The Second Leg Down E-Book

Hari P. Krishnan

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Series
• Sprache: Englisch
• Veröffentlichungsjahr: 2017

Seitenzahl: 482

Beschreibung

Cut risk and generate profit even after the market drops The Second Leg Down offers practical approaches to profiting after a market event. Written by a specialist in global macro, volatility and hedging overlay strategies, this book provides in-depth insight into surviving in a volatile environment. Historical back tests and scenario diagrams illustrate a variety of strategies for offsetting portfolio risks with after-the-fact options hedging, and the discussion explores how a mixture of trend following and contrarian futures strategies can be beneficial. Without a rational analysis-based approach, investors often find themselves having to cut risk and buy protection just as options are at their most over-priced. This book provides practical strategies, expert analysis and the knowledge base to assist you in recovering your portfolio. Hedging strategies are often presented as expensive and unnecessary, especially during a bull market. When equity indices and other unstable assets drop, they find themselves stuck - hedging is now at its most expensive, but it is imperative to hedge or face liquidation. This book shows you how to salvage the situation, with strategies backed by expert analysis. * Identify the right hedges during high volatility * Generate attractive risk-adjusted returns * Learn new strategies for offsetting risk * Know your options for when losses have already occurred Imagine this scenario: you've incurred significant losses, you're approaching risk limits, you must cut risk immediately, yet slashing positions would damage the portfolio - what do you do? The Second Leg Down is your emergency hotline, with practical strategies for dire conditions.

Leseprobe

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Table of Contents

Cover

Title Page

Copyright

Dedication

Preface

Acknowledgements

About the Author

Chapter 1: Introduction

The Airplane Ticket Trade

The Bull Cycle

The Renegades

Claws of the Bear

Zugzwang

The Sceptics

A Sad Truth

Common Mistakes

Imprecise but Effective

Hedging Against Implausible Scenarios

A Black Swan in Correlation

Taking Profits

The Good, the Bad and the Ugly

The Great Escape

Having a Plan

Trend Following as a Defensive Strategy

Taking the Offensive

The Pre-Conditions for Market Crises

Banks: The Great Multiplier

A Change in Risk Regime

Endnotes

Chapter 2: “Safe” Havens and the Second Leg Down

The Matterhorn

Mrs. Watanabe's No. 1 Investment Club

The Risk of What Others are Holding

The Risk of What Others are Likely to Do

Here We Go Again

Summary

Endnotes

Chapter 3: An Overview of Options Strategies

The Building Blocks: Calls and Puts

Why Buy a Call or Put?

The Black–Scholes Equation and Implied Volatility

The Implied Volatility Skew

Hedging Small Moves

Delta Hedging: The Idealised Case

Practical Limits of Delta Hedging

Hedging Options with Other Options

Put and Call Spreads

Straddles and Strangles

The Deformable Sheet

Skew Dynamics for Risky Assets

The 1×2 Ratio Spread and Its Relatives

The Batman Trade

Implied Correlation and the Equity Index Skew

From Ratios to Butterflies

Calendar Spreads

Summary

Chapter 4: Hedging the Wings

Taking the Other Side of the 1×2

Comparing the 25 and 10 Delta Puts

Hedging Sovereign Bond Risk

Selling Put Ratio Spreads on the S&P 500

The Hypothetical Implied Distribution

Our Findings So Far

Back-Tests: A Cautionary Note

A Short Digression: Delta-Neutral or Comfortably Balanced?

The 665 Put

Implications of the Square Root Strategy

Futures vs Spot

A Dramatic Example

A Cross-Sectional Study

The “New” VIX: Model-Independent, Though Not Particularly Intuitive

The Spot VIX: Oasis or Mirage?

Migrating to VIX Options

Reflections on Figure 4.36

Migrating to Different Markets: The V2X

Risk-Regime Analysis

Conditional Performance of Hedging Strategies

Summary

Chapter 5: The Long and the Short of It

Short-Dated Options

The Physicists Weigh In

Buying Time

Long-Dated Options

Far from the Madding Crowd

R Minus D

The Lumberjack Plot

Selective Application of the Weekly Options Strategy

Summary

Chapter 6: Trend Following as a Portfolio Protection Strategy

What is Trend Following?

