Statistical arbitrage and pairs trading
Nikos S. Thomaidis, PhD1
Dept. of Financial Engineering & ManagementUniversity of the Aegean, GREECE
email: [email protected] URL: http://labs.fme.aegean.gr/decision/Personal web site: http://users.otenet.gr/~ntho18
1in collaboration with Nicholas Kondakis, Kepler Asset Management LLC and
NGSQ International Ltd, NY.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
What is pairs trading?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
What is pairs trading?
Developing a pairs trading system from scratch
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
What is pairs trading?
Developing a pairs trading system from scratch
Empirical study: statistical arbitrage betweenDow Jones Industrial Average (DJIA) stocks
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
What is pairs trading?
Developing a pairs trading system from scratch
Empirical study: statistical arbitrage betweenDow Jones Industrial Average (DJIA) stocks
Conclusions
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
What is pairs trading?
Developing a pairs trading system from scratch
Empirical study: statistical arbitrage betweenDow Jones Industrial Average (DJIA) stocks
Conclusions
Trading risks
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
What is pairs trading?
Developing a pairs trading system from scratch
Empirical study: statistical arbitrage betweenDow Jones Industrial Average (DJIA) stocks
Conclusions
Trading risksOpportunities
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Outline
What is pairs trading?
Developing a pairs trading system from scratch
Empirical study: statistical arbitrage betweenDow Jones Industrial Average (DJIA) stocks
Conclusions
Trading risksOpportunities
Future challenges
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: the history
2See [Pole, 2007, Vidyamurthy, 2004] andhttp://www.pairtradefinder.com/pairTrading.pdf for interesting factsand information on the history of the topic.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: the history
Pairs trading is one of the most popular investmentstrategies.
2See [Pole, 2007, Vidyamurthy, 2004] andhttp://www.pairtradefinder.com/pairTrading.pdf for interesting factsand information on the history of the topic.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: the history
Pairs trading is one of the most popular investmentstrategies.Already in the mid 80’s, Morgan Stanley - and perhapsother investment companies - have started developingcomputer programs indicating long and short tradingpositions in the market2.
2See [Pole, 2007, Vidyamurthy, 2004] andhttp://www.pairtradefinder.com/pairTrading.pdf for interesting factsand information on the history of the topic.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: the history
Pairs trading is one of the most popular investmentstrategies.Already in the mid 80’s, Morgan Stanley - and perhapsother investment companies - have started developingcomputer programs indicating long and short tradingpositions in the market2.These strategies have been stronglyquantitative/mechanical in nature (trading signals aregenerated using statistical/mathematical techniques,trades are executed by computer programmes).
2See [Pole, 2007, Vidyamurthy, 2004] andhttp://www.pairtradefinder.com/pairTrading.pdf for interesting factsand information on the history of the topic.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: the history
Pairs trading is one of the most popular investmentstrategies.Already in the mid 80’s, Morgan Stanley - and perhapsother investment companies - have started developingcomputer programs indicating long and short tradingpositions in the market2.These strategies have been stronglyquantitative/mechanical in nature (trading signals aregenerated using statistical/mathematical techniques,trades are executed by computer programmes).The development of a pairs trading system typicallyinvolves the cooperation of experts with diversebackground (mathematicians, statisticians, computerscientists and finance experts).
2See [Pole, 2007, Vidyamurthy, 2004] andhttp://www.pairtradefinder.com/pairTrading.pdf for interesting factsand information on the history of the topic.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: main ideaa
aSee e.g. [Gatev et al., 2006].
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: main ideaa
aSee e.g. [Gatev et al., 2006].
Identify two securities with similar historical pricetrajectories.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: main ideaa
aSee e.g. [Gatev et al., 2006].
Identify two securities with similar historical pricetrajectories.
If at some point in time the relative price distance(spread) exceeds a threshold, simultaneously long theundervalued security and short the overvalued one.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Pairs trading: main ideaa
aSee e.g. [Gatev et al., 2006].
Identify two securities with similar historical pricetrajectories.
If at some point in time the relative price distance(spread) exceeds a threshold, simultaneously long theundervalued security and short the overvalued one.
