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by Hari P. Krishnan
The Second Leg Down
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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Prev
Previous Chapter
Series Pages
Next
Next Chapter
Title Page
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
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