How to Calculate Payoffs to Option Positions

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  • 0:04 Options Terminology
  • 0:42 Long Call Options
  • 2:23 Short Position Calls
  • 2:51 Long Put Options
  • 4:07 Short Position Puts
  • 4:34 Lesson Summary
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Lesson Transcript
Instructor: James Walsh

M.B.A. Veteran Business and Economics teacher at a number of community colleges and in the for profit sector.

Options provide a great way to take a bullish or bearish position on a stock. They limit the investor's downside while keeping the upside unlimited. Let's look at the payoff on options positions with graphs, formulas and examples.

Options Terminology

Dan and Donna work at the trading desk of Big City Bank. Their job is to make all they can in the financial markets with the bank's money. They like to trade in options because of the leverage they provide over just buying and selling the shares of stock. Let's look at a few positions they'e getting ready to take and why options are so appealing.

Let's go over some terms first:

  • The strike price is the price at which the option holder can execute the option up until its expiry date when the option ends.
  • A call option is the right to buy at the strike price.
  • A put option is the right to sell at the strike price.
  • The premium is the amount paid for the option.

Long Call Options

Dan is bullish on a robotics company that he believes has an amazing future. They'll be announcing a new product line of industrial robots soon, and Dan believes that will give the stock a good bump.

Rather than buy shares, he is looking at a long position with call options, as they limit his downside and still allow unlimited gains if the stock price should blow up. Here are some facts about his position and what the payoff will look like at various stock prices on a graph:

Call option

Now let's go a little deeper. The break-even point is the stock price at which an investor's net profit will be zero.

Break-even stock price = Strike price + Premium

In this case its $100 + $3 = $103. Another feature to note is that if the stock price is below the strike price, Dan will just let the options expire without using them and his losses will be limited to the premium he paid for the options. The bank likes that part!

They also like that profits are unlimited as the price goes higher than $103. Here is a formula:

Call payoff per share = (MAX (stock price - strike price, 0) - premium per share

The MAX function means that if stock price - strike price is negative, just use zero.

At a stock price of $97, (MAX ($97 - $100, 0) - $3
= 0 - $3
= ($3) per share loss.

At a stock price of $106, (MAX ($106 - $100, 0) - $3
= $6 - $3
= $3 profit per share.

If the price should jump to $120 Dan would make $17 per share for the bank. If he has options covering 1,000 shares that would be a $17,000 profit!

Short Position Calls

The writer of the call option takes a short or opposite position. His payoff graph is the opposite of the long position we mentioned. Profits are limited to the premium he collects when the strike price exceeds the stock price and the calls are allowed to lapse. Above the strike price he faces increasing losses as the stock price increases. The payoff formula is:

Short call payoff per share = (premium per share - (MAX (0, (share price - strike price))

Long Put Options

Donna has just returned from a major apparel company's fall showing; she was not impressed. She doesn't think they will have a very good back-to-school season and that will cause the stock price to drop. She's preparing to take a long position with put options on the stock. Here are some facts about her position and what the payoff will look like at various stock prices on a graph:

put option

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