This joint bet will generate profit if the spread closesagain in the near future.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
a market-neutral trading strategy: its returns are uncorrelatedwith market movements.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
a market-neutral trading strategy: its returns are uncorrelatedwith market movements.
a statistical arbitrage trading strategy: profits from temporalmispricings of an asset relative to its fundamental value.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
a market-neutral trading strategy: its returns are uncorrelatedwith market movements.
a statistical arbitrage trading strategy: profits from temporalmispricings of an asset relative to its fundamental value.
a long/short strategy: reduces exposure to systematic shocksby simultaneously going long and short in fundamentallyrelated securities.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
a market-neutral trading strategy: its returns are uncorrelatedwith market movements.
a statistical arbitrage trading strategy: profits from temporalmispricings of an asset relative to its fundamental value.
a long/short strategy: reduces exposure to systematic shocksby simultaneously going long and short in fundamentallyrelated securities.
relative-value trading,
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
a market-neutral trading strategy: its returns are uncorrelatedwith market movements.
a statistical arbitrage trading strategy: profits from temporalmispricings of an asset relative to its fundamental value.
a long/short strategy: reduces exposure to systematic shocksby simultaneously going long and short in fundamentallyrelated securities.
relative-value trading, convergence trading,
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
a market-neutral trading strategy: its returns are uncorrelatedwith market movements.
a statistical arbitrage trading strategy: profits from temporalmispricings of an asset relative to its fundamental value.
a long/short strategy: reduces exposure to systematic shocksby simultaneously going long and short in fundamentallyrelated securities.
relative-value trading, convergence trading, and so on...
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
So what is pairs trading?
a market-neutral trading strategy: its returns are uncorrelatedwith market movements.
a statistical arbitrage trading strategy: profits from temporalmispricings of an asset relative to its fundamental value.
a long/short strategy: reduces exposure to systematic shocksby simultaneously going long and short in fundamentallyrelated securities.
relative-value trading, convergence trading, and so on...
Pairs trading → group trading.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Why pairs work: the drunk and his dog
A metaphor adapted from [Murray, 1994] to the context of pairstrading.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Why pairs work: the drunk and his dog
A metaphor adapted from [Murray, 1994] to the context of pairstrading.
A drunk customer sets out from the pub (“Gin Palace”) andstarts wandering in the streets (random walk, unit-root,integrated stochastic process).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Why pairs work: the drunk and his dog
A metaphor adapted from [Murray, 1994] to the context of pairstrading.
A drunk customer sets out from the pub (“Gin Palace”) andstarts wandering in the streets (random walk, unit-root,integrated stochastic process).
The accompanying dog always keeps track of the drunk’sposition.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Why pairs work: the drunk and his dog
A metaphor adapted from [Murray, 1994] to the context of pairstrading.
A drunk customer sets out from the pub (“Gin Palace”) andstarts wandering in the streets (random walk, unit-root,integrated stochastic process).
The accompanying dog always keeps track of the drunk’sposition.
Whenever the drunk moves away, the dog will speed up toclose the gap.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Why pairs work: the drunk and his dog
A metaphor adapted from [Murray, 1994] to the context of pairstrading.
A drunk customer sets out from the pub (“Gin Palace”) andstarts wandering in the streets (random walk, unit-root,integrated stochastic process).
The accompanying dog always keeps track of the drunk’sposition.
Whenever the drunk moves away, the dog will speed up toclose the gap.
Whenever the drunk approaches too close, the dog will tendto widen the in-between distance.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The drunk and his dog: the story continues
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The drunk and his dog: the story continues
Rory and Gary, two regular customers, look outside the pub’swindow and bet on the drunk’s and the dog’ s position.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The drunk and his dog: the story continues
Rory and Gary, two regular customers, look outside the pub’swindow and bet on the drunk’s and the dog’ s position.
They observe the drunk and the dog individually but theircourse looks no different than a random walk (growingvariance in location, lack of predictability).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The drunk and his dog: the story continues
Rory and Gary, two regular customers, look outside the pub’swindow and bet on the drunk’s and the dog’ s position.
They observe the drunk and the dog individually but theircourse looks no different than a random walk (growingvariance in location, lack of predictability).
Suddenly, Gary throws the idea: “Well, it’s all a matter offinding the drunk, the dog should be around”.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The drunk and his dog: the story continues
Rory and Gary, two regular customers, look outside the pub’swindow and bet on the drunk’s and the dog’ s position.
They observe the drunk and the dog individually but theircourse looks no different than a random walk (growingvariance in location, lack of predictability).
Suddenly, Gary throws the idea: “Well, it’s all a matter offinding the drunk, the dog should be around”.
