Introduction - Why Gamma?

A recent trend within trading platforms is to include detailed and well visualized information about each day’s option trading activity. Most brokers today (2019) include not only an asset’s option chain but information about the biggest trades that occured on the chain and overall impressions of option investor’s exposure. This includes things like Put/Call ratio, Net Deltas, Net Premium, etc. An example of this summary can be seen below.

While investors become more knowledgeable about options and explore this data, a wide variety of trading strategies have emerged. Many have speculated about following big fish taking aggressive improbable bets, using the underlying’s Put/Call ratio as a leading directional indicator, or a variety of other strategies based entirely on the activity of an asset’s derivatives and not the underlying asset itself.

As time has passed, CBOE has released tools for investors to better understand the role of equity derivatives and their effect on the market. ‘The VIX’ is a primary example of an index derived solely from the information on the SPX option chain. Since its release the VIX has gone on to have its own set of options as well as futures allowing investors to bet on the implied volatility of the S&P 500.

This is ballooning now to the point where the average retail investor can buy a contract which is a derivative of an ETF which holds derivative futures of an index which is itself derived by the pricing of the derivatives of an index made up of the broader US equity market. I’m always baffled that VXX options are actually honoured by the market and not completely worthless.

The success of the VIX has lead the CBOE to deliver similar indices derived the same way, on mega caps and corporations that make up the largest pieces of the S&P 500. (AAPL, GOOGL, AMZN, etc.)

The reality of the VIX is that it is determined based on the current market spreads for SPX options. Such spreads are currently being set by dealers and market makers who are monetarily incentivized by exchanges to fill as many orders as possible. In theory this leads to dealers competing to make the tightest spreads, giving the best liquidity to discretionary traders. One potential pitfall is that the collective of market makers may now dictate (to a certain degree) the movement of the VIX index.

It is not impossible to conceive that every trade made on the SPX option chain is filled by a dealer. Under four assumptions, an indicator similar to the VIX can be produced. It will attempt to predict how exposed the liquidity providers books to the movements of the market.

This indicator, known by the few who use it as “Gamma Exposure Index (GEX)”, attempts to condense the positioning of market dealers down to a single number. Most examples of this indicator denominate GEX in dollars or shares. It is further assumed that GEX is the number of shares or dollars the dealers have at risk on any given day. Notable changes in the behaviour of the underlying asset occurs when the number of shares approaches or exceeds the average daily trading volume of the asset.

Further information about this phenomenon can be found in the SqueezeMetrics white paper, or on the Spot Gamma website. Finally, for those of us who don’t care about the integrity of our sources, Seeking Alpha has had authors discussing market gamma exposure for sometime now. Additional reading into a common option strategy known as “Gamma Scalping” is also useful background knowledge.

Stealing Their Signals

SqueezeMetrics

One subscription service (Squeeze Metrics) has been providing investors with their own GEX data since 2017. Recently(Q2 2019) a secondary service, Spot Gamma, with a slightly different derivation process has also sprouted onto the scene. It is widely known that wealth management firms release “Gamma Reports” to their clients.

While SqueezeMetrics keeps their signal behind a paywall of 200-1000$/month, they do release all historical data for free. They also have a very plain website with adequate security. While I couldn’t fudge my way into a subscription I was able to discover a hidden file on their site. An unpublished white paper from 2017, when they first released their GEX(tm) index. In this white paper they outline the major assumptions they make and the equations they use to derive GEX. I am unsure as to why they do not make the white paper publicly available, or at least more accessible. Below I have explored their historical data and its ability to produce excess returns when used as a leading indicator for the S&P 500.

SqueezeMetrics GEX indicator is a single number and does not vary based on option expiry. Spot Gamma’s indicator is primarily for the next expiry on the S&P 500 chain, and includes price levels for where the dealers exposure turns negative (more on this later), and which strikes are likely to act as pins moving into expiry (Max Pain theory). Spot Gamma keeps their entire process proprietary. They do however, release their historical data and are explicit about what input data is required for the derivation of their results.

Spot Gamma

Spot Gamma’s website is wordpress which made crawling their directories fairly straight forward. It was clear that they use the same server to host their model’s data as they do to host their website. Unfortunately, they were smart enough to keep the model out of reach. (To me, at least.) I was able to uncover a couple intermediary data tables as well as access to their subscription data. In reality, I should just pay them the 20$/month considering I stole their model.

Using both the historical input data and its results, I was able to reverse engineer their model. This process involved a Random Forest Recurrent Neural Network. This process is fairly simple in actuality. If I know; bananas, yogurt and strawberries go in and a smoothie comes out, the neural network can turn itself into a blender with relative ease. Computers are really good at math.

While the model is only able to reproduce Spot Gamma’s numbers within a 0.05% margin of error, that is well within an acceptable level of confidence. I am currently allowing the model to improve itself day over day with unsupervised learning and by validating its results against what is published by Spot Gamma for subscribers. Again, they deserve my 20$/month.

Why Will It Break?