Trend Following Dogma

The Crisis Alpha Debate

An Aside: Diversifying Across Time

Taking Advantage of a Correction

The Niederhoffer Argument

Chasing 1-Day Moves

Pushing the Analogy Too Far

Analysing the Data Directly

LEGO Trend Following

Summary

Notes

Chapter 7: Strategies for Taking Advantage of a Market Drop

The Elastic Band

Trading Reversals

More Texas-Style Hedging

Selling Index Put Spreads

Breathing Some Life into the Equity Risk Premium

Buying VIX Puts

Selling VIX Upside

The Remarkable Second Moment

Summary

Chapter 8: “Flash Crashes”, Crises and the Limits of Prediction

Lord of the Fireflies

Cascading Sales

A Concrete Example

An Aside

Paths, Prints

The Role of the Central Bank

Credit Cycles at the Zero Bound

The Monetary Policy Palette

Reading the Tea Leaves

Summary and Conclusion

Glossary

References

Index

End User License Agreement

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Guide

Table of Contents

Begin Reading

List of Illustrations

Chapter 2: “Safe” Havens and the Second Leg Down

Figure 2.1 EUR/CHF exchange rate before the peg was removed

Figure 2.2 There she goes

Figure 2.3 Daily range of EUR/CHF

Figure 2.4 Parkinson's volatility estimate

Figure 2.5 1 month TED spread

Figure 2.6 Up the stairs and down the lift

Figure 2.7 30 day trailing volatility for the AUD/JPY cross

Figure 2.8 The first leg down

Figure 2.9 The second leg down – liquidation time

Figure 2.10 “Black Monday” in focus

Figure 2.11 Black Monday, bird's-eye view

Figure 2.12 Historical performance of a bare bones risk parity portfolio

Figure 2.13 Historically, US equity and bond volatility have had a mild

positive

correlation

Chapter 3: An Overview of Options Strategies

Figure 3.1 Payout shape for a call option at maturity

Figure 3.2 Payout shape for a long put at maturity

Figure 3.3 One-step binomial model with variable volatility

Figure 3.4 Sensitivity of Bund calls to changes in volatility

Figure 3.5 Bell-shaped gamma curve as a function of underlying return

Figure 3.6 Construction of a split-strike risk reversal

Figure 3.7 Evolving payout of a risk reversal on the iShares MSCI Brazil ETF

Figure 3.8 Extracting alpha from a call that is overpriced in implied volatility terms

Figure 3.9 Arbitrage at its finest when implied volatility is severely mispriced

Figure 3.10 Impact of jumps on P&L

Figure 3.11 Impact of removing 10 largest down days from cumulative S&P performance

Figure 3.12 Normalised S&P 500 1-minute moves, 2 October 2015

Figure 3.13 Normalised 1-minute moves for US 10 year note futures, 2 October 2015

Figure 3.14 Evolution of payout curve for a put spread

Figure 3.15 Profit/loss of a straddle at maturity

Figure 3.16 Evolution of gamma curve for a straddle, as time elapses

Figure 3.17 The “strangler” at maturity

Figure 3.18 Qualitative depiction of an implied volatility surface

Figure 3.19 Variable response of term structure to changes in 3-month implied volatility

Figure 3.20 Implied volatility skew for a risky currency

Figure 3.21 Negative skewness in the Aussie 25 delta risk reversal

Figure 3.22 Unpredictable skew dynamics for US 10-year futures

Figure 3.23 Dependence of S&P skew on 6-month trailing move

Figure 3.24 “Safe” zone for a long 1×2 put ratio

Figure 3.25 Sensitivity of 1×2 put ratio to a spike in volatility

Figure 3.26 Put ladder payouts, expanded view

Figure 3.27 Payout of 2-sided ratio spread (Batman structure) at maturity

Figure 3.28 Profit/loss profile over a range of benign scenarios

Figure 3.29 Batman payout: expanded view – the dark underbelly of ratio spreads

Figure 3.30 Performance of buy-write strategy relative to static long position in index

Figure 3.31 Implied correlation increases as the S&P declines

Figure 3.32 Symmetric “smile” for each stock in index

Figure 3.33 Hypothetical implied correlation skew

Figure 3.34 Component smiles mapped to index skew via implied correlation

Figure 3.35 CBOE implied correlation skew conditioned on trailing return

Figure 3.36 Hypothetical put fly, payout at maturity

Figure 3.37 A defensive structure that actually cheapens when volatility increases

Figure 3.38 Impact of steepening skew on the cost of a put fly

Figure 3.39 Vega trajectory for fixed-width put fly

Figure 3.40 Payout of a broken fly on the USO close to maturity

Figure 3.41 Iron butterfly payout at maturity

Figure 3.42 Historical put skew for the S&P 500

Figure 3.43 Historical put skew for US 10-year note futures

Figure 3.44 Payout of a calendar spread, fixed volatility assumption

Figure 3.45 Profit/loss diagram for a calendar spread, assuming parallel shift in volatility

Chapter 4: Hedging the Wings

Figure 4.1 Payout at maturity for short put ratio strategy

Figure 4.2 10 delta S&P puts offer more “bang for the buck”

Figure 4.3 Relative performance of 4-week 10 and 25 delta puts, constant risk budget

Figure 4.4 Our view on the differential between “true” returns and those implied by the skew

Figure 4.5 Punchiness of volatility-adjusted returns for various deltas, 2008

Figure 4.6 Profit/loss at maturity for a short 1×2 put ratio on the SX5E index

Figure 4.7 Payout of short 1×2, constant volatility assumption

Figure 4.8 Payout of short 1×2, volatility “jacked up” by 20 points

Figure 4.9 Historical performance of short 1×2 on the S&P 500, gross of costs

Figure 4.10 Convex payout of short 1×2 when initiated in low volatility regime

Figure 4.11 Distance between strikes in 1×2 increases in tandem with ATM volatility

Figure 4.12 Short put ratio returns for the FTSE 100, gross of costs

Figure 4.13 Convex payout of short 1×2 put ratio spread

Figure 4.14 Spread between implied and historical volatility for Bund futures and the DAX

Figure 4.15 Bund futures can have a call or put skew, depending on regime

Figure 4.16 A relatively long data set with few incidences of sell-offs

Figure 4.17 Close up of price dynamics in 2015

Figure 4.18 Relative performance of naked put and “sombrero” for German Bund futures

Figure 4.19 Historical performance of a call spread buying strategy on German Bund futures

Figure 4.20 Superficially, selling puts looks like a fine idea

Figure 4.21

A strategy and its inverse can both converge to 0 if gearing is too high

Figure 4.22

Inverting a losing strategy does work after dialing down leverage (gross of costs)

Figure 4.23 Estimated margin requirements for short 665 put

Figure 4.24 2-sided ratio spread, payout at maturity

Figure 4.25 Mythical yield curve: roll down, rather than absolute yield, can generate attractive returns

Figure 4.26 Maintaining a continuous long position in a market where the term structure is in backwardation

