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If You Can Follow Basketball, You Can Trade Options

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Using March Madness to understand complex market moves.

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Author's Note: Back in the early 1990s, near the end of a close NCAA tournament game, it hit me that lead changes, especially rapid ones near the end, provide a great framework for understanding gamma. Gamma, probably the single most important option "Greek," refers to the change in the option's sensitivity to stock moves.

As we approach the Final Four, even without Toddo's beloved Orange, I'd like to offer you my thoughts on this, which originally ran on the
Forbes website.


Understanding how option prices -- from SPY to SPX and beyond -- change in response to changes in other variables can be tricky. The Greek (delta, gamma, theta, etc.) and pseudo-Greek (vega) names used to measure option sensitivities do not necessarily make things clearer. Options do, however, make intuitive sense if they can be viewed in an easily understood framework, such as basketball.

Delta (Probability of an option finishing in the money)

An option's delta is its most frequently observed characteristic. Delta is, strictly speaking, a hedge ratio, measuring the sensitivity of the option's price to very small changes in the price of the underlying instrument. But for most shorter-dated options it also approximates the likelihood that an option will finish its life "in the money" (e.g., that a call option will expire with the underlying asset at a higher price than the call's strike). A nearly exact analogy in a basketball game is the probability that one of the teams will win.

Suppose Teams A and B are about to play and the game is considered a toss up. Before the game starts, each team has an equal chance of winning. With options, 50% is a typical delta for an at-the-money option with a relatively short term to expiration, say one month. The fact that the option is at the money (i.e., the underlying asset's price is equal to the option's strike price) is important for preserving the basketball analogy because each team is neither ahead nor behind, just as the option is neither in nor out of the money.

Suppose now that in a game, Team A is a heavy favorite. It has a delta of, say, 80%. Since the game has not yet begun, we must still say that the option is at the money. How can an at-the-money option have such a high delta? It can if there is strong reason to believe the underlying asset will exceed the strike price at expiration (we will continue to use calls in our example, although the logic can also be used for puts). What might be the rationale for such a belief?

Consider a 10-year at-the-money call option on an index of non-dividend-paying stocks. The opportunity cost of keeping money in stocks for this long a period is quite high: funds invested in low-risk securities could easily double because of compounding interest. Thus it doesn't seem reasonable to expect the stock index to have a lower nominal value at the end of the period than at the beginning.

Just as Team A is heavily favored to beat Team B, a 10-year at-the-money call option is heavily favored to finish in-the-money. Consequently, the delta, or the approximate probability of the option being in the money, will be much greater than neutral (50%). Note that this logic clearly does not apply to short-term options, since their value is dictated by price moves over a handful of days, and the randomness of these moves will dominate the relatively minor amount of forgone interest income over such a short period of time.
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No positions in stocks mentioned.

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