Share-equivalent risk

The "fair value" of a call or put depends on five parameters:

Other parameters held equal, call options become more valuable as the stock rises, and puts decline. The exact sensitivity of an option's price to small changes in stock price is known as the option's delta, which can be calculated from option price theory equations. 

When the stock price is very near the option strike price, a call's delta is close to 0.5 (50%). This means that when the stock price rises 10 cents, the call will appreciate by 5 cents. Similarly, when the stock is near the option strike price, a put's delta is close to -0.5 and the put will decline 5 cents if the stock goes up 10 cents.

A standard option contract is for 100 shares. Therefore, if you own a call contract with delta = 0.5 you will gain or lose the same amount of money as if you owned 50 shares of stock. We say that the contract's share equivalent risk is 50. 

Delta is very immediate: generally you want to know the share equivalent risk right now. Here's a picture of the share equivalent risk for owning a 100-strike call on AHSO when the stock is at 101. By default, Options Laboratory sets the project date slider all the way to the left for this graph. You can see that the share equivalent risk is about 52 shares at the current stock price (dashed magenta line).

These graphs can be more structurally complex when applied to option combinations. Some combinations even move from positive to negative share equivalents in certain price ranges: they suddenly start acting like short stock positions instead of long ones.

How to use this information

Options Laboratory calculates net share equivalent risk for an entire combination position (all options plus any shares). If the share equivalent risk is negative, that's like "shorting" the stock. If it's positive, you are effectively "long" the stock.

In general, you should be just as happy in the very short term to own an option combination as you would be to own (or be short) the equivalent number of shares. However, share equivalent risk changes with as the stock price moves, and as time passes. If the line slopes upward to the right, when the stock price goes up you are effectively gaining the benefit as if you owned or controlled more shares.

As expiration approaches, the share equivalent risk can become much more sensitive to stock price changes; a small price change may suddenly turn a winner into a loser. You should move the projection date slider over to the right to see if this is the case, because you might then wish to close out your position a few days before expiration to avoid the increased uncertaintly.