Figure 4.27 Impact of futures term structure on long-term returns for various physical commodities

Figure 4.28 Prospective natural gas futures returns actually drop when the curve goes into backwardation

Figure 4.29 Cross-sectional dependence of returns on level of backwardation

Figure 4.30 Impact of 10% spot VIX allocation to S&P index returns

Figure 4.31 Impact of adding VIX futures to static long S&P 500 position

Figure 4.32

Historical VIX futures premium over spot VIX

Figure 4.33 Front month VIX futures premium over second month, historical perspective

Figure 4.34 Front month VIX futures are relatively responsive to changes in the spot VIX

Figure 4.35 Convex payout of strategy where VXX calls are overbought

Figure 4.36 VIX 25 delta calls have traditionally traded at a large premium to ATM calls

Figure 4.37 Strong structural linkage between VIX changes and S&P returns

Figure 4.38 Santa sells V2X futures while attempting to buy global equities

Figure 4.39 By comparison, the December dip in VIX futures is modest

Figure 4.40 Weekly changes in currency and equity index implied volatility are inter-linked

Figure 4.41 The CVIX, MOVE and VIX indices become increasingly correlated as the VIX rises

Figure 4.42 When the CVIX is high, the MOVE and VIX indices tend to be switched on as well

Figure 4.43 Our international bar code risk indicator

Figure 4.44 Decline in risk regime persistence since 2013

Figure 4.45 Relative performance of variable delta puts, conditioned on risk regime from previous week

Figure 4.46 Conditional performance of VXX calls with variable deltas

Chapter 5: The Long and the Short of It

Figure 5.1 Time

decay for a fixed delta option accelerates as maturity is approached

Figure 5.2 At-the-money protection rapidly cheapens near maturity

Figure 5.3 Mechanically refreshing weekly puts can be expensive

Figure 5.4 Frequency of 2+ standard deviation returns in S&P 500, based on partition width

Figure 5.5

Frequency of 2+ standard deviation returns, DAX/FTSE blend

Figure 5.6 Frequency of 2+ standard deviation returns in global bond futures markets

Figure 5.7 Impact of volatility expansion on a long-dated 1×2 put ratio

Figure 5.8 Short vega exposure for a 1×2 put ratio, as a function of moneyness

Figure 5.9 Long-dated puts have relatively high premium and vega, but relatively low gamma near the strike

Figure 5.10 Vega/theta as a metric for selecting options

Figure 5.11 Commodity implied volatility lagged during the global financial crisis

Figure 5.12 Historical beta of Euro Stoxx 50 dividend futures to 2

nd

contract

Figure 5.13 Rho has relatively large magnitude for long-dated options

Figure 5.14 Long-dated options have relatively high sensitivity to changes in volatility

Figure 5.15

The relative cost of weekly puts is inelastic to the level of volatility

Chapter 6: Trend Following as a Portfolio Protection Strategy

Figure 6.1 Trends can persist longer than one might expect

Figure 6.2 Historically, CTAs have performed admirably during S&P 500 draw downs

Figure 6.3 A significant allocation to CTAs is justified by a naive portfolio optimiser

Figure 6.4 Trend followers tend to outperform when equity index returns are significantly higher or lower than normal

Figure 6.5 Systems with different lookback windows and expected holding periods are diversifying

Figure 6.6 Bond futures have delivered relatively high absolute returns as well as protection during a crisis

Figure 6.7

Roll down overcomes randomness in interest rate paths when the term structure is in significant backwardation

Figure 6.8 Even if rates are ratcheting up, bond futures can have positive expected return

Figure 6.9 1-day momentum returns have a moderately positive correlation to changes in the VIX

Figure 6.10 Random switching between puts and calls is not analogous to a long volatility position

Figure 6.11 Moderate historical correlation between trend following returns on the S&P 500 and changes in the VIX

Chapter 7: Strategies for Taking Advantage of a Market Drop

Figure 7.1 Shiller's CAPE ratio as a precursor to equity market crises

Figure 7.2 M2 money stock has a powerful trend

Figure 7.3 1 year deviations from trend for M2 money stock

Figure 7.4 The V2X as a barometer of risk aversion for European large cap stocks

Figure 7.5 Buying the nasty 1-day dip, NIKKEI 225

Figure 7.6 Trading the coastline, when the signal to noise ratio is low

Figure 7.7

Selling the skew after a risk event can be attractive

Figure 7.8 The AUD put skew also has positive sensitivity to changes in ATM volatility

Figure 7.9 Elevated put skews can create intriguing risk reversal trading opportunities

Figure 7.10 Selective selling of put spreads can generate interesting risk-adjusted returns

Figure 7.11 The premium from selling an OTM put varies roughly linearly as implied volatility increases

Figure 7.12 Historical performance of rolling long put strategy on the VXX

Figure 7.13 Porcupine exposure of VIX implied volatility relative to VIX level

Figure 7.14 Currency implied volatility tends to be mean reverting over 6-month horizons

Figure 7.15 The VIX tends to revert over 6-month horizons, too

Chapter 8: “Flash Crashes”, Crises and the Limits of Prediction

Figure 8.1 Small unidirectional trades collectively have larger impact than a single block

Figure 8.2 Nuts and bolts implementation of Sornette's crisis indicator, Shanghai Composite Index

Figure 8.3 Liquidity is the tide that lifts all boats

Figure 8.4 Time series of CrossBorder Total Liquidity Index, Global

List of Tables

Chapter 4: Hedging the Wings

Table 4.1 Historical performance of S&P puts with variable deltas (volatility-adjusted)

Chapter 7: Strategies for Taking Advantage of a Market Drop

Table 7.1 Standard deviation has the tightest sampling distribution

The Second Leg Down

Strategies for Profiting After a Market Sell-Off

HARI KRISHNAN

This edition first published 2017

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Set in 9/11 and SabonLTStd by SPi Global, Chennai, India.