He is right because no matter how far apart the two fellowsmay currently be, their courses will soon converge(co-integration).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The drunk and his dog: the story continues
Rory and Gary, two regular customers, look outside the pub’swindow and bet on the drunk’s and the dog’ s position.
They observe the drunk and the dog individually but theircourse looks no different than a random walk (growingvariance in location, lack of predictability).
Suddenly, Gary throws the idea: “Well, it’s all a matter offinding the drunk, the dog should be around”.
He is right because no matter how far apart the two fellowsmay currently be, their courses will soon converge(co-integration).
Rory and Gary eventually agree to play the following game:
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The drunk and his dog: the story continues
Rory and Gary, two regular customers, look outside the pub’swindow and bet on the drunk’s and the dog’ s position.
They observe the drunk and the dog individually but theircourse looks no different than a random walk (growingvariance in location, lack of predictability).
Suddenly, Gary throws the idea: “Well, it’s all a matter offinding the drunk, the dog should be around”.
He is right because no matter how far apart the two fellowsmay currently be, their courses will soon converge(co-integration).
Rory and Gary eventually agree to play the following game:
“Why not betting on their relative distance rather than theirabsolute positions?”
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
An actual traded pair
Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
GTHPQ
Figure 1 : Normalised price paths of Goodyear (GT) and HewlettPackard (HPQ).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Why pairs trading is successful?
A behavioural-finance explanation3:
Investors quickly incorporate new information in securityprices through their market positions.
As a consequence, stock price movements reflect all publiclyavailable information (future earnings prospects, corporatenews, political events)(market efficiency).
Fundamentally-related securities respond similarly to incomingnews.
Overreaction and herding behaviour of uninformed and“noisy” investors often drives prices apart.
But, any deviation is temporary.
In the long run, rational traders will likely correct mispricingsand close the “gaps”.
3See literature on “limits to arbitrage”.Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Basic steps in developing a pairs trading systema
aSee also [Gatev et al., 2006].
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Basic steps in developing a pairs trading systema
aSee also [Gatev et al., 2006].
Group formation
Pick fundamentally-related stocks and detect stable relativeprice relationships (synthetic assets).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Basic steps in developing a pairs trading systema
aSee also [Gatev et al., 2006].
Group formation
Pick fundamentally-related stocks and detect stable relativeprice relationships (synthetic assets).
Group trading
Determine the direction of the synthetic (divergence,re-convergence).Market timing: when to open and close a trade on thesynthetic.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Basic steps in developing a pairs trading systema
aSee also [Gatev et al., 2006].
Group formation
Pick fundamentally-related stocks and detect stable relativeprice relationships (synthetic assets).
Group trading
Determine the direction of the synthetic (divergence,re-convergence).Market timing: when to open and close a trade on thesynthetic.
Risk management
Minimise divergence risk (i.e. the risk that the gap betweenstocks further widens).Fine-tune parameters with respect to a trading performancecriterion (maximise expected return, maximise a reward-riskratio, etc).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Group formation strategy
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Maximum price correlation (MPC) criterion
1 Choose a charting time-frame.
2 Compute the correlation of historical price series, e.g.
Correlation coefficient
Pair 1 Stock 1 Stock 3 0.91Pair 2 Stock 1 Stock 5 0.87Pair 3 Stock 2 Stock 4 0.81Pair 4 Stock 8 Stock 10 0.76... ... ...Pair 19 Stock 13 Stock 26 0.26Pair 20 Stock 26 Stock 27 0.17
3 Pick the top 20% of pairs (i.e 4 pairs) with the highesthistorical correlation.
4 Formed groups: {1, 3, 5}, {2, 4}, {8, 10}.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Minimum normalised price distance (MNPD) criterion
Quite popular in the literature[Gatev et al., 2006, Andrade et al., 2005].
For each stock i = 1, 2, ...,N, compute the cumulative return
over the estimation sample period
crt,i ≡
t∏
τ=1
(1 + rτ,i), t = 1, 2, ...,T
where cr0,i = 1 and rt,i is the t-period’s return on stock i .
Introduce a “distance” measure:e.g. Euclidean distance
d(i , j) ≡ |cr⋆,i − cr⋆,j | ≡T∑
t=1
(crt,i − crt,j)2
Rank stock pairs based on increasing values of d - pick thetop a% of the list for group formation.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Identify stationary relationships (1/5)
Applying techniques from co-integration analysis
[Engle and Granger, 1987, Burgess, 2000, Vidyamurthy, 2004].
