Unpacking Gamma—Delta’s Evil Enabler

Poor old delta always gets the blame when a stock goes against an option position. If you short a put and the stock drops, the put’s long delta is causing the pain. If you short a call vertical and the stock rallies, the vertical’s short delta is costing you every point the stock goes up.

There’s a Helper Lurking

But delta has an accomplice. An evil enabler that should, in a fair world, get its share of blame for the “l” half of “p/l.” Gamma, we’re looking at you.

First, the textbook definition of gamma: It’s the second derivative of the option’s price with respect to the stock’s price. It’s how much an option’s delta changes when the stock price changes $1. Some traders leave it at that—potentially, to their peril.

Let’s say you’re bullish on a $100 stock, and you short a $95 put for a $1 credit with 45 days to expiration. The put has a delta of 0.23, giving it risk equivalent to about 23 shares of long stock. You’re cool with that. Two weeks pass, the stock is still at $100, and your short put’s price has dropped to $0.65—time decay in action! The put’s delta has dropped to 0.19, which means you now have less delta risk than you did two weeks ago. What’s not to love?  

You’re still bullish as the stock moves up and down a little for the next 28 days, but with three days to expiration, the stock has dropped to $97. The put’s now worth about $0.13—still profitable—and its delta is only about 0.14. You figure you can handle the risk of 14 shares of stock. So, you keep the short put on until expiration, confident the stock won’t drop below $95 in the next three days.

But It Does. Ouch.

While you were watching the stock’s price and the put’s delta, the gamma of that short put went from a tame -4 when it had 45 days to expiration and the stock was at $100, to a wild -12 with three days to expiration and the stock at $97. So for every point the stock moved down, the short put would be manufacturing three times as many long deltas as when you first put the trade on. Your delta risk now fluctuates much more as the stock price changes.

With one day to expiration, the stock is at $95, the put’s delta is 0.50 (which may be more risk than you’re comfortable with), and the put’s gamma has grown to -0.38. As the stock drops from $95 to $94, the put’s delta grows to 0.83. As the stock moves back to $96, the put’s delta drops to 0.16. Your risk is fluctuating dramatically with every point the stock changes. Yes, your p/l is being driven by the put’s delta. But it’s really the put’s short gamma that’s making the trade’s risk tough to manage.

Negative gamma manufactures negative deltas when the stock rises, and positive deltas when the stock drops. Positive gamma manufactures positive deltas when the stock rises, and negative deltas when the stock drops.

Gamma is what makes your delta go from mild to ferocious, from small to large. If you trade options, you’ll have gamma. If gamma didn’t exist and the option’s delta stayed constant, an option would act a lot more like shares of stock (which have delta, but no gamma). Then you’d only have to worry about the price of the stock going up or down. But an option’s delta doesn’t stay constant. And the instability of that delta depends on the option’s gamma.

Likewise, gamma itself isn’t constant. All things being equal, gamma is highest for the at the money (ATM) options and is lower the further an option is out of the money (OTM). Gamma is also higher the closer an option is to expiration. In other words, the ATM option at expiration has the highest gamma.

This is often why traders get excited about expirations. Expirations are busy times—rolling positions, adjusting hedges, getting ready to exercise or be assigned on in-the-money (ITM) positions. Those activities become more urgent around expiration, partly because deltas can fluctuate from big to small with relatively minor price changes for stocks and indices. And that’s caused by large gamma.

If gamma’s so important, where can you find it? On the thinkorswim^® platform from TD Ameritrade, you can see each option’s gamma on the Option Chain on the Trade page. Load gamma as one of the columns to see that gamma is higher for ATM options, for example, and how gamma changes from one expiration to another.

You can see the gamma of your positions on the Position Statement section of the Monitor page (Figure 1).

Here you see how much gamma you have relative to your deltas. The position can also be beta-weighted to show how much beta-weighted gamma could affect beta-weighted deltas.

Say the beta-weighted gamma is -1.34, and the beta-weighted SPX delta is -77. If the SPX moves up a point, your delta would theoretically go from -77 to -78.34, and if the SPX moves down a point, the delta would theoretically go from -77 to -75.66.

Yet, as time passes, that gamma could grow, even if the deltas don’t. Which is why you need to monitor your portfolio’s gamma as much as its delta.

Scalp Gamma?

Yup, gamma’s important enough to get its own trading strategy. Gamma scalping hedges the deltas manufactured by gamma as the price of the stock moves up and down. Traditionally, gamma scalping is done with a long straddle, which has relatively low deltas, because the ATM call and put have deltas close to 0.50. So the +0.50 delta from the call offsets the -0.50 delta from the put. But the straddle has a lot of gamma and negative theta.

If you think a stock might make a big move in a certain direction, gamma scalping can help offset that negative theta. Imagine a straddle that has zero delta and, say, 50 gamma. That means that as the stock moves up $1, the straddle’s delta rises to 0.50. If the stock drops $1, the straddle delta moves back to zero. Then if the stock drops $1, the straddle’s delta goes to -0.50. Gamma scalping hedges the straddle’s delta with stock when it reaches some amount.

Or, imagine the stock rises $1. The straddle delta is now 0.50, and you sell 50 shares of stock. That gets the delta of the whole position (straddle plus stock) close to zero. Now if the stock drops down $1, the delta of the straddle plus stock is -0.50, and you can buy those 50 short shares back to get the position delta back to zero. You just scalped 50 shares for $1 and made $50 to help offset the negative theta.

Gamma scalping can also be done from the short straddle side, but the stock hedges lose money against the short straddle’s positive theta. Either way, gamma scalping is commission and capital intensive, and it isn’t a strategy that many retail traders use.

Gamma Manager

Rather than gamma scalp a position’s deltas, you could consider simply managing a position’s gamma. And that has to be done with options, because stock has zero gamma.

For example, going back to our short $95 put: as gamma grew, the ratio of gamma to delta also grew. The put’s delta was becoming more sensitive to changes in the stock price and could fluctuate. One way to reduce the position’s gamma is to roll that $95 put to a further expiration. Rolling to the same strike price will maintain roughly the same delta but can reduce gamma exposure.

Another possible way is to buy a lower-strike put to turn that short $95 put into a short put vertical. If you bought the $94 put, for example, its gamma would be fairly close to the gamma of the $95 put. The long gamma of the $94 put will offset some of the short gamma of the short $95 put, also reducing your gamma and delta exposure.

In both cases, rolling to a further expiration and turning the short option into a vertical also reduces the positive theta of the original short put, and incurs commissions.

But don’t be down on gamma. It’s just an option greek—a metric used to gauge the level of risk for a position or portfolio. Delta may be the greek that determines the p/l of an option trade. But gamma shines a light on delta.

Maybe gamma isn’t the evil enabler, but rather delta’s best friend that, like all best friends, can sometimes help and sometimes hurt.

Watch Gamma Move

To see how much your position’s gamma might increase or decrease as a stock price or time changes, use the Analyze page on thinkorswim (Figure 2). The Price Slices area, below the Risk Profile, shows a position’s gamma. Here, at the index’s prevailing price, it’s -0.12. And if the index rises 10%, it would likely go to -0.02. If the index drops 10%, it would likely go to -0.01.

Two days before expiration, all things being equal, the position’s gamma likely increases, and if the index drops or rises 10%, the gamma likely drops to zero. Using the full functionality of the Analyze page lets you see how gamma (and delta) change when the stock price changes, time passes, and volatility goes higher or lower.