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POSITIONAL OPTION TRADINGAn Advanced GuideEuan Sinclair
Copyright © 2020 by Euan Sinclair/John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data
Names: Sinclair, Euan, 1969- author.
Title: Positional option trading : an advanced guide / Euan Sinclair.
Description: Hoboken, New Jersey : Wiley, [2020] | Series: Wiley trading series | Includes bibliographical references and index.
Identifiers: LCCN 2020008849 (print) | LCCN 2020008850 (ebook) | ISBN 9781119583516 (hardback) | ISBN 9781119583523 (adobe pdf) | ISBN 9781119583530 (epub)
Subjects: LCSH: Options (Finance) | Financial futures.
Classification: LCC HG6024.A3 S56225 2020 (print) | LCC HG6024.A3 (ebook) | DDC 332.64/53—dc23
LC record available at https://lccn.loc.gov/2020008849
LC ebook record available at https://lccn.loc.gov/2020008850
Cover Design: Wiley
Cover Image: © blackred/Getty Images
INTRODUCTION
You know nothing, Jon Snow.
—Ygritte in A Storm of Swords by George R. R. Martin.He is not the only one.
We are not in a time where reason is valued. In economics, the idea that marginal tax cuts pay for themselves is still advanced, even though all evidence says they don't.
Forty percent of Americans do not believe in evolution. Forty-five percent believe in ghosts. These beliefs are not based on any evidence. They are manifestations of another philosophy, whether it is economic, religious, or sociological. Usually these opinions reveal more about what people want to be true rather than any facts that they know. And many people know few facts anyway. Evidence is seen as irrelevant and arguments are won by those who shout loudest and have the best media skills.
The idea that opinions are as valid as facts also affects trading and investing. Many investors rely on methods that are either unproven or even proven to be ineffective. The few of these investors who keep records will see that they are failing but rely on cognitive dissonance to continue to believe in their theories of how the markets behave. One would think that losing money would prompt reexamination, but the persistence of losers is remarkable. And even when some people give up or are forced out, there is always new money and new participants to replace the old.
The only way to learn about anything is through the scientific method. This is an iterative procedure where theory is modified by evidence. Without evidence we are just in the realm of opinion. Most of what I present here is backed by evidence. There are also some opinions. My justification for this is that experience is also a real thing. But I'm no less prone to self-delusion than anyone else, so feel free to pay less attention to these ideas.
Trading is fundamentally an exercise in managing ignorance. Our ability to judge whether a situation presents a good opportunity will always be based on only a simplified view of the world, and it is impossible to know the effects of the simplification. Our pricing model will be similarly compromised. It will be a simplification and possibly a very unrealistic simplification. Finally, the parameters the models need will have estimation errors and we generally won't know how large these are.
It is impossible to understand the world if you insist on thinking in absolute terms. The world is not black and white. Everything has shades of gray. You won't learn much from this book is you aren't comfortable with this.
This is clear for “risk.” Everyone has a different risk tolerance, whether this is personal or imposed by management or investors. But more important, risk is multidimensional. We are comfortable with this idea in some areas of life. Imagine you have a choice of going on vacation to either Costa Rica or Paris. Both are nice places and any given person could reasonably choose either one. But Paris has no beaches and Costa Rica doesn't have the Pompidou Centre. There is no one correct choice in this situation. And that is also the case in most investing decisions.
Many of the ideas I write about can be extrapolated to a ludicrous level. But if you do, don't blame me or credit me with the resulting conclusions.
In no particular order here are some facts that are often misrepresented:
• There is usually a variance premium. This does not mean there is always a variance premium.
• There is usually a variance premium. This does not mean you should always be short volatility.
• Short volatility can be risky. This does not mean that short volatility has to have unlimited risk.
• Some theories (e.g., GARCH, BSM, EMH, returns are normally distributed) have limitations. This does not mean the theories are stupid or useless.
• The Kelly criterion maximizes expected growth rate. This does not mean you should always invest according to it.