Assume that a group of stocks with price vectorPt = (Pt1, Pt2, . . . ,PtN )
′ satisfy the relationship:
Pt1 = c + β2Pt2 + · · · + βnPtN + Zt
where Zt is the mispricing index (captures temporal deviationsfrom equilibrium).
The coefficients of the relationship can be estimated usingOrdinary Least Squares (OLS).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Identify stationary relationships (2/5)
Construct a portfolio (synthetic asset) as follows:
Stocks 1 2 3 · · · N
Positions +1 -β2 - β3 · · · - βN
where βi is the OLS estimate of βi , computed over theformation period, and “+” (“-”) indicates a long (short)position.
The portfolio value Zt ≡ β′
· Pt , where
β ≡ (1, −β2, −β3, . . . , −βN)′
is by construction mean-reverting (fluctuates around c,the OLS estimate of c).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Identify relationships with OLS (3/5)
0 50 100 150 200 2505
10
15
Group formation sample
Pric
es
Stock 1Stock 2
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Identify relationships with OLS (4/5)
5.5 6 6.5 7 7.5 8 8.511
11.5
12
12.5
13
13.5
14
14.5
Stock 1
Sto
ck 2
actual price pairsequilibrium relationship
negativemispricing
positivemispricing
Equilibrium relationship: −−−−−−−−−−−−−−−−−− P
2 = 14.843 − 0.257 P
1
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Identify relationships with OLS (5/5)
0 50 100 150 200 25013
13.5
14
14.5
15
15.5
16
16.5
Rel
ativ
e m
ispr
icin
g
Group formation sample
Zt=P
2 + 0.257 P
1
Stock 2 overpriced relative to Stock 1
Stock 2 underpriced relative to Stock 1
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Conditions for meaningful capital allocations
The money invested on each stock (average
price × number of shares) must be on averagebelow 80% and above 5% of the available
capital.
The ratio between the maximum and the
minimum number of shares held from each assetshould not exceed 10.
and so on...
These place restrictions on the beta coefficients(stock holdings) → restricted OLS estimation
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Group trading
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (1/2)
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (1/2)
Open a position in a group whenever the mispricing indexexceeds a certain threshold:
Buy the portfolio, if Zt < ZL,αt
Sell the portfolio, if Zt > ZH,α
t
where(
ZL,αt , Z
H,α
t
)
is a 100 × (1− 2α)% confidence
“envelope” on the value of the mispricing.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (1/2)
Open a position in a group whenever the mispricing indexexceeds a certain threshold:
Buy the portfolio, if Zt < ZL,αt
Sell the portfolio, if Zt > ZH,α
t
where(
ZL,αt , Z
H,α
t
)
is a 100 × (1− 2α)% confidence
“envelope” on the value of the mispricing.
Unwind the position after h periods of time
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (1/2)
Open a position in a group whenever the mispricing indexexceeds a certain threshold:
Buy the portfolio, if Zt < ZL,αt
Sell the portfolio, if Zt > ZH,α
t
where(
ZL,αt , Z
H,α
t
)
is a 100 × (1− 2α)% confidence
“envelope” on the value of the mispricing.
Unwind the position after h periods of time unless
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (1/2)
Open a position in a group whenever the mispricing indexexceeds a certain threshold:
Buy the portfolio, if Zt < ZL,αt
Sell the portfolio, if Zt > ZH,α
t
where(
ZL,αt , Z
H,α
t
)
is a 100 × (1− 2α)% confidence
“envelope” on the value of the mispricing.
Unwind the position after h periods of time unless themispricing index continues to diverge (does not cross up thelower bound or cross down the upper bound).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (1/2)
Open a position in a group whenever the mispricing indexexceeds a certain threshold:
Buy the portfolio, if Zt < ZL,αt
Sell the portfolio, if Zt > ZH,α
t
where(
ZL,αt , Z
H,α
t
)
is a 100 × (1− 2α)% confidence
“envelope” on the value of the mispricing.
Unwind the position after h periods of time unless themispricing index continues to diverge (does not cross up thelower bound or cross down the upper bound).
Close the position earlier and open a new position if thesynthetic re-converges and crosses the opposite bound.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (2/2)
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (2/2)
The two bounds(
ZL,αt , Z
H,α
t
)
could be of the form c ± zασZ .
