 to be steeper than the outer portions. It looks kind of like a really really slanted bull graph. Do you get what I mean? Am I graphing it right?

5. I thought it was going to look like that, too, but if you look at the slope from where the line crosses the x-axis (at s=100), it's the same above as it is below (150/100).

6. Thanks bayou, I understand now.

7. Originally Posted by cactus smash
I'm going over one of my practice exams and I think there may be a mistake in the way the question was written.

It asks for the portfolio that produces the given payoff diagram. The correct answer is "A short put with exercise price of 50 plus long call with exercise price 150." My answer was "A short put with exercise price 150 plus long call with exercise price 50."

Don't both of those produce the same payoff diagram?

______/
/
I just thought of this, correct me if I am wrong.

The graph looks like a written collar. Since a collar is sell a call and buy a put at a lower price, (the opposite of the above graph) the written collar would be buy a call and sell a put at a lower price.

How does that sound?

8. Originally Posted by bayoubelle
I thought it was going to look like that, too, but if you look at the slope from where the line crosses the x-axis (at s=100), it's the same above as it is below (150/100).
I get the slope of the line from x=0to50 : m=1
from x=50to150 : m=2
from x=150toinfinity : m=1

Amirite?

9. Yeah, that's what I got. So you're right, it's not exactly a long forward, but it's close. It also kinda looks like a collar. But if you read the DM book, it says that a collar looks kinda like a forward from a distance. I think the point of the problem is that the answer in the solution manual was correct. The easiest way I've found to answer these types of questions is to do a chart similar to the one I did earlier.

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