If what I write is unclear or incorrect, that is a problem of my making. But if you choose to ignore nuance, that is your issue.
Trading as a Process
I have made no attempt here to write a comprehensive option trading book. I don't cover the definitions and specifications of various types of options. There are no derivations of option pricing models. I expect the reader to know about the common option structures such as straddles, spreads, and strangles. Many books cover these topics (e.g., Sinclair, 2010). A very brief summary of the theory of volatility trading is provided in Chapter One, but this is not a book for beginners.
This is a book for experienced traders who want the benefits of including options in their strategies and portfolios but who are unwilling or unable to perform high-frequency, low-cost dynamic hedging. Again, there are many books on this type of positional option trading, but none are theoretically rigorous, and most ignore the most important part of trading anything: having an edge.
One of the things that distinguishes professionals from amateurs in any field is that professionals use a consistent process. Trading should be a process: find a situation with edge, structure a trade, then control the risk. This book documents these steps.
The book's first section explores how to find trades with positive expectation.
In Chapter Two, we look at the efficient market hypothesis and show that the idea leaves plenty of room for the discovery of profitable strategies. This insight lets us categorize these “anomalies” as either inefficiencies or risk premia. These will behave differently and should be traded differently. Next, we briefly review how behavioral psychology can help us and also its limitations. We examine two popular methodologies for finding edges: technical analysis and fundamental analysis.
Chapter Three looks at the general problem of forecasting. No matter what they say, every successful trader forecasts. The forecast may not be one that predicts a particular point value, but probabilistic forecasting is still forecasting. We introduce a classification of forecasting methods. Forecasts are either model based, relying on a generally applicable model, or situational, taking advantage of what happens in specific events. We very briefly look at predicting volatility with time-series models before moving on to our focus: finding specific situations that have edge.
The most important empirical fact that an option trader needs to know is that implied volatility is usually overpriced. This phenomenon is called the variance premium (or the volatility premium). Chapter Four summarizes the variance premium in indices, stocks, commodities, volatility indices, and bonds. We also present reasons for its existence.
Having established the primacy of the variance premium, Chapter Five gives eleven specific phenomena that can be profitably traded. The observation is summarized, the evidence and reasons for the effect are given, and a structure for trading the idea is suggested.
The second section examines the distributional properties of some option structures that can be used to monetize the edge we have found. We need to have an idea of what to expect. It is quite possible to be right with our volatility forecasts and still lose money. When we hedge, we become exposed to path dependency of the underlying. It matters if a stock move occurs close to the strike when we have gamma or away from a strike when we have none. If we don't hedge, we are exposed to only the terminal stock price, but we can still successfully forecast volatility and lose because of an unanticipated drift. Or we can successfully forecast the return and lose because of unanticipated volatility.
Chapter Six discusses volatility trading structures. We look at the P/L distributions of straddles, strangles, butterflies, and condors, and how to choose strikes and expirations.
In Chapter Seven we look at trading options directionally. First, we extend the BSM model to incorporate our views on both the volatility and return of the underlying. This enables us to consistently compare strikes on the basis of a number of risk measures, including average return, probability of profit, and the generalized Sharpe ratio. Chapter Eight examines the P/L distributions of common directional option structures.
The final section is about risk. Good risk control can't make money. Trading first needs edge. However, bad risk management will lead to losses.
Chapter Nine discusses trade sizing, specifically the Kelly criterion. The standard formulation is extended to allow for parameter estimation uncertainty, skewness of returns, and the incorporation of a stop level in the account.
The most dangerous risks are not related to price movement. The most dangerous risks are in the realm of the unknowable. Obviously, it is impossible to predict these, but Chapter Ten explores some historical examples. We don't know when these will happen again, but it is certain that they will. There is no excuse for blowing up due to repeat of a historical event.
It is inevitable that you will be wrong at times. The most dangerous thing is to forget this.
Summary
• Find a robust source of edge that is backed by empirical evidence and convincing reasons for its existence.
