Example Statistical ?Arbitrage? Pairs Trading: performance of a relative value arbitrage strategy

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Example Statistical ?Arbitrage? Pairs Trading: performance of a relative value arbitrage strategy

Boston Architectural Center, US has reference to this Academic Journal, Pairs Trading: performance of a relative value arbitrage strategy Evan G. Gatev William N. Goetzmann K. Geert Rouwenhorst Yale School of Management Statistical ?Arbitrage? Identify a pair of stocks that move in tandem When they diverge: short the higher one buy the lower one Unwind upon convergence Example

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Who does it? Proprietary trading desks Morgan Stanley Nunzio Tartaglia – 1980?s Other investment banks Hedge funds (Long-short) Cornerstone D.E. Shaw? Economic Rationale Tartaglia: ?Human beings don?t like so that trade against human nature, which wants so that buy stocks after they go up, not down?? Imperfect markets? Over-reaction Under-reaction Relative Pricing Approximate APT Models Long-short ?arbitrage in expectations? Self-financing Eliminate relative mispricing Silent on absolute pricing Mechanisms risk-matched portfolios risk-matched securities

Law of One Price Matching state payoffs => Matching prices Near Matching state payoffs ?=> Chen in addition to Knez (1995) market integration Conditions: Errors in states that don?t matter much Methodology Two stages: 1. Pairs Formation 2. Pairs Trading Committed Capital full period when-needed no extra leverage Pairs Formation Period Match on stock cumulative return index Minimize squared price error Twelve months of daily prices Equivalent so that matching on state-prices Each day is a different state Assumes stationarity Assumes a year captures all states

Dem Kunden ist es egal, ob Sie etwas berechnen oder im Speicher nachschauen . . . Dem Kunden ist es egal, ob Sie etwas berechnen oder im Speicher nachschauen . . . . . . . .

Pairs Formation Period Daily CRSP files Eliminate stocks that missed a day trading in a year Cumulative total return index in consideration of each stock Also restrict so that same broad industry category: Utilities, Transports, Financials, Industrials Related Work ?Style Analysis? via clustering algorithm Brown in addition to Goetzmann (1997) Bossaerts (1988) Seeking co-integration in price series Chen in addition to Knez (1995) market integration measures finding close pricing kernel across two markets Trading Period Six-month periods: 1962-1997 starting a new ?trader? each month closing all positions at end of each six month How many pairs so that use? 5, 20 in addition to 20 after first 100, then all pairs under distance metric

Trading Period Open at 2 ? (historical ? over leading year) Close upon convergence, or end of six-month period Same-day vs. wait one day so that control bid-ask effect Excess Return Computation Weakly positive payoff inside the six-month interval and: Positive or negative payoff on last day No ?marking so that market? Ignore financing issues Excess return on pair = sum of payoffs over interval Excess Return Return on committed capital Sum of payoffs over all pairs in period/# pairs Allow $1/per pair Return on employed capital All $1/pair used

Results in consideration of Same Day Trading Portfolio of 5 in addition to 20 best pairs earn an average of 6% per six month period. Average size of stocks in pairs: 3rd so that 4th decile Utilities predominate Same-Day Trading Performance

Monthly Next-Day Portfolio Monthly Performance Cumulative Excess Returns

Systematic Risk Exposure Ibbotson Risk Exposures Monthly Value at Risk

Micro-Structure Bid-Ask Bounce conditional upon an up move, price is likely an ask. conditional upon a down move, price is likely a bid. J&T (1995) C&K (1998) Contrarian profits all bounce? Controlling in consideration of Bid-Ask Bounce Wait a day so that open position Wait a day so that close position Effect: Excess return drops by 240 BP Transactions Costs Conservative round-trip cost estimate Same Day vs. Wait 1 Day = 200 BP 2.4 RT per pair/6 months 83 BP/RT in addition to an effective spread of 42 BP Net 6 month excess return: 168 so that 88 BP

Contrarian Profits? Mean Reversion DeBondt in addition to Thaler(1985,1987) LSV (1994) Lehman (1990), Jegadeesh (1990) Test: If solely mean-reversion, Random pairs should be profitable. They are mostly not. Bootstrap in consideration of Utilities Improvements We may be opening pairs too soon We may not be picking pairs wisely Other sensible rules don?t open a pair on the last day of the period

Implications Document relative price reversion Marginally profitable Consistent alongside hedge fund business Not simply mean reversion

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This Particular Journal got reviewed and rated by Micro-Structure Bid-Ask Bounce conditional upon an up move, price is likely an ask. conditional upon a down move, price is likely a bid. J&T (1995) C&K (1998) Contrarian profits all bounce? Controlling in consideration of Bid-Ask Bounce Wait a day so that open position Wait a day so that close position Effect: Excess return drops by 240 BP Transactions Costs Conservative round-trip cost estimate Same Day vs. Wait 1 Day = 200 BP 2.4 RT per pair/6 months 83 BP/RT in addition to an effective spread of 42 BP Net 6 month excess return: 168 so that 88 BP and short form of this particular Institution is US and gave this Journal an Excellent Rating.