Gamma Squeezes and Schelling Points

>Intro

After Gamestop’s eye watering rally Friday Jan 22 and Monday Jan 25, several discussions have occurred in the financial newsletter circles (Nope, it's Lily, Kris Sidial, Benn Eifert, Matt Levine, among many others). Particularly regarding gamma squeezes, short squeezes, and Schelling points. Each of those listed above has done an incredible job outlining what happened, so please take a look at their articles as well.

The general consensus of the price movement seems to be that a short squeeze was somewhat a factor, but not the driver. And that the driver was actually a gamma squeeze. And that for the gamma squeeze to occur, there has to be a focal point (or Schelling point), as if investors collectively used a magnifying glass to focus their energy on one stock, like magnified sunbeams on an unwitting ant. This is where the “Schelling Point” is important. We’ll get to that later. First, what happened with Gamestop?

>Gamma Squeeze

Succinctly, a gamma squeeze occurs because of market makers delta hedging their positions.

^Let’s break this down.

1. Investors buy out-of-the-money call options.
2. Market makers (MMs) sell these options to the investors.
3. In order to hedge themselves, MMs will buy some amount of stock in the case of assignment, determined by the Delta of the contract.¹
4. As the price of the underlying goes up, the Delta of the contract goes up, and MMs buy more shares to cover their position and hedge back to delta neutral.
5. This additional buying results in higher prices, adding fuel to the momentum, which causes a loop back to Step 1.

This same cycle actually occurs on the Put side as well. As MMs sell Put contracts, they also sell short the appropriate, delta-hedged number of shares. And as the underlying price rises, MMs unwind their Put hedges by purchasing shares, covering their short positions.

Gamma is a measure of how much Delta changes as the underlying moves (the 2nd derivative). It is highest at-the-money, and tapers off in each direction, in- and out-of-the-money. Because of this, “delta hedging” occurs most with at-the-money contracts.

What’s interesting with GameStop, is that we could watch this unfold in real time, particularly because the highest strike contract available on Friday Jan 22 was $60 (market closed at $41 on Jan 21). So the “gamma squeeze” cycle occurred exponentially through $60 to $74, where the price eventually recovered, and leveled off at $65. At this point, all outstanding call contracts available were in-the-money.

At this price, most of the outstanding contracts approached a delta of 1. This means that MMs didn’t have to buy as many shares as rapidly (given that the highest gamma is at 0.5 delta), because they had already bought so many shares to delta hedge their positions previously. Since all contracts were in-the-money, most of the gamma had already been surpassed as the price rose past $60. This effectively eliminated the fuel from the gamma squeeze beyond $60.

Nope, it's Lily also goes into further detail about why the contracts expiring the same day, with 0 DTE, were significant contributors to this phenomenon as well (longer dated contracts had less of an effect).

So in all likelihood, the effect on GameStop was a gamma squeeze. But why was it not a short squeeze if 140% of the outstanding float was shorted?

>Short Squeeze

First of all, it’s harder to prove that it was not a short squeeze than it is to prove that it was a gamma squeeze (still could be both). However, there are some clues:

• The “140% shorted shares” number is widely used to point to a short squeeze. The number alone is not enough information, though. Simply the low amount of shares outstanding could be cause for the 140% shorted number. There could be an unlimited line of short seller “chains” — Person A lends shares to person B who shorts them to person C, who then repeats the process. Matt Levine describes this process well.
• The amount short interest has not really budged for several weeks, implying that the short positions may have not yet been covered as the price has increased (this of course could have changed during the day on Friday Jan 22).
• Institutional investors are rarely permitted by their risk teams to assume unlimited risk. So if they are short shares, they likely also purchased out-of-the-money call options at the time of entry as a hedge, capping their total losses. Or, as Nope, it's Lily explains well, they could simply long Put options, as Melvin Capital did with 54,000 Put contracts late last year.
• The largest detractor to the previous argument is that Melvin Capital had to be bailed out by Citadel and Point72 for $2.75bn on Monday Jan 25, because Melvin was down 30%, implying that their risk limits were quite high, and actually have been burned by the price rise. The equity injection does, however, mean that Melvin likely hasn’t yet covered their short position, and that they are digging in to ride out the storm. This is further evidence that this was not a short squeeze (a short squeeze would require them to cover).
• Short selling availability: Data is mixed here. Andrew Left from Citron Research, publicly known to be short Gamestop, released a video on Thursday Jan 21, saying the stock is easy and cheap to borrow. Now, it’s very hard to believe the guy who’s best interest is to make it seem like a short squeeze is far away. He is however, clearly very convicted on the trade. So maybe he is long Puts (as opposed to outright short selling), or has favorable terms with him prime broker, giving Citron breathing room on the price spike, or maybe he is just putting on a show, who knows. On the other hand, Nope, it's Lily points out that Fintel claims that only 4,000 shares were available to borrow. Counter to that, though, is that block trades and dark pools likely make the availability much larger.

So again, the data on a short squeeze is rather mixed and limited, but in general, these dynamics point to a gamma squeeze rather than a short squeeze.

>Schelling Points

In order for either of these squeezes to occur, there has to be insatiable demand. The demand has to come from somewhere, and it could have happened to any outstanding stock, so why GameStop?

Gamestop has acted as a Schelling Point for the “game” of the stock market.

A Schelling Point is effectively an agreed upon focal point without direct communication regarding its selection. For example, in the coordination game below, 2 contestants are asked to pick any 1 of the 4 squares, without communicating. If they and the other contestant both pick the same square, they each win a prize, otherwise they win nothing. With no other information, most rational people would pick the red square, simply because it is different from the others. They could have both picked the top left blue square and still won. Regardless of the quality of any of the squares, as long as both agree on the same square, both win.

