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Extreme Returns The Case of Currencies

Extreme Returns The Case of Currencies. Carol Osler Brandeis University Tanseli Savaser Williams College. Extreme Returns in FX. Reality October 7, 1998: Dollar-yen fell 11% … without news October, November 2008: Frequent dollar moves of 2, 4, even 7% High frequency of extreme moves

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Extreme Returns The Case of Currencies

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  1. Extreme Returns The Case of Currencies Carol Osler Brandeis University Tanseli Savaser Williams College QWAFAFEW July 20, 2010: Extreme Returns in FX

  2. Extreme Returns in FX • Reality • October 7, 1998: Dollar-yen fell 11% … without news • October, November 2008: Frequent dollar moves of 2, 4, even 7% • High frequency of extreme moves • More frequent than normal distribution • But … reasons to expect returns distributed normally • Great variety of market shocks and Central Limit Theorem • Surprising to financial economists • In economic models, only information brings abrupt moves QWAFAFEW July 20, 2010: Extreme Returns in FX

  3. Extreme Returns Matter • Matter for risk management • Major market disruption: Funds go bankrupt • Value-At-Risk • How big IS tail risk? • Is it constant? • Matter for option pricing • What IS a “jump process,” anyhow? • What determines likelihood, size of “jumps”? QWAFAFEW July 20, 2010: Extreme Returns in FX

  4. Contributions • 4 Ways Price-Contingent Trading Increases Extreme Returns • Affect Distribution of Order-Flow Itself Three Ways • Distribution of trade sizes • Clustering of trades at times of day • Clustering of trades at exchange-rate levels • Fourth Effect: Feedback from Order Flow to Returns • Evaluate Importance of Each Contribution • Most important single factor: Fat tails in order-size distribution • Interactions among factors also very important • Generalize? Algorithmic and Technical Trading in Equities QWAFAFEW July 20, 2010: Extreme Returns in FX

  5. Extreme Returns, Fat Tails, & Kurtosis • Fat tails: High frequency of extreme outcomes • Benchmark: Normal Distribution • Broader Concept: Kurtosis • Fat Tails • Tall Skinny Middle • Kurtosis of normal distribution = 3 • Kurtosis of financial returns >> 3 • Equities • Bonds • Forex • I (incorrectly) use “fat tails” and “kurtosis” interchangeably QWAFAFEW July 20, 2010: Extreme Returns in FX

  6. Kurtosis in Exchange-Rate Returns Link QWAFAFEW July 20, 2010: Extreme Returns in FX

  7. Kurtosis in Exchange-Rate Returns Example: 53 % of orders within 1/2 standard deviation of mean 38 % of observations within 1/2 std dev. for normal distribution Ratio: 1.4 = 53/38 Tall Skinny Middle Fat Tails QWAFAFEW July 20, 2010: Extreme Returns in FX

  8. Kurtosis in Exchange-Rate Returns • Earlier: Statistical description of return distribution • Normal Distribution ("Gaussian")? No • Student t distribution? Stable Paretian? Mixed evidence … • Mixture-of-normal distributions? (What’s that?) • Pick a group of random variables: X,Y,Z,A,B,C …. • All from normal distributions with same mean (say, 0) • But different standard deviations • Say: X,Y,Z have std.dev.= low; A,B,C have std.dev.=high • Distribution of the group X,Y,Z,A,B,C has fat tails • Little attempt at understanding • Assumes distribution is constant … which seems unlikely QWAFAFEW July 20, 2010: Extreme Returns in FX

  9. Outline • Data • 3 Key Features of Price-Contingent Orders • Distribution of individual order sizes • Time-of-day clustering • Exchange-rate clustering • How much kurtosis? • 4th Factor: Feedback, Order Flow  Returns • How much kurtosis? • Linear feedback • Concave feedback • Summary QWAFAFEW July 20, 2010: Extreme Returns in FX

  10. Data • Royal Bank of Scotland • Currently 5th largest FX dealing bank worldwide (Euromoney, 2007) • Complete book of stop-loss, take-profit orders • 2 time periods • 1 September, 1999 - 11 April, 2000 • 1 June, 2001 through 9 September, 2002 • 3 major exchange rates • Euro-dollar, Dollar-yen, Sterling-dollar • Contemporaneous exchange rates • Minute-by-minute indicative quotes Reuters FXFX QWAFAFEW July 20, 2010: Extreme Returns in FX