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (2/2)
The two bounds(
ZL,αt , Z
H,α
t
)
could be of the form c ± zασZ .
c , σZ are the sample mean and standard deviation of thesynthetic value over the formation period and zα is a criticalvalue from a N(0, 1) distribution.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (2/2)
The two bounds(
ZL,αt , Z
H,α
t
)
could be of the form c ± zασZ .
c , σZ are the sample mean and standard deviation of thesynthetic value over the formation period and zα is a criticalvalue from a N(0, 1) distribution.
This is the standard trade-triggering criterion adopted by moststudies dealing with pairs trading (see e.g.[Andrade et al., 2005, Gatev et al., 2006]).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading strategy (2/2)
The two bounds(
ZL,αt , Z
H,α
t
)
could be of the form c ± zασZ .
c , σZ are the sample mean and standard deviation of thesynthetic value over the formation period and zα is a criticalvalue from a N(0, 1) distribution.
This is the standard trade-triggering criterion adopted by moststudies dealing with pairs trading (see e.g.[Andrade et al., 2005, Gatev et al., 2006]).
Still, one could employ a more flexible criterion bydynamically-adjusting confidence bounds (see e.g.[Thomaidis et al., 2006, Thomaidis and Kondakis, 2012]).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Example: trading a group of 2 stocks (1/2)
0 20 40 60 80 100 12034
36
38
40
42
Trading period
Pric
e ($
)
GOODYEAR (GT) vs HEWLETT PACKARD (HPQ)
0 20 40 60 80 100 12018
19
20
21
22
23
24
Trading period
Mis
pric
ing
Mispricing index Confidence bounds Long positions Short positions
12
14
16
18
20
Pric
e ($
)
GTHPQ
Zt=P
GT −1.06 P
HPQ
Figure 3 : Mispricing index: Zt = PGT − 1.06PHPQ , Trading parameters: Hold-out
period (HOP) = 1day , αL = 10%, αH = 5% .
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Example: trading a group of 2 stocks (2/2)
0 20 40 60 80 100 12018
19
20
21
22
23
24
Trading period
Mis
pric
ing
Mispricing index Confidence bounds Long positions Short positions
0 20 40 60 80 100 120−2
0
2
4
6
8
Trading period
Cum
ulat
ive
retu
rn (
%)
Figure 4 : HOP=1 day, αL = 10%, αH = 5% .
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Example: trading a group of 4 stocks (1/2)
0 50 100 150 200 2500.8
1
1.2
1.4
1.6
Trading period
Nor
mal
ised
pric
es
0 50 100 150 200 250−4
−3
−2
−1
0
Trading period
Mis
pric
ing
AA AXP CAT IBM Long positions Short positions
Mispricing index Confidence bounds Long positions Short positions
Figure 5 : HOP=1 day, αL = 20%, αH = 20% .
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Example: trading a group of 4 stocks(2/2)
0 50 100 150 200 250−4
−3
−2
−1
0
Trading period
Mis
pric
ing
0 50 100 150 200 250−10
0
10
20
30
Trading period
Cum
ulat
ive
retu
rn (
%)
Mispricing index Confidence bounds Long positions Short positions
Figure 6 : HOP=1 day, αL = 20%, αH = 20% .
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
System performance measurementa
aSee also [Gatev et al., 2006].
⋆ Are there parametrisations of the StatArb system that deliver consistentlypositive return?
⋆ Performance indicators (mean, std, downside std, information ratio (IR),downside IR).
⋆ How does the performance vary with market conditions,business/economic cycles?
⋆ Can superior returns be explained by exposure to systematic risks(market, industries, size factor, value factor, etc.)?
⋆ Are we capturing other patterns of stock movements (price reversals)?
⋆ How skillful is our system in terms of picking the right pairs/finding priceequilibriums?
⋆ How able is our system to “sense” price deviations and predict the pointof re-convergence?
⋆ Do our strategies involve too intense trading?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Experimental setting
Daily prices of 30 stock members of Dow Jones IndustrialAverage (DJIA) index (with dividends reinvested)4.
Sample period: 3 Jan 1994 to 24 Feb 2010.Group formation:
Window length (WL) {125, 250} days.Thin-trading criterion: disregard DJIA stocks that do not tradeon a regular daily basis.Choose matching stocks based on MNPD and MPC criteria(form groups from the 5%, 20% or 50% highest-ranking pairsof the list).