To Sudarshan and Kailash

Preface

There have been times when I have looked into the abyss as a portfolio manager, yet found a way to avoid disastrous losses. My trading accounts have weathered the 2008 crisis, the 2010 Flash Crash, the European Crisis of 2011 and the volatility spike from nowhere in August 2015, with varying degrees of success. Things have not always gone as well as I had hoped, yet I have always come away with a collection of new tactics for survival. For a fund manager, it is about survival after all. Aside from the money, your reward for decent performance is another year of money management. You don't want to take the path of boxers, who only decide to retire after a series of devastating knockouts. It is nice not to have to go out on your shield. This book has been inspired by the various crises I have faced as a money manager and the techniques I have learned and devised for managing through them. As every crisis is somewhat different, finding the most efficient hedge is a never-ending quest. I do hope that readers will find something that they can use to avert catastrophic losses.

The style of this book is casual and conversational, yet it attempts to be as accurate and realistic as possible. I have been asked who the ideal reader of this book might be. The best answer I can give is me, 20 years ago. This is a more pedestrian effort than Rilke's Letters to a Young Poet. Still, if I had followed the roadmap laid out in the pages that follow, I would have avoided numerous mistakes over the course of my career. More pragmatically, the book is targeted at a wide range of potential readers. Pension fund managers might find value in the discussion of duration hedging, bespoke trend following and roll down as a source of return for bond portfolios. The introductory options sections are designed to give a buy-side perspective on a topic that is usually discussed in terms of arbitrage, precise replication and stochastic calculus. I try to address why someone might want to use particular options structures. I also highlight specific structures that portfolio managers actually use and what might predicate a certain trade.

It is common for portfolio managers to hide their best ideas. In some cases, they might even publish strategies that didn't quite work, for implementation reasons. This leads to a situation where people who don't have any money management experience write extensive books about investing, while those who have the most to contribute are relatively silent. How is it possible to provide some valuable content without giving too much away? In this book, I have tried to veer from the norm. By focusing on hedging, rather than alpha generation, I have been able to go into some detail about specific strategies, without pretending to offer a cook book for making money. These have actually been battle-tested in the markets, for institutional clients.

Acknowledgements

The following people have had a profound effect on the contents of this book. I would like to thank them directly.

My wife Lalitha (using her considerable literary talents) edited large sections of the book and improved the flow of the writing.

Diego von Buch provided the initial impetus for the book, calling me from his French chateau and offering a hedging mandate just as market conditions were deteriorating in 2007.

Jerry Haworth deserves a great deal of credit for introducing me to the subtleties of long-dated options and his imprint can be found in Chapter 5.

Marc Malek exerted a large influence on the regime index and trend following sections.

Roy Niederhoffer also played an important role, as a source of original ideas about trend following strategies.

Michael Howell's insights into the relationship between “funding liquidity” and the market cycle were the inspiration for Chapter 8. I can only hope that I have not watered down his ideas to the point where they are unrecognisable.

Pablo Carbajal also deserves special thanks, as he has been the sounding board for many of the ideas presented in this book.

I hashed out many of the ideas in this book with Lee Collins, who encouraged me to put things in simple and concrete terms. His way of talking about trades had a large impact on Chapter 3.

Alex Manzara and Aaron Brown were kind enough to read the entire manuscript, providing valuable perspective on options execution in extreme market conditions.

My mother and father-in-law supported me by selflessly taking care of the boys and freeing up time for me to slog through the manuscript.

Others who provided valuable advice and inspiration for the book were (in no particular order): Jasper McMahon, Ben Paton, Nick Denbow, Norman Mains, Niels Kaastrup-Larsen, Pertti Tornberg, David Murrin, Karthik Bharath, Thomas Hyrkiel, Steve “explain things in a nutshell” Crutchfield, Dan DiBartolomeo, Lee Cashin, John Mallet-Paret (lean and mean writing style) and Izzy Nelken. Finally, I would like to thank my parents for encouraging creativity and independent thinking since I was a young boy.

About the Author

Hari P. Krishnan is a fund manager at CrossBorder Capital in London. He specialises in global macro, volatility and hedging overlay strategies. Previously, he managed a CTA strategy for a multi-family office based in London and was an executive director at Morgan Stanley. Hari also worked as an options trading strategist for a market-making firm at the CBOE and as a senior economist at the Chicago Board of Trade. He holds a PhD in applied math from Brown University and was a post-doctoral research scientist at the Columbia Earth Institute.

Chapter 1Introduction

Finance is full of colourful stories and the most exciting ones tend to involve someone on the verge of collapse. We feel a mix of thrill and schadenfreude when we read about the traders who blew up or the elite hedge funds that had to liquidate after failing to meet their margin calls. In a moment of panic, investors can do the strangest things and this can make for great theatre. Arrogance and overconfidence are punished by the markets, which seem to have a life force of their own. Many shrewd investors have completely lost their way in a moment of crisis. There are numerous stories of portfolio managers who have patiently extracted profits from the markets for years, then had a large and unexpected loss. It might have been advisable for them to exit the position (“cutting their losses”) and try to claw back using their core strategy over time. Yet, the temptation is to put all the chips on black in an attempt to make the money back quickly. In principle, this is a wretched idea, as the profit from a long series of rational trades over time may be overwhelmed by a single irrational bet.

