Positional Option Trading

An effective way to learn is to organize our current knowledge. Sometimes this makes it clear that we don't understand certain things, but even if no such gaps become apparent the thought that goes into a classification scheme is helpful. Science often starts by classifying knowledge. We knew about species before we knew about speciation through natural selection. We knew that elements could be grouped into the periodic table before we knew about atomic structure. We knew about dominant and recessive genes before we knew about DNA structure.

We have already classified trading opportunities into inefficiencies and risk premia. This distinction is important on a strategic level. Mispriced risk premia can last for a long time. A business can be built on harvesting risk premia. Inefficiencies aren't likely to be as persistent. These need to be aggressively traded while they last, and we can assume that they won't last long.

There is also an important classification of trades at the tactical level (strategy defining the high-level goals and tactics being the methods we use to reach them). Trades are either model driven or event driven.

With a model-driven trade, we have a theoretical model of a situation that lets us calculate a fair value or edge. At any moment, we will have an opinion based on the model. For example, if we have an option pricing model, we can continually generate a theoretical value for all of the options on a given underlying. An event-driven trade is based on a specific unusual situation. Noticing that implied volatility declines after a company releases earnings would be the basis for an event-driven trade.

All types of trading, investing, or gambling can be classified like this. In blackjack, card counting is model driven. The player's counting scheme assigns a value for each card that is dealt. As cards are played, the player updates the count, and modifies her edge estimate accordingly. At any point in the dealing, she will know what her edge is. But there is an event-driven method as well: ace tracking. Ace tracking is based on the fact that shuffles aren't perfect randomizers. Cards that are close together in one shoe will tend to stay close together in the next shoe. So an ace tracker notes the cards that are located close to aces and when those same cards are dealt in the next shoe she knows that there is a heightened chance of an ace being close. Because the player advantage in blackjack is due to the 2–1 blackjack payout, having a better than random idea where aces are is enough to give a significant edge. Ace tracking can be more effective than card counting.

Stock investing can be similarly classified. We can rank stocks with a factor model such as Fama-French-Carhart, or we could buy stocks that have had positive earnings surprises. In horse racing, an example of a model would be Beyer's speed figures, whereas an event-driven strategy would be to back horses in certain traps.

Both of these approaches have strengths and weaknesses.

For a model-driven approach to be effective we need a good model. Some situations lend themselves to this more than others. For example, there are very good option valuation models, but stock valuation methods are crude. Sometimes, the work required to build a model is not worth it. But if we have a model, we will always be able to trade. We will have a theoretical value for every trade opportunity. This means the approach scales very well and has great breadth of applicability. We will also be able to scale our trades based on our perceived edge.

The largest problem with this approach is that models have to be vastly simplified views of reality. Often a model's apparent effectiveness isn't due to its effectiveness but more because data gathering and processing is being rewarded. In the 1980s collecting daily closing prices and calculating volatility from those was enough to give a volatility edge in the options markets. Now that this data is free and easy to automatically process, it seems like there is no edge left in this volatility arbitrage model. But there never was any edge in the model at all: the edge was in data collection and processing.

Event-driven trades have two great strengths. The process for finding and testing them is very simple. What happens to stocks in the three days after a FED meeting? What does the VIX do on Mondays? Are teeny options overpriced? All we need to test these ideas is data and a spreadsheet.

Most important, trades that are based on specific events or situations can be very profitable. I have one trade that has literally never lost money. It only sets up a few times a year and is quite liquidity constrained, but it has an unblemished record. This profitability is probably linked to the fact that there is huge uncertainty about why this situation is lucrative.

A drawback of event-based trades is that we must wait for the event, and some events don't occur very often. It is hard to structure a business based on a strategy that might not trade for years at a time. Also, it is often hard to know why the trade exists. This isn't always true. For example, ace tracking is profitable for a very clear reason. But sometimes even a trade with compelling statistics has no obvious reason. I don't do trades if I have no idea why they exist, but sometimes it is easy to come up with a post-hoc reason. For example, many sports fans have convinced themselves that home field advantage is due to travel fatigue. This seems plausible, but it is wrong. Even when teams share the same ground the home team has an advantage. There is no magic answer to this dilemma. The weaker the evidence for a cause is, the stronger the statistical evidence needs to be.

Related to this problem is that if we have only a vague idea for why a trade works, we will have a hard time knowing if it has stopped working or if we are just experiencing a bad period. This is particularly true if the proposed reason is a psychological one. It is always tempting to ascribe any anomaly to psychology. This inevitably leads to overconfidence in the trade. After all, human psychology isn't going to change so why would these trades ever stop working?