  11. Data • Basics: • 47,312 orders placed worth $253 billion • 27 percent executed • Otherwise deleted or remained open • Most orders executed within one day • In fact, most executed within a few hours • Mean order size: $5.4 million • Max order size: €858 million QWAFAFEW July 20, 2010: Extreme Returns in FX

  12. Stop-Loss and Take-Profit Orders • “Price-contingent” market orders • Stop-loss orders: Positive-feedback trading • If market falls to $1.30, sell €50 million (exactly) at market price • If market rises to ¥125/$, buy $25 million (exactly) at market price • Take-profit orders: Negative-feedback trading • If market falls to $1.30, buy €50 million (exactly) at market price • If market rises to ¥125/$, sell $25 million (exactly) at market price • Unlike limit orders • These orders absorb liquidity (especially stop-loss orders) • These orders used in quote-driven markets • Customers assign dealers to monitor the market for them QWAFAFEW July 20, 2010: Extreme Returns in FX

  13. Who Places Stop-Loss and Take-Profit Orders? QWAFAFEW July 20, 2010: Extreme Returns in FX

  14. Outline • Data • 3 Key Features of SL and TP Orders • Distribution of individual order sizes • Time-of-day clustering • Exchange-rate clustering • How much kurtosis? • 4th Factor: Feedback, Order Flow  Returns • How much kurtosis? • Linear feedback • Concave feedback • Summary QWAFAFEW July 20, 2010: Extreme Returns in FX

  15. SL, TP Create Kurtosis In Order Flow • Reminder: Order flow = Buy-initiated – Sell-initiated • E.g., Market buy orders – market sell orders • Why kurtosis of order flow … instead of kurtosis of returns? • Order flow drives returns • Crudely: Exchange-rate return  Constant • OrderFlow • Return distribution isomorphic to order-flow distribution • If order-flow distribution : Normal,Mean=0, Stand.Dev.=1 • And if “constant” = 2 • Return distribution of : Normal,Mean=0, Stand.Dev.=2 QWAFAFEW July 20, 2010: Extreme Returns in FX

  16. Distribution of Order Sizes • High kurtosis in distribution of individual order sizes • EUR: 725! GBP: 21 JPY: 26 Tall Skinny Middle Fat Tails QWAFAFEW July 20, 2010: Extreme Returns in FX

  17. Distribution of Order Sizes • Suppose 1 order executed per half-hour • Each period, random pick of one order size • Also, random sign (Buy = +, Sell = -) • Maybe x = €2.3 million sold = - €2.3 million • Order flow across the day is sequence of X’s • All sampled from same distribution with high kurtosis • So kurtosis of order-flow  kurtosis of order-flow sizes: • EUR: 725 GBP: 21 JPY: 26 QWAFAFEW July 20, 2010: Extreme Returns in FX

  18. Distribution of Order Sizes • If 1 order executed per 1/2-hour • Kurtosis order-flow same as kurtosis of order-flow sizes: • EUR: 725 GBP: 21 JPY: 26 • If N = 2 orders executed per 1/2-hour • Each period, random pick of two order sizes • Assign random sign (buy/sell) • Order flow = x1 + x2 • Maybe x1 = -€2.3 million and x2 = 1.0 million • So order flow = - €1.3 million • With many orders/period, OF distribution loses fat tails • Distribution  xiNormal (kurtosis = 3) as N  QWAFAFEW July 20, 2010: Extreme Returns in FX

  19. Distribution of Order Sizes • Distribution of order flow  Normal as N  • How fast? • Answer from simulation: Picking order sizes at random • How many orders executed per 1/2-hour, in reality? • Back-of-the-envelope: 3 or 4. We go with 4 QWAFAFEW July 20, 2010: Extreme Returns in FX

  20. Intraday Volatility Pattern and Kurtosis Exchange-Rate Levels Crossed per Half Hour New York London Asia QWAFAFEW July 20, 2010: Extreme Returns in FX

  21. Intraday Volatility Pattern and Kurtosis • Key: Number of orders depends on number of rates crossed • From 1.0010 to 1.0011 • Execute orders ending in 11 • From 1.0010 to 1.0015 • Execute orders ending in 11, 12, 13, 14, and 15 • If order sizes distributed normally • In each ½-hour, order flow distributed normally • Sum of variables with same normal distribution is normally distributed • Order flow standard deviation high if N is high • Vice versa QWAFAFEW July 20, 2010: Extreme Returns in FX