• Choose the appropriate option structure to monetize the edge.
• Size the position appropriately.
• Always be aware of how much you don't know.
CHAPTER 1
Options: A Summary
Option Pricing Models
Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad.
—Box (1976)Some models are wrong in a trivial way. They clearly don't agree with real financial markets. For example, an option valuation model that included the return of the underlying as a pricing input is trivially wrong. This can be deduced from put-call parity. Imagine a stock that has a positive return. Naively this will raise the value of calls and lower the value of puts. But put-call parity means that if calls increase, so do the values of the puts. Including drift leads to a contradiction. That idea is trivially wrong.
Every scientific model contains simplifying assumptions. There actually isn't anything intrinsically wrong with this. There are many reasons why this is the case, because there are many types of scientific models. Scientists use simplified models that they know are wrong for several reasons.
A reason for using a wrong theory would be because the simple (but wrong) theory is all that is needed. Classical mechanics is still widely used in science even though we now know it is wrong (quantum mechanics is needed for small things and relativity is needed for large or fast things). An example from finance is assuming normally distributed returns. It is doubtful anyone ever thought returns were normal. Traders have long known about extreme price moves and Osborne (1959), Mandelbrot (1963), and others studied the non-normal distribution of returns from the 1950s. (Mandelbrot cites the work of Mitchell [1915], Olivier [1926], and Mills [1927], although this research was not well known.) The main reason early finance theorists assumed normality was because it made the equations tractable.
Sometimes scientists might reason through a stretched analogy. For example, Einstein started his theory of the heat capacity of a crystal by first assuming the crystal was an ideal gas. He knew that this was obviously not the case. But he thought that the idea might lead to something useful. He had to start somewhere, even if he knew it was the wrong place. This model was metaphorical. A metaphorical model does not attempt to describe reality and need not rely on plausible assumptions. Instead, it aims to illustrate a non-trivial mechanism, which lies outside the model.
Other models aim to mathematically describe the main features of an observation without necessarily understanding its deeper origin. The GARCH family of volatility models are phenomenological, and don't tell us why the GARCH effects exist. Because these models are designed to describe particular features, there will be many other things they totally ignore. For example, a GARCH process has nothing to say about the formation of the bid-ask spread. The GARCH model is limited, but not wrong.
The most ambitious models attempt to describe reality as it truly is. For example, the physicists who invented the idea that an atom was a nucleus around which electrons orbited thought this was actually what atoms were like. But they still had to make simplifying assumptions. For example, when formulating the theory, they had to assume that atoms were not subject to gravity. And, in only trivial situations could the equations be analytically solved. The Black-Scholes-Merton (BSM) model was meant to be of this type.
But it isn't used that way at all.
The inventors of the model envisaged that the model would be used to find a fair value for options. Traders would input the underlying price, strike, interest rate, expiration date, and volatility and the model would tell them what the option was worth. The problem was that the volatility input needed to be the volatility over the life of the option, an unknown parameter. Although it was possible for a trader to make a forecast of future volatility, the rest of the market could and did make its own forecast. The market's option price was based on this aggregated estimate. This is the implied volatility, which became the fundamental parameter. Traders largely didn't think of the model as a predictive valuation tool but just as an arbitrage-free way to convert the quickly changing option prices into a slowly changing parameter: implied volatility. For most traders, BSM is not a predictive model; it is just a simplifying tool.
This isn't to say that BSM can't be used as a pricing model to get a fair value. It absolutely can. But even traders who do this will think in volatility terms. They will compare the implied volatility to their forecast volatility, rather than use the forecast volatility to price the option and compare it to the market value. By using the model backwards, these traders still benefit from the way BSM converts the option prices into a slowly varying parameter.
We need to examine the effects of the model assumptions in light of how the model is used. Although the assumptions make the model less realistic, this isn't important. The model wasn't used because it was realistic; it was used because it was useful.