THE AIRPLANE TICKET TRADE

The legend of the airplane ticket trade is an extreme example of bad judgment under pressure, yet it is sometimes presented as rational decision-making. The story goes as follows. A trader has been losing money and is unlikely to collect much of a bonus this year. So the trader decides to dial up risk in an attempt to make it all back in one go. This backfires horribly, leading to further losses. The trader expects risk to be cut at any moment now, so he does two things. He makes a very large short-term trade that will either make or lose a large amount and he simultaneously buys a ticket to South America. It's a tactical play, with little edge but lots of risk. The trader then goes to the airport and repeatedly checks his price feed in the lounge. If the trade goes in his favour, he closes the position then goes back to the office. If it goes belly up, he buys a bottle of vodka from the duty free then takes the flight. The trader's behaviour might seem reasonable at 30,000 feet. In the best scenario, he gets a large bonus; in the worst, he takes a long tropical holiday. There doesn't seem to be much downside and one could argue that from the trader's standpoint, he is long an option. But would you want to be that trader at the moment of crisis? If the position is going slightly against you, are you willing to hang on for dear life, with no conviction that you are making the right trade? If it is your own money, do you want to risk everything on a roll of the dice? If you are a fund manager, how can you rationalise what you have done to clients if it all goes wrong?

THE BULL CYCLE

In reality, most institutional losses and disasters are not caused by trading reminiscent of the Wild West. Rather, they are caused by somewhat predictable behaviour through the market cycle. In bull markets, portfolio managers tend to increase exposure in an effort to chase the market and outperform competitors and benchmarks. Ten basis point differentials in performance seem important. By the “market”, we mean risky assets such as stocks and corporate bonds. Investors eagerly buy into every dip in the market, dampening volatility. As the value of collateral increases and volatility declines, banks lend more and the market eventually becomes overextended. This applies to equities, corporate bonds and other risky assets. When risky assets appear to be vectoring toward infinity, we would argue that it is a good time to hedge. Risk embedded in the system has increased, yet the market is practically giving away insurance. The painful memories of the last crash have been erased, making investors particularly vulnerable to a random shock.

Investors who chase returns after a large sustained move tend to have relatively low pain thresholds. They worry that they have missed the move, but are equally likely to bail out at the first sign of trouble. So long as the rally persists, the cost of insurance (i.e. options) tends to be low. The latecomers to the market do not want to erode their return by hedging and the longstanding bulls are complacent. You could sensibly argue that if the market continues to rally, hedging costs should be more than offset by profits in the rest of the portfolio. Yet there is a natural human reluctance to “waste” money on insurance when everything seems fine.

As the animal spirits take over, investors attempt to rationalise their behaviour in a variety of ways.

“This time it's different.” There is a central bank put on the market, as monetary conditions will be eased whenever there is a risk event. Regulators can prevent extreme intra-day moves by disqualifying trades that occur very far away from recent prices.

Calm periods are persistent: they tend to last for a long time. Not very much happens from day to day, suggesting that there is plenty of time to prepare for the next correction.

Over the long term, hedging is largely unnecessary. For example, some institutions don't hedge their currency risk. Over the long term, they assume that currency moves will wash out. Buying insurance on risky assets such as equities is a losing strategy over the long term. According to academic theory, hedging must have a negative risk premium, as it reduces the non-diversifiable risks in your portfolio. Insurance companies are generally profitable because they sell individual policies that are statistically overpriced. So long as the policies are relatively uncorrelated, insurers are able to collect more than they pay out over the long term.

If you are not careful, you can convince yourself that selling insurance is an unbeatable strategy. Short volatility strategies tend to perform magnificently in back-tests, without much parameterisation. All you need to do is persistently sell downside protection on equity indices, risky currencies and corporate bonds, or so it would seem. When volatility is low, these options appear to be slightly but consistently overpriced. It is tempting to conclude that you can make small but very steady returns in this environment. As volatility rises, your profits become less reliable from day to day. However, this might be more than compensated for by an increase in the premium you collect when volatility is high. Most active management strategies are short volatility in one way or another. Whether you buy equities, take long positions in risky bonds or engage in spread trades, you will tend to perform better in flat to rising markets than highly volatile ones. The vast majority of hedge fund strategies are structurally short volatility. The incentive structures for many hedge funds and proprietary trading desks favour collecting pennies in front of the bulldozer. However, this does not imply that selling volatility universally has a positive expected return. Once you put a back test into action, you are vulnerable to large jumps that may not have appeared in the sample past. As soon as you introduce leverage, you are vulnerable to risk and margin constraints that can force you out of a trade at the worst possible time. Markets don't usually collapse because investors want to sell, but because they have to. Liquidation is forced, in the presence of margin calls. We will examine the effect of margin constraints on short volatility strategies in Chapter 4.

THE RENEGADES

There is a small but dedicated group of defensive, bear market managers in the investment universe. The financial media trots them out every so often, typically after a market sell-off. However, in rising markets these managers are largely invisible or the subject of criticism. Profiting from panics, bankruptcies and liquidations requires patience and does not necessarily win you many friends. When equities are ramping up, bear-biased managers spend more time banging their heads against the wall than raising assets. The cost of insurance is steadily declining, yet there are no takers. The inveterate bears write long and engaging manifestos in an attempt to identify cracks in the financial system. In rising markets, the potential end users of these products generally can't or don't want to buy them. Some institutions take a crude “line item” approach, where they rank their funds according to recent performance and periodically redeem from underperforming managers. This approach seems oblivious to the idea of marginal risk, i.e. how much you can improve the risk-adjusted performance of an existing portfolio by adding a new asset or strategy. In reality, if you can find a strategy that performs strongly during crises yet doesn't lose too much over a market cycle, it can have a dramatic impact on portfolio performance over the long term.

