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## Do you say “I lost \$X” or “I lost -\$X”?

August 29th, 2007

I got this great question from a student:

I believe there is an error on problem 18 of Section B chapter 2.
The third choice in the true/false statements says:

A short put’s maximum loss is:
Strike price – FV (put premium)

The solution for this questions says that the above statement is true.

However, based on the notes from the 4th video of this chapter and the text book page 43, if the statement is going to be true it should be:

A long put’s maximum gain is:
Strike price – FV (put premium)

or

A short put’s maximum loss is:
FV (put premium) – Strike price

Please let me know if I am missing something.

Here was my response:

This is really just a difference in how you say you lost \$X. Do you say I lost \$X or I lost -\$X. Hopefully the exam wouldn’t contain something like this.

If you short a put what is the worst case scenario? Well a put option has value when the stock price goes down, so the worst case scenario for a short put is a spot price at expiration of 0. You have to buy the stock at the strike price and you’ve accumulated the FV(premium). So FV(premium) – Strike price will be a negative number. Let’s say the FV(Premium) is \$5 and the strike price is \$100. Then according to the book you have a loss of \$5 – \$100 = -\$95. To me it doesn’t make sense to say I lost -\$95 (losing -\$95 means winning \$95 IMO). I would say I lost \$95 = \$100 – \$5 = Strike Price – FV(premium).

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