  22. Intraday Volatility Pattern and Kurtosis • Key: N depends on number of exchange rates crossed • Suppose individual order sizes distributed normally • Order flow distributed normally in each 1/2-hour • Order flow std. dev. high if number of orders is high, vice versa • Strong intraday variation in volatility • Dailyorder flow includes order flow from every time of day • That is, mixes normal distributions with varying standard deviations • So: Overall order flow has fat tails • Currency returns will have fat tails QWAFAFEW July 20, 2010: Extreme Returns in FX

  23. Exchange-Rate Preference and Kurtosis • People prefer to place orders at certain rates • Special preference for round numbers, for example $1.7600/£ QWAFAFEW July 20, 2010: Extreme Returns in FX

  24. Exchange-Rate Preference and Kurtosis • People prefer to place orders at certain levels • End digit 0 preferred to 5 ….. 5 preferred to 2,3,7,8 …. ….. 2,3,7,8 preferred to 1,4,6,9 • Orders executed depend on specific rates (St) crossed • If Stcrosses level ending in “00,” many orders (5 %) • If Stcrosses level ending “39,” few orders (0.3 %) • Suppose individual order sizes normally distributed • Number of orders per period varies due to exchange-rate preferences • So … standard deviation of order flow varies across period • So … mixture of normals, order flow has high kurtosis unconditionally • And currency returns have high kurtosis QWAFAFEW July 20, 2010: Extreme Returns in FX

  25. Exchange-Rate Preference and Kurtosis • Executed take-profits and stop-losses might tend to offset • Example: Rate rise triggers take-profit sells and stop-loss buys • If same amount of each, no effect on returns • But orders cluster at different levels, so less offsetting • Lots of take-profits or lots of stop-losses • More big returns Level Take-Prof Sell Stop-Loss Buy Time Exchange Rate Level Take-Prof Sell Stop-Loss Buy Time Link Exchange Rate QWAFAFEW July 20, 2010: Extreme Returns in FX

  26. How Much Kurtosis? • Simulations isolate effect of each factor on order-flow kurtosis • 5 years of trading days • Half-hour horizon, 24-hours per day • 4 orders per half hour, on average • No other trades • Calibrated simulations match properties of original orders data • 30 simulations per case • Standard errors calculated across simulations QWAFAFEW July 20, 2010: Extreme Returns in FX

  27. Order Size Has Biggest Direct Impact • What if all three sources operate at once? QWAFAFEW July 20, 2010: Extreme Returns in FX

  28. Interactions Dominate QWAFAFEW July 20, 2010: Extreme Returns in FX

  29. Outline • Data • 3 Key Features of SL and TP Orders • Distribution of individual order sizes • Time-of-day clustering • Exchange-rate clustering • Interactions more powerful than individual factors in isolation • 4th Factor: Feedback, Order Flow  Returns • How much kurtosis? • Linear feedback • Concave feedback • Summary QWAFAFEW July 20, 2010: Extreme Returns in FX

  30. Feedback from Order Flow to Returns • Price Cascade • Rate falls through 00 to 95 • Triggers stop-loss sell orders • Rate falls further • More stop-loss sell orders • Rate falls even further … • Generates extreme returns, fat tails of return distribution • Common in FX • According to market participants • Once per week? Many times per week? QWAFAFEW July 20, 2010: Extreme Returns in FX

  31. Feedback from Order Flow to Returns • Price Halt • Rate falls through 110 to 105 • Triggers take-profit buy orders • Buy orders impede rate from falling further • With stopped rate, no orders triggered next period • With no orders, rate stays put • Generates tiny returns, tall skinny middle of return distribution QWAFAFEW July 20, 2010: Extreme Returns in FX

  32. Feedback Has Modest Direct Effect • Dynamic simulations OrderFlowt = F(St, St-1) ln(St+1) - ln(St) =Constant •OrderFlowt • Simulations calibrated to match original RBS data • True order size distribution • True intraday exchange-rate volatility pattern • True exchange-rate preferences • Many other features of data QWAFAFEW July 20, 2010: Extreme Returns in FX

  33. Simulated Rates Look Realistic • One simulated exchange-rate path Price Halts Price Cascades QWAFAFEW July 20, 2010: Extreme Returns in FX

  34. Calibration Actual Simulated QWAFAFEW July 20, 2010: Extreme Returns in FX

  35. Feedback Has Modest Direct Effect • Direct effect: Assume away order-flow factors • Size distribution, clustering … QWAFAFEW July 20, 2010: Extreme Returns in FX

  36. Feedback Has Huge Indirect Effects • Direct effect: Assume away order-flow factors • All effects: Restore order-flow factors QWAFAFEW July 20, 2010: Extreme Returns in FX