Uncontaminated bear strategies have a hard time competing in a world where allocators believe that emerging markets, high yield bonds and carry trades are “diversifying” investments. While it is true that these asset classes can reduce realised volatility during normal market conditions, they typically amplify losses when conditions become extreme. Some strategies, such as the FX carry trade, seem innocuous during bull markets. They grind their way upward with low volatility. However, it is categorically not true that a strategy with relatively low volatility in a bull market will dampen risk during a crisis. If the strategy collects premium while taking extreme event risk, the opposite is in fact true. A manager who combines carry strategies with a modest number of equity index puts will often appear to be over-hedged most of the time and severely under-hedged when the protection is most needed.

In rising markets, dedicated bears have to overcome time decay as well as markets that are moving in the wrong direction. The portfolio manager who takes the opposite side of the trade by selling insurance has an optical advantage. Investors seem to prefer a sequence of returns of the form {+1%, +1%, +1%, +1%, +1%, –5%} to {–1%, –1%, –1%, –1%, –1%, +5%}, even though the compounded return of the second strategy is a bit higher. In the first scenario, you can always say to your client that you are an alpha manager who had a few issues with risk control that have now been resolved. This cynical approach may well salvage the mandate. Even the most dedicated bears are incentivised to scale down their hedges when threatened with redemptions.

The best time to buy outright volatility is when it is low, in a counter-cyclical way. You want to swim against the tide of short-sighted overconfidence. Investors are more than happy to sell volatility when they are feeling confident. However, implied volatility is low precisely because there is virtually no demand for hedging or long volatility strategies in general. Hence, long volatility managers struggle to raise assets in situations when the best risk-adjusted returns are available. Our book acknowledges the perverse nature of hedging mandates. When assets are pouring in, outright volatility tends to be overpriced. We try to identify ways to minimise drag while still offering protection after markets have started to tumble.

CLAWS OF THE BEAR

[T]o borrow the term, your sense of time does change when you are running real money. Suppose you look at a cumulative return of a strategy with a Sharpe ration of 0.7 and see a three year period with poor performance. It does not phase you one drop. You go: “Oh, look, that happened in 1973, but it came back by 1976, and that's what a 0.7 Sharpe ratio does.” But living through those periods takes – subjectively, and in wear and tear on your internal organs – many times the actual time it really lasts. If you have a three year period where something doesn't work, it ages you a decade. You face an immense pressure to change your models, you have bosses and clients who lose faith, and I cannot explain the amount of discipline you need.

– Cliff Asnessi

Once you put real money behind a short volatility strategy, the situation changes. Now you have some skin in the game and things aren't quite so comfortable. Your margin levels can change dramatically over time, requiring that you cut positions that look very attractive from a valuation standpoint. In Chapter 4, we show that wildly fluctuating margin requirements can force you out of a short volatility strategy at the worst possible moment. A historical series of daily NAVs is devoid of emotion and assumes that you have sufficient capital to keep playing indefinitely. It can't capture gut wrenching intraday moves or account for price action that is different from what has been observed in the past. If the worst 1 day historical loss is –10% and your strategy is down –9% at mid-day, there is no guarantee that losses will be bounded at roughly –1% thereafter. In rising markets, investors are quite happy to sweep latent risk under the carpet as risk and margin limits are never reached. Inevitably, at some point, risky assets take a significant leg down. The “stocks go up in the long term” bulls can no longer buy the dip as they approach their risk limits. Large institutions spend ages deciding whether “this is the one”, whether credit and equity markets will plunge further into the abyss. Their portfolios might already be down –5% or –10% on an unlevered basis and they really can't take much more. Do they hang on, cut exposure or hedge?

It has often been remarked that “hope is not an investment strategy”. Hanging on is a sign of desperation or delusion. Sometimes, an overconfident investor can become convinced that the market has to move a certain way and goes all in. It is almost as though the investor believes it is possible to move the market by force of mind. Solipsism doesn't seem to be a viable strategy, either. Some investors doggedly hold onto losing positions using “fair value” arguments. When combined with leverage, this approach can be toxic. The standard argument is that the expected return of a static portfolio goes up as its price drops, i.e. price and expected return move inversely. While this may be true over long horizons, there is a point at which every institutional manager has to cut risk. Most of us do not have an infinite investment horizon in which to capture a risk premium. There is a saying for the leveraged deep value investors who hang on during crises: “it looks good at 90, looks great at 80, looks absolutely fantastic at 70 and you're out of business at 60”. This is the classic value trap that needs to be avoided.

ZUGZWANG

In chess, zugzwang refers to a situation where a player has to move, but every move worsens the player's position. When a portfolio manager's risk limits are hit or losses are thought to be unacceptable, the situation is quite the same. There are two choices: cut risk or buy insurance. Neither seems appealing. If the manager slashes positions, the potential for further losses is reduced. This can be agonising for investors who believe that, given enough time, their portfolio is bound to bounce back. Some portfolios are large and complex, implying that they cannot be liquidated in one go. Finally, suppose an investor has been making small bets for years and now has to divest a large percentage of his or her portfolio. This one action can offset a large number of good decisions and successful trades. Some funds scale in and out of positions almost continuously as risk changes. They generally have sophisticated techniques for sampling volatility and correlation over time. However, even these funds are exposed to gap risk (i.e. when a currency peg is released) or situations where their alpha-generation systems have stopped working.