Finally, we will often have no way to differentiate between “good” and “bad” trades of the same class. If all we know is that selling options over earnings is profitable, we won't know if it is better to sell Apple options or IBM options. This makes sizing difficult. We only have statistics for the entire class of trades. We need to be very conservative.

Models can give a false sense of security. No model can account for everything. No event has a single cause. Most events have many causes. A situational strategy directly acknowledges this uncertainty and generally traders who are comfortable with uncertainty will do best. So, although creating models is not a bad idea, you also need to become comfortable trading with the ambiguity inherent with specific events.

Our focus in this book is finding situations where we can do better than the consensus. This is covered in detail in Chapter Five. The ease of finding and manipulating financial data has considerably lessened the efficacy of forecasting volatility using time series models (the primary forecasting tool used in Volatility Trading [Sinclair, 2013]), but measuring and forecasting volatility in this way is still necessary for trade sizing and allocation. Econometricians are still writing endless papers about different members of the GARCH family, but there have been no fundamentally different advances in volatility measurement and forecasting in the last 20 years.

For a summary of these time-series methods refer to Sinclair (2013) and for more detail refer to Poon (2005). Here, I have two general observations.

The GARCH Family and Trading

The simplest forecasting model is to assume that the volatility over the next N days will be the same as it was over the previous N days. Mathematically,

(3.1)

This has two major problems. First is the “windowing” effect where a large single return affects the volatility calculation for N days, then drops out of the sample. This creates jumps in the volatility measurements and hence the forecast. An example is given in Figure 3.1, where we calculate the 30-day volatility of Maximus, Inc. (MMS) from June, 15, 2019, to September, 30, 2019.

FIGURE 3.1 The rolling 30-day close-to-close volatility of Maximus, Inc.

The typical daily move of this stock was about 0.7% but on August 8 it jumped by 12% because of earnings. This caused the 30-day volatility to jump from 17.8% to 39.3%. Thirty days later, the earnings day dropped out of the calculation and volatility again dropped to 23.3%. If we can know what events are outliers, we can avoid this problem by removing them from the data. We can just throw out the earnings day return.

A bigger problem is that this method doesn't take volatility clustering into account. Periods of exceptionally high or low volatility will persist for only a short time. The exponentially weighted moving average (EWMA) model takes this into account. This says variance evolves as

(3.2)

where λ is usually chosen to be between 0.9 and 1.

The GARCH (generalized autoregressive conditional heteroskedasticity) family of models extend this idea to allow for mean reversion to the long-term variance. The GARCH(1,1) model (so-called because it contains only first-order lagged terms) is

(3.3)

where α, β, and γ sum to 1 and γV is the long-term variance.

GARCH is both an insightful improvement on naively assuming future volatility will be like the past and also wildly overrated as a predictor. GARCH models capture the essential characteristics of volatility: volatility tomorrow will probably be close to what it is today and volatility in the long term will probably be whatever the historical long-term average has been. Everything in between is interpolation, and it is in the interpolation that the models in the family differ. As an example, Figure 3.2 shows the term structure of forecast volatility for SPY on August 1, 2019, using GARCH(1,1) and GJR-GARCH(1,1), which also accounts for the asymmetry of positive and negative returns. Both models are estimated from the previous four years of daily returns using MLE.

From a practical perspective, the difference is negligible. And this is what has led to the proliferation of GARCH-type models. They are all roughly the same. No model is clearly better than the others. In any situation where there are many competing theories it is a sign that all of the theories are bad. There is one Schrödinger equation. It works very well. There are thousands of GARCH variants. None work very well.

In fact, it has been shown that the forecasts from GARCH generally are no better than a simple EWMA model, and most professional traders are reluctant to use GARCH. Part of the reticence is due to the instability of the MLE parameters. These can change considerably week to week. MLE also requires about a thousand data points to get a good estimate. This means that if we are using daily data, our forecast will be using information from four years ago. This isn't good.

But there is a practical way to combine the robustness of EWMA and the decay to a long-term mean that GARCH allows. When a trader uses EWMA, he arbitrarily chooses the decay parameter instead of fitting to historical data and using MLE. We can do the same with GARCH. Choose a model, choose the parameters, and use it consistently. This means that eventually we will develop intuition by “seeing” the market through the lens of this model. For indices, choosing α in the range of 0.9 and β between 0.02 and 0.04 seems to work.

FIGURE 3.2 Term structure of forecast volatility for SPY using GARCH(1,1) (solid line) and GJR-GARCH (dashed line).

Implied Volatility as a Predictor

Implied volatility can be used to predict future realized volatility if we account for the variance premium. So a forecast of the 30-day volatility for the S&P 500 would be given by subtracting the appropriate variance premium for the current VIX level (refer to Table 4.3) from the VIX.

