# Understanding Long and Short Gamma

01/18/2010 10:58 am EST

Focus: OPTIONS

I often mention the option Greek gamma, and refer to "long gamma" or "short gamma" when describing a position. I bet many of you wonder what exactly that means, and/or how to manage said position. So I'll explain.

Gamma is used to measure the rate of change in an option's delta as the underlying security (stock, ETF, index) moves. In a positional context, long gamma means your option position is such that if the stock rallies (or declines), your share equivalent position (also known as delta) gets you longer (or shorter).

Example of a Long Gamma Position

Let's say you own 1,000 shares of Apple (AAPL) and you own 20 AAPL Feb 210 puts.

With AAPL trading around \$210, your 210 puts have roughly a 50 delta. That means that each put you own is the equivalent of being short 50 shares of stock. So, right here, right now, owning 20 puts is the share equivalent of shorting 1,000 shares of AAPL. Since I am physically long 1,000 shares of AAPL, my share equivalent position is 0, or flat.

But let's say AAPL rallies. The share equivalent (delta) position of my puts declines. For arguments sake, let's say they now have 40 delta, making me equivalent to short 800 shares via the puts (40 x 20). My stock position obviously stays the same at 1,000 shares, making my net position the equivalent of long 200 AAPL shares (1,000 - 800).

Conversely, had AAPL declined a similar amount, and the delta of the puts increased to 60, I'd be the equivalent of short 200 AAPL shares (60 x 20) - 1,000.

That's a long gamma position. Sounds great, right? Stock rallies and I get longer; stock declines and I get shorter. Who wouldn't want that? I can sell AAPL into rallies and buy it on declines, and not have to worry about being wrong. If it rallies more, I can just sell more!

But remember, this sort of position costs money each day. Options are a decaying asset. The less time remaining until expiration, the lower the value of an option, all else being equal. Another option Greek, theta, measures your daily decay. And that's your cost of holding a position like this in Apple.

For this particular example, let's assume the volatility of the option remains static. In order to earn money on a long gamma position such as this, we need to offset our daily decay.

There are two extreme ways to do this.

One is to aggressively trade AAPL stock and hope to earn enough "flipping" to offset the cost of the position. Remember that you get longer as it goes up and shorter as it goes down. It's the equivalent of trading with a safety net, so you're literally able to trade against every move up until you've bought (sold) 1,000 more shares.

The other option is to just sit until expiration and hope AAPL has moved far, far away from \$210. Let's say you paid \$10 for those puts. If AAPL closes above \$230 or below \$190, you win. The higher above or the lower below those levels, the more you win.

Of course, in real life, you will likely have an approach somewhere between these two extremes.

For example, you'll likely sell some into strength and leave some. You'll get lucky sometimes and wake up to gaps in AAPL. You'll get unlucky sometimes and have AAPL stick near the strike for long stretches of time.

Part of successfully managing a long gamma position involves making judgments as to whether we're in a "trend" environment or a "range" environment.

If we're trendy, you want to remain more patient about hedging. Last sale is often best sale.

If it's a range day, week, or month, then you really need to get in there and flip the stock on any "noise."