Obviously, it is possible to trade options without any valuation model. This is what most directional option traders do. We can also trade volatility without a model. Traders might sell a straddle because they think the underlying will expire closer to the strike than the value of the straddle. However, to move beyond directional trading or speculating on the value of the underlying at expiration we will need a model.
The BSM model is still the benchmark for option pricing models. It has been used since 1973 and has direct ancestors dating to the work of Bachelier (1900) and Bronzin (1906). In terms of scientific theory, this age makes it a dinosaur. But just as dinosaurs were the dominant life form for about 190 million years for a reason, BSM has persisted because it is good.
We want an option pricing model for two reasons.
The first is so we can reduce the many, fast-moving option prices to a small number of slow-moving parameters. Option pricing models don't really price options. The market prices options though the normal market forces of supply and demand. Pricing models convert the market's prices into the parameters. In particular, BSM converts option prices to an implied volatility parameter. Now we can do all analysis and forecasting in terms of implied volatility, and if BSM was a perfect model, we would have a single, constant parameter.
The second reason to use a pricing model is to calculate a delta for hedging. Model-free volatility trading exists. Buying or selling a straddle (or strangle, butterfly, or condor, etc.) gives a position that is primarily exposed to realized volatility. But it will also be exposed to the drift. The most compelling reason to trade volatility is that it is more predictable than returns (drift) and the only way to remove this exposure is to hedge. To hedge we need a delta and for this we need a model. This is the most important criterion for an option trader to consider when deciding if a model is good enough. Any vaguely sensible model will reduce the many option prices to a few parameters, but a good model will let us delta hedge in a way that captures the volatility premium.
In this chapter we will examine the BSM model and see if it can meet this standard. By BSM model I mean the partial differential equation rather than the specific solution for European vanilla options. The particular boundary conditions and solution methods aren't a real concern here.
Derivations of BSM can be found in many places (see Sinclair, 2013, for an informal derivation). Here we will look at how the model is used.
Option Trading Theory
Here we will very briefly summarize the theory of option pricing and hedging. For more details refer to Sinclair (2010; 2013).
An option pricing model must include the following variables and parameters:
• Underlying price and strike; this determines the moneyness of the option.
• Time until expiration.
• Any factors related to carry of either the option or the underlying; this includes dividends, borrow rates, storage costs, and interest rates.
• Volatility or some other way to quantify future uncertainty.
A variable that is not necessary is the expected return of the underlying. Clearly, this is important to the return of an option, but it is irrelevant to the instantaneous value of the option. If we include this drift term, we will arrive at a contradiction. Imagine that we expect the underlying to rally. Naively, this means we would pay more for a call. But put-call parity means that an increase in call price leads to an increase in the price of the put with the same strike. This now seems consistent with us being bearish. Put-call parity is enough to make the return irrelevant to the current option price, but (less obviously perhaps) it is also enforced by dynamic replication.
This isn't an option-specific anomaly. There are many situations in which people agree on future price change, but this doesn't affect current price. For example, Ferrari would be justified in thinking that the long-term value of their cars is higher than their MSRP. But they can build the car and sell it at a profit right now. Their replication value as a manufacturer guarantees a profit without taking future price changes into account. Similarly, market-makers can replicate options without worrying about the underlying return. And if they do include the return, they can be arbed by someone else.
The canonical option-pricing model is BSM. Ignoring interest rates for simplicity, The BSM PDE for the price of a call, C, is
(1.1)
where S is the underlying price, σ is the volatility of the underlying, and t is the time until expiration of the option.
Or using the standard definitions where Γ is the second partial derivative of the option price with respect to the underlying and θ is the derivative of the option price with respect to time,
(1.2)
This is then solved using standard numerical or analytical techniques and with the final condition being the payoff of the particular option.
This relationship between Γ and θ is crucial for understanding how to make money with options. Imagine we are long a call and the underlying stock moves from St to St+1.The delta P/L of this option will be the average of the initial delta, Δ, and the final delta, all multiplied by the size of the move. Or