Most underlying products do not have a calculated VIX index. The first way to deal with this is to follow the CBOE's published methodology and construct a VIX. An easier way is to create a weighted average of the appropriate ATM volatilities and use that as a proxy. This methodology was used to create the original VIX (ticker symbol VXO). VXO and the VIX returns have an 88% correlation and the average difference between their values is about 0.5% of the VIX level. This approximation isn't ideal but will usually be the best there is.

Ensemble Predictions

The volatility market is now mature enough that any time series–based volatility method will probably not provide forecasts that are good enough to profit in the option market. A better approach is to combine a number of different forecasts. This idea of the usefulness of information aggregation is far from new. One of the earliest advocates for the “wisdom of crowds” was Sir Francis Galton. In 1878, he photographically combined many different portraits to show that “all the portraits are better looking than their components because the averaged portrait of many persons is free from the irregularities that variously blemish the look of each of them.” His experiment has been repeated and his conclusions validated numerous times using more advanced equipment.

An aggregate forecast can be better than any of the components that make it up. This can be demonstrated with a simple example. Imagine that we ask 100 people the multiple-choice question, “What is the capital of Italy?” with the possibilities being Rome, Milan, Turin, and Venice. Twenty of the group are sure about the correct answer (Rome). The remaining 80 just guess so their choices are equally divided among all the choices, which get 20 votes each. So, Rome receives 40 votes (the 20 people who knew and 20 votes from guesses) and the other cities get 20 votes each. Even though only a small proportion of the people had genuine knowledge, the signal was enough to easily swamp the noise from the guesses of the guessers.

This example also shows that for forecast combinations to be most useful they need to contain diverse information. We need the people who are wrong to be uncorrelated sources of noise. That isn't the case with volatility time series models. Most models will have very high correlation with each other. However, simply averaging the predictions from a number of simple models will still improve predictions. I used five volatility models to predict subsequent 30-day S&P 500 volatility from 1990 to the end of 2018. Table 3.1 shows the summary statistics for each model and also for a simple average.

The error of the average is only beaten by that of the simple 30-day average (the least sophisticated model) but it beats it when we consider the dispersion of results. Interestingly averaging the 0.9 and 0.95 EWMA models also leads to a slight improvement. This is shown in Table 3.2.

Even very similar models can be usefully averaged. This is probably the best way to apply this concept. Average over every GARCH model possible, a wide range of time scales, and a wide range of parameters. Ideally, the models that are averaged would be based on totally different ideas or data, but with volatility this won't happen.

TABLE 3.1 Thirty-Day Volatility Forecasts for the S&P 500 from 1990 to the End of 2018

TABLE 3.2 Thirty-Day Volatility EWMA Forecasts for the S&P 500 from 1990 to the End of 2018

Conclusion

Realized volatility is reasonably forecastable for a financial time series. Unfortunately, this means that it is hard to make a good forecast that differs significantly from the market's consensus. However, volatility predictions are essential even when they are not the basis for finding edge. In particular, any sensible sizing scheme will need a prediction of future volatility.

Summary

• All trading strategies can be categorized as either model driven or based on special situations. Each type has weaknesses and strengths.

• An ensemble prediction of volatility will usually outperform time series methods.

CHAPTER 4

The Variance Premium

In finance, everything that is agreeable is unsound and everything that is sound is disagreeable.

—Winston Churchill

The variance premium (also known as the volatility premium) is the tendency for implied volatility to be higher than subsequently realized volatility.

This is not a recent phenomenon. In his 1906 book The Put and Call, Leonard Higgins writes how traders on the London Stock Exchange first determine a statistical fair value for options, then “add to the ‘average value’ of the put and call an amount which will give a fair margin of profit.” That is, a variance premium was added.

The variance premium exists in equity indices, the VIX, bonds, commodities, currencies, and many stocks. It is probably the most important factor to be aware of when trading options. Even traders who are not trying to directly monetize the effect need to know of it and understand it. It is the tide that long option positions need to overcome to be profitable. Even traders who only use options to trade directionally need to take this into account. Even if directional predictions are correct, it is very hard to make money if one is consistently paying too much for options (see Chapters Six and Seven for more discussion of this point).

This effect can be monetized in many ways. The size and persistence of the variance premium is so strong that the precise details of a strategy often aren't very important. Practically any strategy that sells implied volatility has a significant head start on being profitable if the premium is there.

In this chapter we will discuss the characteristics of the variance premium in various products; look at the relationships among the variance premium, correlation, and skewness; and give some possible reasons for the existence of the effect.