Faced with the choice of liquidating positions or hedging, institutions finally pick up the phone and contact managers who can protect capital during a crisis. Managed accounts that have not been used for months are reactivated, with a hedging overlay mandate. Assets begin to flow into bear-biased strategies. As the demand for hedging increases, its cost sky rockets. To a patient on the operating table in a life-or-death situation, money is no object. Survival is all that matters. And so it goes for an individual or institution on financial life support, who hedges regardless of cost. The long volatility manager who gets the call is in two minds about it. On the one hand, the manager is more than happy to have a new allocation. It serves as vindication, as well as a new source of fees. On the other, hedging looks expensive now. If only the call had come a few weeks earlier, when there was a wide range of inexpensive hedges to choose from! Previously, an overlay could have been slowly and carefully constructed, with an emphasis on finding inexpensive hedges across a variety of asset classes. Now it's a case of making the best of a bad situation. You have to make sure that the patient survives (i.e. that there is a floor on further losses), while ensuring that you don't spend too much along the way. Once markets recover, your performance will be mercilessly scrutinised. Did you make enough on the way down? Did you monetise enough gains to avoid giving it all back during the recovery?

Whether you allocate to another manager or hedge yourself, the pressures are quite the same. Most of the time, you will be incentivised not to hedge, even when you can identify good short opportunities. Indirect hedges, such as buying calls on the VIX to hedge against long exposure to the S&P 500, will generally add to your exchange margin requirements. This reduces the degree to which you can lever the rest of your portfolio. Even if leverage is not an issue, hedging suffers from an optical standpoint. Unless you can bury your hedges in the rest of your portfolio, your supervisors and clients will see long strings of mildly negative returns punctuated by the occasional lumpy positive one. Once things get ugly, you will be asked whether you have hedged enough. Are you making money on every little drop in risk assets? Have you put a floor on how much can be lost in the overall portfolio?

THE SCEPTICS

Some investors, especially those with a “stocks for the long run” bias (e.g. Siegel, 1998), might argue that hedging is intrinsically wasteful. The hedging sceptics tend to intersect with the true believers in the equity risk premium. If you are prepared to wait long enough, there's no need to hedge, as equity market returns will exceed inflation. Over rolling 10-year horizons, the S&P 500 has nearly always outperformed CPI inflation on an annualised basis. It follows that, if equities deliver a positive real return over the long term, hedging must have a negative risk premium. After all, you are paying a premium to take a short position on the market, is that not so? Theory suggests that you earn a premium for bearing an undiversifiable risk. Conversely, an instrument that offsets market risk should have a negative expected return. Insurance companies are in business precisely because insurance is overpriced on average. Historical back-tests in the markets tend to support this idea. Insurance eats into your long-term expected return. Static options hedges tend to lose money at an alarming rate, with modestly positive spikes along the way. On paper, the appropriate strategy involves buying into market sell-offs, as risk premiums go up whenever the prices of risk assets go down. It would seem as though the last thing you want to do is buy options after volatility has gone up. If an option was expensive before, it must be egregious after a risk event. Our view is that listed options are somewhat different from insurance policies. While typical hedges are probably overpriced, as there is excess institutional demand for them, options are subject to the same cycles of greed and fear as equity markets.

A SAD TRUTH

Recently, a number of books and articles have appeared covering topics such as “tail risk protection”, “crisis alpha” or “extreme event hedging”. Many of these are thorough treatments of how institutions think about truncating the left tail of their return distribution. Bhansali (2014) is a thoughtful treatise on the nature of asset class distributions and institutional quality hedging strategies. However, they invariably ignore a sad truth. Almost no one wants to hedge much when the going is good. Institutional investors generally do not pay much attention to the independent economists and hedge fund managers who warn that a new crisis is brewing. In bull markets, articles that focus on doomsday scenarios are viewed as nothing more than fearmongering. Indeed, it is notoriously difficult to predict where the next crisis will come from. Will it be credit derivatives, emerging markets or a change in Central Bank policy?

Several well-known hedge fund managers try to engage in crisis prediction by identifying potential cracks in the system. They typically screen for excessive leverage in some part of the economy and then direct their hedges to the places where danger seems to be lurking. This is a substantial improvement on not hedging at all, but it assumes that extreme events are predictable in place and time. If the manager places the doomsday bet too early, there may be a long string of losses before any material gain is realised. In the meantime, investors might redeem from the strategy. If the bet is placed too late, the risk of default may already be priced into the market, reducing potential returns. Most of us don't have the foggiest idea when the next crisis is coming and should be honest enough to admit it. Note that we will discuss crisis prediction in Chapter 8. It might seem contradictory that we are taking a stab at a problem as difficult as this. For the purposes of this discussion, however, it is best to assume that predicting financial crises is like predicting earthquakes. We can identify situations (geological fault lines) which are unstable, but can't with any certainty say when an event will occur.

Returning to the original problem, let us generalise and assume that investors only want to hedge after risk assets have taken a leg down. Hedging is not going to be cheap, as there is more demand for insurance. So what can you do to protect a portfolio against a systemic risk event, that isn't too bad? That is what this book is all about.

COMMON MISTAKES

In the chapters that follow, we identify strategies for protecting a portfolio of risky assets after a sell-off. Investors have suddenly become wary and are no longer just giving away protection at discount levels. It is not wise to just go in and buy index puts, as these are bound to be overpriced. Yet many institutions do exactly that. They react to an increase in perceived risk by identifying “plausible” downside scenarios and choosing options that target those scenarios. The risk committee might have a discussion about how bad things could get, before reaching a consensus on what constitutes a tolerable and plausible loss. We believe that this approach is flawed. While it is reasonable to average forecasted returns, taking an average of downside scenarios understates the risk of an extreme event.