In the case of GameStop, it has brand recognition, a comeback story, and a “big brother” enemy of institutional short selling. These 3 pieces are the “spark” of a Schelling Point. And then the kicker is that, unlike a Schelling Point where no communication occurs, communication regarding the focal point here can and does occur. The hype-build up on r/wsb (and eventually to other news sources as well) adds a vicious cycle of buying and re-buying. To paraphrase Matt Levine: “Take 1 person who is long for fundamental reasons, add 100 people who are long for personal amusement reasons, and then add 1,000 people who are long because everyone else is long.”

>The Big Takeaway

I wrote this more for my understanding of the phenomenon rather that to come to any conclusion. However, what’s the point of analysis without a conclusion? Therefore I offer a couple points:

1. What is going to happen next with Gamestop?

Predicting the top of a bubble is the fastest way to paint yourself into a corner. So I won’t try to predict the top, but I will predict this: In the short term, there’s room for Gamestop to get squeezed much higher. And in the long term, the bubble will likely pop as fast as bitcoin in Dec 2017, and tulips in the 17th century. Here’s why:

Short Term Bull:

• If Melvin Capital is still solvent, and still holding on to their short position, that means a short squeeze hasn’t happened yet. And given their conviction, they would likely dig in deeper and deeper as the price keeps grinding higher. This will add a lot of pressure, both on Melvin and in the media, causing further price spikes. UPDATE Jan 27: Well, this aged like milk. Both Melvin and Citron announced they closed their short positions. On the other hand, the stock is over $300 today, so could have been short squeezed yesterday.
• The conditions for a gamma squeeze were present last week, and they are still present today. As long as CBOE continues to provide higher strike contracts, and the share price continues to rise above the highest strike, the gamma squeeze situation can continue to occur (Note that driving the price above the highest strike contract does not increase the effects of a gamma squeeze, it actually detracts from it, because all contracts are then in-the-money, reducing the need for delta hedging, because most of it has already occurred at lower strikes. My point here is that CBOE can continue to add contracts, opening the door for further squeezes).
• The hype only continues to grow on the internet. Reddit and Twitter are flooded with discussions on Gamestop. There’s only 1 clear breaking point, and it’s $1,000/share as discussed on r/wsb. Unlikely to reach this point, but of course anything is possible.

Long Term Bear:

• The obvious point: fundamentals. Gamestop is not a $5.4bn company, plain and simple. This in itself is an entire discussion, so I won’t touch on that here. I will clarify though that when I say “fundamentals”, I’m referring to its value proposition story as a company (come on, it’s the blockbuster of video games), its money-losing financials, its absurd market cap valuation, etc.
• Bubble history: There are countless examples. Regardless of actual value, they always end up the same. Shortly after the pop, they remain at or near their levels prior to the hype up.
• With the price as high as it is, Gamestop themselves should sell stock to investors. And on Dec 8, 2020, they did file to do so. Up to $100 million in fact. And if levels stay as elevated as they are, they should (and likely will) continue to sell, adding additional downward pressure on the stock.
• Lastly and interestingly, one of the points above for short term bull applies here for long term bear as well: Melvin Capital’s (and others) commitment to short selling this stock. If they ride out the storm — and it appears that they will — they will help drive the price back down to a reasonable level. UPDATE: Again, aged like milk.

I won’t be taking any positions here, but if I were, I’d structure the following trade:

• -1 ATM Call, expiring in ~3 months
• +1 0.30 Delta Call, expiring this week or next
• +1 -0.30 Delta Put, expiring in ~3 months
• -1 ATM Put, expiring this week or next

2. Could this happen again? And if so, how would you predict it?

Yes, this could definitely happen again, and in fact, I predict it will continue to happen again and with more frequency. Note that this phenomenon already has been increasing in both frequency and intensity, primarily since the pandemic started (“Boredom markets hypothesis”, thanks Matt).

• The conditions for a gamma squeeze, short squeeze, and Schelling point are actually quite simple. Throw in a few assisting factors, particularly low share count (low supply), and a small number of traders can change the market price (Just for clarification, it is highly illegal to incite these squeezes for your own profit, which I am not proposing here).
• Most, if not all, of the highly volatile “meme stocks” started or were catalyzed by r/wsb. Therefore, a very real trading strategy could be harvesting volatility from these stocks, or simply joining the bandwagon, by using r/wsb as a source. This is where you find the Schelling Points.²
• Once you have found the next “Schelling Point” (or tested the waters on multiple, possible, Schelling Points), the next step would be finding the right conditions for a gamma and/or short squeeze. (Again, not proposing to incite this!) This would include, but is not limited to: low share count, high short interest, high public attention (or at least fuel for future attention), and limited number of option contracts, but high call volume and Open Interest. Also for some reason, most of these meme stocks are money-losing, bankrupt companies, so search for that too.

At the end of the day, I will not be participating in any of these strategies given the high level of unnecessary risk. There are much more sound and strategic methods of investing, and I wrote the above analysis purely for my own understanding of the unique, and yes, entertaining situation.

Cheers

Footnotes:

1. This is the crux of Delta hedging. The actual amount of stock a MM buys is determined by the Delta of the call option contract. What Delta actually measures is the change in option price as the change in the underlying moves. However, it also serves as a proxy to “probability of being in-the-money”. Therefore, if the assignment is 100 shares, and the delta (between 0 and 1) represents the probability of being assigned, the number of shares to purchase is 100*delta. At-the-money options have a delta of ~0.5.
2. This is an extremely gut-wrenching investing method, using a subreddit for investment advice (or at least a starting point). There are definitely more sophisticated methods of taking advantage of the situation rather than the highly risky, short-dated out-of-the-money call buying. But I need to think on this one. Put selling could work, but still risky. Volatility harvesting would probably work best here.