In both cases, Spot and Squeeze, there exists four primary assumptions. The pitfalls of this strategy may be exploited here. As outlined in their white paper, Squeeze assumes that every trade is facilitated by a market maker. They further assume that call options are SOLD by investors and are BOT by market makers. This means that the makers are short for every open call contract. Subsequently, the inverse is assumed to be true for puts. The final assumption is that marmet makers want to have a completely delta neutral book. Market makers intend to sell theta premiums and are looking to remain neutral to the movement of the underlying asset.

The Data

While this market microstructure should exist in any optionable asset that has market makers providing the liquidity, we will only explore the SPX. Attempts to reproduce these results on canadian equities has been mixed.

SqueezeMetrics data goes back to 2004, allowing for a far more insightful picture into the effect of dealer exposure to the market compared to the 6 months of Spot Gamma data. We may begin by evaluating the market same-day returns against the market gamma exposure (GEX).

While the returns of the SPX are fairly well distributed two trends are apparent. Volatility, in terms of absolute movement, is heavily stifled when market gamma reaches positive extremes. What’s more, is that the largest intraday moves occur when market gamma exposure is negative.

Negative Gamma Exposure?

When the GEX is measuring positive numbers, it is suggesting that dealers hedge by trading the underlying, they are taking trades that go AGAINST the movement of the asset. For example, if the GEX is >4bn then the makers will sell as the asset rises and buy as the asset declines. When GEX is negative or < 0, makers will sell into weakness and buy into strength. This phenomenon may explain why the largest moves occur when the makers are negatively exposed. Their trading activity exemplifies the movement already occurring as opposed to counteracting it.

Observant readers will already be foaming at the mouth for an opportunity to trade this statistical advantage, but we shall continue to explore the data in an attempt to better our understanding of this signal and produce a trading strategy that may produce excess returns.

The following shows market’s 5-day and 20-day returns against the SqueezeMetrics GEX signal.

For posterity, the same three figures have been produced by the Spot Gamma Machine Learning model.

A quick review of these plots make the trend abundantly clear. When market makers have money on the line, they destroy volatility. When market makers benefit from movement, they help push the index around. In either case, the hedging activities of market dealers clearly impacts the returns of the market.

Earlier in this report we discussed the possibility that market makers control every print of the VIX. Before exploring the use of GEX as a trading signal, it felt worthwhile to evaluate the VIX’s performance alongside the GEX signal. Our assumption is that dealers will tank the VIX index when they have large amounts of money at risk.

Using the above charts it can be concluded that our GEX model of maker positioning has some correlation to the VIX index. So now the question must be asked, is this simply a case of the tail wagging the dog? What if we’ve simply fit the data and the four assumptions are false? I don’t need to know why, I need to make money.

The Money Maker

Some additional extrapolation from the above figures must be done in order to develop this signal into a viable trading strategy. Many quantitative investors may seek to optimize against the data and find the optimal threshold of GEX to fit their desired risk tolerance. I’m quite happy to draw some lines in the sand and trade around those.

The following data displays the 5-day and 20-day returns for the S&P 500 when market gamma is above 4bn(Squeeze) or below 0.

While these trends are impressive, a rudimentary strategy has produced even better numbers. This is so disgustingly profitable that I worry about putting the ideas in writing. Often times it feels like signals work right up until the moment the first trade hits the market.

The following result (Figure 16) is from purchasing 6-8 Day-to-Expiry, Nearest To The Money, Call Options. 1 contract is purchased at the day’s open if the GEX is above 4bn. Options are sold at +100% gain, otherwise held to expiry.

The following result (Figure 17) is from purchasing 10-12 Day-to-Expiry Straddles. Contracts are purchased at market open whenever the GEX is negative.

Aside from the obvious next steps towards making money with this system, there are a few other avenues that are potentially worth exploring. The first being further correlations to the VIX index. A combination of VIX and GEX could lead to more meaningful signals allowing the system to take trades more frequently, hopefully leading to increased returns. Earlier, it was mentioned that VIX indexes have been produced for mega cap corporations. It would be worthwhile to evaluate a GEX on those mega cap corporations who could have their liquidity providers affecting their share price in a similar vein they affect the S&P 500. These listings include; AAPL, GOOGL, AMZN, GS, IBM. They also have these indices for sector ETFs, Bonds and Commodities. Should similar trends and results be found market wide, it would suggest that the GEX truly is a leading indicator and would validate not only the system’s assumptions, but also it’s results.

Work with individual canadian equities has been done, but the results have been inconclusive. The most likely reason for this is a lack of liquidity takers (discretionary traders making option trades) to allow the market makers to build up heavy books. It is clear from the SPX results that the effects of GEX are most notable and reliable when the books are the heaviest.

Future Work

The following work still needs to be done in order to bring this system to a live trading environment. Additional backtesting with exact contract closing prices, and improved granularity needs to be done. These tests will provide insight on the system’s trading technique, drawdowns and risk. Once that is complete, a better picture of the system’s methodology and profitability will be clear. From here, modern portfolio metrics will allow a system to be catered based on risk tolerances and expected returns. It is notable that no metrics like; Sharpe Ratio, Max Drawdown, Avg Returns, Value at Risk, Beta, Alpha, Skewness, etc. were included in the results. Too many assumptions were made in producing a rudimentary backtest that those metrics would be useless and non-reflective of a live environment.

At present there are no intentions of automating such a system should a profitable one arise after the necessary research is complete.