  37. Feedback Has Huge Indirect Effects • Huge return kurtosis with all factors • For EUR, almost 1,000! • But: Exchange-rate kurtosis <<< 1,000! • Note: No linear relationship, order flow to returns • Large orders are managed, effect on returns is not proportionate • Next: Simulation where diminishing marginal effect of order flow OrderFlowt = F(St, St-1) ln(St+1) – ln(St)=Constant • OrderFlowt QWAFAFEW July 20, 2010: Extreme Returns in FX

  38. Concave Feedback  Realistic Kurtosis • Simulations: OrderFlowt = F(St, St-1) St+1 - St Constant • OrderFlowt QWAFAFEW July 20, 2010: Extreme Returns in FX

  39. Concave Feedback  Realistic Kurtosis • Simulations: OrderFlowt = F(St, St-1) ln(St+1) – ln(St)=Constant • OrderFlowt QWAFAFEW July 20, 2010: Extreme Returns in FX

  40. Summary • Three properties of SL, TP orders generate kurtosis in returns • Order size distribution • Clustering in execution across trading day • Clustering across exchange-rate levels • Feedback with exchange-rate returns • SL, TPs produce substantial return kurtosis • Accounts for ½ - 2/3 of excess kurtosis at one-hour horizon Price-contingent order flow important source of extreme returns QWAFAFEW July 20, 2010: Extreme Returns in FX

  41. Risk Management: Why Might Tails Get Fatter? • More kurtosis in order size distribution Greater use of barrier options • More extreme intraday volatility pattern Much has to do with sleeping/waking patterns, and how many people place orders at different hours Rising international trade — More fat tails? Bank consolidation — Less fat tails? • Stronger preference for round numbers • Stronger differences between stop-losses and take-profits QWAFAFEW July 20, 2010: Extreme Returns in FX

  42. Extensions • News? • Rising order flow? • The rest of order flow? QWAFAFEW July 20, 2010: Extreme Returns in FX

  43. Influence of News? • Add actual U.S. macro statistical releases, 2004-2009 • 8 significant items • The usual suspects • Effect very small • But much news excluded QWAFAFEW July 20, 2010: Extreme Returns in FX

  44. Influence From Rising Trading Volume? • Lowers kurtosis at shortest horizons • More orders, less fat tails • Raises kurtosis at longer horizons • More feedback effects QWAFAFEW July 20, 2010: Extreme Returns in FX

  45. Kurtosis From the Rest of Order Flow? • Kurtosis in size distribution of EBS (interdealer) trades: 99 • Time-of-day clustering in EBS trades? Yes QWAFAFEW July 20, 2010: Extreme Returns in FX

  46. How Much Order-Flow Kurtosis? • How do we get these numbers? • Calibrated simulations • E.g.: Contribution of intraday volatility pattern to kurtosis • Each period, choose number of exchange-rate levels to cross • Calibrate order execution frequency so average orders/half hour = 4 • Pick order sizes from normal distribution, mean zero QWAFAFEW July 20, 2010: Extreme Returns in FX

  47. Exchange-Rate Preference and Kurtosis • Stop-loss and take-profit orders cluster differently • Take-profit: Cluster BEFORE round numbers Exchange Rate Round Number Take-Prof Buy Time Take-Prof Sell Time Exchange Rate QWAFAFEW July 20, 2010: Extreme Returns in FX

  48. Exchange-rate Preferences and Kurtosis • Stop-loss and take-profit orders cluster differently • Take-profit: Cluster BEFORE round numbers • Stop-loss: Cluster AFTER round numbers Exchange Rate Stop-Loss Buy Round Number Time Time Stop-Loss Sell Exchange Rate QWAFAFEW July 20, 2010: Extreme Returns in FX

  49. Exchange-rate Preferences and Kurtosis • Stop-loss and take-profit orders cluster differently • Take-profit: Cluster BEFORE round numbers • Stop-loss: Cluster AFTER round numbers • With different clustering, higher likelihood of order clumps • Lots of take-profits, or lots of stop-losses • With more clumps, less offsetting, more big returns Link Back QWAFAFEW July 20, 2010: Extreme Returns in FX

  50. Existence of 4th Moments? • Not an issue: For us, 4th moment just descriptive device • But DO they exist? Maybe not at shortest horizons • Hill estimates of tail indexes, a; Moment of order q exists if q > a • k is fraction of observations included in Hill estimate Link Back QWAFAFEW July 20, 2010: Extreme Returns in FX

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