If everyone is buying options to cover the risk of moderate losses, those options are likely to be overpriced. Our approach is to find other options to buy. We argue that an option does not have to wind up in the money to be profitable. All that is needed is a repricing of risk. Just as the price of hurricane insurance goes up when there is a thunderstorm, the price of extreme event insurance rises when there is a moderate sell-off in the equity market. You can always sell an option back to the market if it reprices substantially. In any case, implausible scenarios can appear plausible after a plausible scenario has occurred. This may sound thoroughly convoluted, but it is not meant to be. Our goal is to be as clear as possible. At first sight, a –30% one month collapse in the S&P 500 seems highly unlikely. Even in October 2008, the peak to trough drop was less than that. But suppose that the index drops –10% in the first week. Suddenly, that –30% drop does not seem so unlikely and investors are clamouring for insurance at levels (i.e. option strikes) far below what could be imagined. This is partly a function of perception. It is also based on the idea that in certain scenarios, markets exhibit positive feedback. A drop cannot be viewed in isolation, because that drop may force others to sell as they hit their risk limits. Sell-offs can occur in cascades.

Another common idea is to hedge extreme event risk using currency options. This is a play on the “Mrs. Watanabe trade”, which will be analysed in greater depth in Chapter 2. Mr. Watanabe has a demanding job, so he delegates the family's personal investments to his wife. There is no point in depositing money at a local bank, since the bank rate is effectively 0%. The Nikkei 225 is still well below its peak in 1989 and there is no cult of equities in Japan, as there is in the US. The equity premium puzzle is irrelevant, as there is no premium to speak of. Investors are distrustful that Japanese equity indices will deliver a positive return over the long term. So why not sell the Yen to buy Australian dollars (AUD) or another high yielding currency? When you buy Australian dollar forwards, you implicitly capture the Australian bank deposit rate. If a 1 year deposit yields 5% in Australia, you gain 5% carry in Australian dollars while borrowing Japanese Yen virtually for free. Theory suggests that the forward rate bias should be offset by an expected –5% annual decline in AUD. In practice, Kritzman (1999) and others have observed that spot exchange rates are not very correlated to yield differentials. If anything, high yielding currencies tend to outperform even in spot terms, as investors chase income. Assuming that AUD does hold its value relative to the Yen, you collect nearly 5% per year. This is a huge source of income in a deflationary environment. Once the carry trade gathers momentum, Mrs. Watanabe's investment club piles into the trade. Things sound rosy so far. Ultimately, the trouble with the trade is that it can become overleveraged and overcrowded. This poisonous combination can cause very steep declines when investors are exposed the most. Eventually, a random shock turns into a major reversal as the investment club heads screaming for the exits along with larger institutions.

Given that carry currencies go up the stairs and down the lift, it seems reasonable to hedge extreme event risk using puts on carry trades such as the Australian Dollar/Japanese Yen cross. More precisely, carry trades are negatively skewed, implying that the probability of downside surprises is higher than the probability of ones that work in your favour. The longer-dated the put, the more time you have to wait for a blow up. However, the shape of the currency forward curve can have a dramatic impact on the performance of a hedge. Once you buy the Aussie put, two forces are conspiring against you. Every day that passes, you lose money on time decay and drift as the forward rolls up to the spot. So the currency hedge usually winds up a loser.

IMPRECISE BUT EFFECTIVE

The hedges described in this book are not precise. We are not going to tell you to hedge your long position in Apple with Apple puts. While this may be the most accurate way to soften the impact of sell-offs, it is often egregiously expensive. If you really don't feel comfortable with Apple downside, your best strategy is probably to reduce the position. Yet institutional practice often suffers from a literal and somewhat narrow-minded approach to hedging. Many consultants in the pension fund industry seem overly focused on precise hedges. The solvency of a pension fund is often calculated relative to the present value of its liabilities. The liabilities are the expected payments the fund will have to make to its beneficiaries in the future. If interest rates drop, the value of those liabilities today will increase. This necessitates hedging against rate risk. A common solution is to use an actuarial number called the “average duration” of the liabilities as a crucial variable in the hedge. This is the time-weighted average of expected payments to beneficiaries. It is an imprecise number, based on projections of who will retire and when. Still, consultants often think of average duration as an exact number and offset rate risk with swaps or other instruments that precisely target it. While there may be regulatory reasons for transacting in this way, this approach seems wasteful. In a low interest rate environment, receiving fixed payments does not seem like the best idea. There may be other, slightly less precise-looking hedges that offer greater protection and are likely to cost less in the long term. If your shoe size is 8.5, do you want or need a shoe that is precisely calibrated to size 8?

We focus on overlay strategies as a mechanism for controlling portfolio risk. Our goal is to identify areas where insurance is relatively inexpensive, while recalling the idea that our hedges need to make money in a severe risk event. Most of the strategies involve exchange-traded options in deep and liquid markets, such as equity indices, the VIX, interest rates and currencies. We start with a non-technical overview of options theory. The goal is not to price options but rather to express the value of an option in terms of its implied volatility. Focusing on volatility, we can identify different combinations of options in different markets that are relatively cheap at a given point of time.

If an emerging markets index drops from 100 to 90 in a day, a 75 strike put may have a larger percentage gain than a 95 strike put, even though the stock hasn't come close to 75. The implausible scenario (a sudden –25% drop) has suddenly become plausible. As we will see, large moves sometimes beget even larger moves as the market enters a positive feedback loop. When investors start to worry about a major loss, they bid up the prices of puts that are far out of the money. This causes those silly strike options to make multiples of what was initially paid.

HEDGING AGAINST IMPLAUSIBLE SCENARIOS

In Chapter 4