Dissecting Gamma: GameStop’s Trip to the Moon

This morning, GameStop opened at $90, 50% above Friday’s closing price. It then proceeded to rally to $159 in a spectacular fashion before falling 50% to close around $75.

You won’t find even the strongest proponent of the Efficient Market Hypothesis to defend this move as one demonstrating “efficient markets.” But to us options traders, the move is not only understandable, but predictable.

We just witnessed a Gamma squeeze.

Checking in on Delta

Before we get into Gamma, let’s first review Delta. Delta is the unit that measures how much the price of an option changes with a $1 change in the price of the underlying stock. At-the-money options are 0.50 Deltas, meaning that a $1 change in the price of the underlying stock will change the price of the at-the-money option by $0.50.

However, since the price of the stock has now changed, a different option is at-the-money. And the Deltas of the original option change to reflect one that is in-the-money or out-of-the-money. The next $1 move (assuming it’s in the same direction) is going to impact the price of the option by more or less than $0.50.

Deep in-the-money options have a higher Delta, which means that the option acts more and more like stock. A $1 move in the price of the stock might move the price of the deep in-the-money option by $0.80 or $0.90. High Delta options give way to the stock replacement options strategy.

Conversely, out-of-the-money options will have a smaller Delta, meaning that a $1 price move in the stock might only change the option price by $0.20.

Intuitively, this should make sense. If an option is $20 out-of-the money, then a $1 change in the price of the stock doesn’t impact the intrinsic value of the option. All of the value gained by that option is going to be extrinsic value.

However, if the option is $20 in-the-money, that $1 move is a $1 move in the intrinsic value of the option. That value will carry through in larger percent to the price of the option.

Measuring Gamma

Gamma is a measure of how Delta changes; it’s the sensitivity of the Delta.

Both Delta and Gamma are dynamic, meaning that each measure differs based on whether it is out-of-the-money, at-the-money, or in-the-money. An option with a Delta of 0.50 and Gamma of 0.10 will have a different Delta and Gamma as the price of the stock changes.

So, if a stock with a 0.50 Delta has a 0.10 Gamma, then a $1 move in the price of the stock will cause the price of the option to move $0.50. But, the Delta will also move. In this instance, the option then becomes a 0.60 Delta option. The next $1 move in the price of the stock will cause the price of the option to move $0.60.

Gamma is highest for at-the-money options. Again, back to our earlier example, an at-the-money option is moving from no intrinsic value to some intrinsic value as the price of the stock moves in the right direction. So, in the example above, that $1 change in the at-the-money option is going to change Delta more than a $1 change in either an in-the-money or out-of-the-money option.

Market-Making Firms and the Gamma Squeeze

Ok, so if we understand Gamma and Delta, we can start to understand how this exponential move in price happened.

At options market-making firms, their goal is to collect an option’s extrinsic value–also known as Theta or time premium. To do this without any risk, they keep themselves Delta neutral by trading stock against the options. Delta neutral means that you have 0.00 long or short Deltas.

A simple example: if a firm sells an at-the-money call option (going short 0.50 deltas), they would offset that by purchasing 50 shares of the stock. Then, as the price of the stock moved up and down, they would adjust the amount of stock they own by how many Deltas they are long or short. If the stock went up $1 and they were now short a 0.60 Delta option, they would have to buy 10 more shares of stock to offset the changing Deltas. If the stock kept going higher, the market-making firm would keep buying the underlying stock.

When you multiply this by the amount of options that were being bought at the open in GameStop, market-making firms had to buy… and keep buying the underlying GameStop stock. As the stock went higher, they had to buy more. And then more and more.

In an environment where there are thousands of traders adding out-of-the-money calls that then need to be hedged by going long stock, the buying pressure creates more buying.

The only way that the buying pressure from market-making firms abates is when the call buying abates. There has to be someone else on the other side of the trade. This is where the particulars of GameStop come into play. GameStop has huge short interest—most recently at more than 100%. The stock is labelled “hard to borrow.” And today, it became even harder to borrow. There was no one on the other side of the trade. The only people selling GameStop were long GameStop. But those who were short were forced to buy. It was a perfect storm.