Pairs Trading: performance of a relative value arbitrage strategy
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Yale School of Management
Pairs Trading: performance of a relative value arbitrage strategy
Evan G. Gatev William N. GoetzmannK. Geert Rouwenhorst
Yale School of Management
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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
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P(1) - P(2)
On Off
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?
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Economic Rationale
Tartaglia: “Human beings don’t like to trade against
human nature, which wants to buy stocks after they go up, not down…”
Imperfect markets? Over-reaction Under-reaction
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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
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Law of One Price
Matching state payoffs => Matching pricesNear Matching state payoffs ?=>
Chen and Knez (1995) market integrationConditions:
Errors in states that don’t matter much
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Methodology
Two stages: 1. Pairs Formation 2. Pairs Trading
Committed Capital full period when-needed no extra leverage
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Pairs Formation Period
Match on stock cumulative return index Minimize squared price error Twelve months of daily prices
Equivalent to matching on state-prices Each day is a different state Assumes stationarity Assumes a year captures all states
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Pairs Formation Period
Daily CRSP filesEliminate stocks that missed a day trading in
a yearCumulative total return index for each stockAlso restrict to same broad industry
category: Utilities, Transports, Financials, Industrials
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Related Work
“Style Analysis” via clustering algorithm Brown and Goetzmann (1997)
Bossaerts (1988) Seeking co-integration in price series
Chen and Knez (1995) market integration measures finding close pricing kernel across two markets
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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 to use? 5, 20 and 20 after first 100, then all pairs under
distance metric
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Trading Period
Open at 2 (historical over leading year)Close upon convergence, or end of six-
month period Same-day vs. wait one day to control bid-
ask effect
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Excess Return Computation
Weakly positive payoff inside the six-month interval and:
Positive or negative payoff on last day No “marking to market”Ignore financing issuesExcess return on pair = sum of payoffs over
interval
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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
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0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96102108114120
Pair 4, Kennecott and UniroyalStarting Month 19620801
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Results for Same Day Trading
Portfolio of 5 and 20 best pairs earn an average of 6% per six month period.
Average size of stocks in pairs: 3rd to 4th decile
Utilities predominate
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Same-Day Trading Performance
T op 5 T op 2 0 20 - 1 00 A ll
6 -m onth M ean 5 .9 8 % 6 .0 1 % 4 .5 1 % 4 .1 0 %
U tilit ie s 8 1% 8 2% 33 % 9%T ransportation 1 % 1 % 2 % 3%
F in ancia l 4 % 4 % 16 % 12%In dustria l 1 3% 1 3% 48 % 76%
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Monthly Next-Day Portfolio
T op 5 T op 2 0 20 - 1 00 A llM onth ly E xc e ss
R eturn 0 .6 0 % 0 .6 4 % 0 .5 7 % 0 .4 7 %S T D 1 .34% 1 .02% 1 .04 % 0.98%
S ha rpe R a tio 0 .454 0 .636 0 .557 0 .480
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Monthly Performance
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Cumulative Excess Returns
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Systematic Risk Exposure
T o p 5 t o p 2 0 2 0 a 1 0 0 A ll E R PI n t e r c e p t 0 .0 0 5 6 0 .0 0 6 1 0 .0 0 5 6 0 .0 0 4 4 0 .0 0 7 0
U .S . E q u it y P r e m . 0 .0 1 0 2 0.0080 -0.0067 - 0 .0 1 6 7
S m a ll - B ig 0.0404 0.0511 0 .0 4 6 5 0 .0 6 8 8 0 .2 1 1 7
H ig h B /M - L o wB /M
0 .0 7 9 1 0 .0 2 1 0 0 .0 1 8 0 0 .0 6 8 9 - 0 5 8 4 7
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Ibbotson Risk Exposures
T o p 5 t o p 2 0 2 0 a 1 0 0 A ll E R PI n t e r c e p t 0 .0 0 5 9 0 .0 0 6 4 0 .0 0 5 7 0 .0 0 4 7 0 .0 0 3 5
U .S . E q u it y P r e m . - .0 2 9 6 -.0259 -0.0206 - 0 .0 4 0 8
S m a ll S t o c k P r e m . 0.0477 0.0494 0 .0 3 4 9 0 .0 4 9 6 0 .1 7 7 1
B o n d D e f a u lt P r e m . 0 .1 2 8 8 0 .1 2 6 6 0 .1 3 4 4 0 .1 6 8 0 0 .7 1 0 3
B o n d H o r iz o n r e m . 0 .0 8 1 5 0 .0 7 4 3 0 .0 4 4 0 0 .0 4 2 9 0 .6 8 0 5
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Monthly Value at Risk
Top 5 T op 2 0 N e xt 20 A ll1 % -0 .0227 -0 .0151 -0 .0198 -0 .01335 % -0 .0121 -0 .0059 -0 .0092 -0 .0066
1 0% -0 .0078 -0 .0034 -0 .0063 -0 .00431 5% -0 .0049 -0 .0015 -0 .0040 -0 .00332 0% -0 .0031 -0 .0004 -0 .0022 -0 .0021
P r re t.< 0 28 .70% 2 2.10% 2 5.60% 32 .30 %M in . -0 .1020 -0 .0618 -0 .0340 -0 .0238
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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?
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Controlling for Bid-Ask Bounce
Wait a day to open position Wait a day to close positionEffect:
Excess return drops by 240 BP
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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 and an effective spread of 42 BP
Net 6 month excess return: 168 to 88 BP
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Contrarian Profits?
Mean Reversion DeBondt and Thaler(1985,1987) LSV (1994) Lehman (1990), Jegadeesh (1990)
Test: If solely mean-reversion, Random pairs should be profitable. They are mostly not.
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Bootstrap for Utilities
P ortfo lio top 5 top 1 0 top 20 A llM ean E xc e ss R e tu rn 0 .0504 0 .0489 0 .0518 0 .0478
N W S ta nda rd E rro r 0 .0047 0 .0041 0 .0038 0 .0031t-statist ic 10 .70 1 1 .93 1 3 .70 1 5 .43
B oo tstrapped d ist r ibu tion o f rando m p a irs
m e a n 0 .0009 0 .0011 0 .0014 standa rd d e viation 0 .0071 0 .0051 0 .0035
p -va lue a c tua lp ro fit s
0 .0000 0 .0000 0 .0000
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Improvements
We may be opening pairs too soonWe may not be picking pairs wiselyOther sensible rules
don’t open a pair on the last day of the period
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Implications
Document relative price reversionMarginally profitable
Consistent with hedge fund businessNot simply mean reversion