Trading strategyTrading period: subsequent {50, 125, 150} daysHold-out period (HOP): {1, 5, 10, 25} daysαL, αH ∈ {1, 5, 10, 20, 40}%
A total of 3, 600 parametrisations.4Data downloaded from Yahoo!Finance as of 24 Feb 2010. See
[Gatev et al., 2006, Andrade et al., 2005] for other examples of applicationdesigns.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Best trading strategies
Design parameters5 Best strategy (Mean return) Best strategy (IR)
Sample: 1994-2010
WL 125 125TP 150 150GFC MPC - 5% MPC - 20%HOP 25 25αL (%) 40 10αH (%) 1 1
5WL: Length of moving window, TP: Trading period, GFC: Group formation criterion, HOP: Position hold-out
period.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Performance of best trading strategies
Trading measures Best strategy(Mean return)
Best strategy (IR) Buy & hold portfolio
Sample: 1994-2010 (784 observations)
Mean(%) 11.65 7.78 5.92Stdev(%) 26.44 9.94 22.00DStdev(%) 23.75 6.48 16.54
IR 0.44 0.78 0.27DIR 0.49 1.20 0.36
Table 1 : Average weekly performance (annualised measures).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Portfolios of good strategies
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Portfolios of good strategies
No portfolio manager would count on a single trading strategyfor making money
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Portfolios of good strategies
No portfolio manager would count on a single trading strategyfor making money
Mixing-up different parameter combinations
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Portfolios of good strategies
No portfolio manager would count on a single trading strategyfor making money
Mixing-up different parameter combinations
“Bundles” of trading strategies
“Distribute your capital evenly between the top-a % of theparameterisations”
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Performance of mixtures - Mean return
StrategiesPercentage of trading strategies Best
strategyBuy &hold100 90 65 35 10
Mean(%) 1.98 2.46 3.42 4.64 6.48 11.65 5.92Stdev(%) 3.65 3.63 3.69 4.00 6.19 26.44 22.00DStdev(%) 2.26 2.19 2.10 2.16 2.71 23.75 16.54
IR 0.54 0.68 0.93 1.16 1.05 0.44 0.27DIR 0.88 1.12 1.63 2.15 2.39 0.49 0.36
Table 2 : Average weekly performance on the full sample period(annualised measures).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Performance of mixtures - Information ratio (1/2)
StrategiesPercentage of trading strategies Best
strategyBuy &hold100 90 65 35 10
Mean(%) 1.98 2.46 3.42 4.43 5.93 7.78 5.92Stdev(%) 3.65 3.63 3.66 3.65 4.31 9.94 22.00DStdev(%) 2.26 2.19 2.09 2.18 2.55 6.48 16.54
IR 0.54 0.68 0.93 1.22 1.37 0.78 0.27DIR 0.88 1.12 1.64 2.03 2.32 1.20 0.36
Table 3 : Average weekly performance on the full sample period(annualised measures).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Performance of mixtures - Information ratio (2/2)
Dec95 Sep98 May01 Feb04 Nov06 Aug09−50
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IR−maximising strategies
top−100top−90top−65top−35top−10best strategybuy & hold
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Systematic risk exposure
Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12−50
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MarketSMBHMLTop−10%(IR)
Figure 7 : Historical performance of the top-10% portfolio (IR) and systematic factors of risk. SMB andHML are the Fama-French size and value factors (available fromhttp://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html ).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Systematic risk exposure
StrategiesPercentage of trading strategies
Best strategy100 90 65 35 10
Alpha 0.00 0.00 0.00 0.00 0.00 0.00(0.12) (0.04) (0.00) (0.00) (0.00) (0.00)
MKT -0.15 -0.15 -0.13 -0.11 -0.15 -0.46(0.01) (0.01) (0.01) (0.04) (0.03) (0.00)
SMB 0.00 -0.00 -0.01 -0.00 0.00 0.02(0.83) (0.89) (0.53) (0.82) (0.89) (0.40)
HML -0.00 -0.00 -0.01 -0.01 -0.03 -0.11(0.98) (0.82) (0.50) (0.49) (0.10) (0.01)
MOM -0.04 -0.04 -0.03 -0.03 -0.03 -0.04(0.00) (0.00) (0.00) (0.00) (0.00) (0.09)
LTR -0.02 -0.01 -0.00 0.00 -0.00 -0.07(0.36) (0.52) (0.87) (0.81) (0.89) (0.06)
STR 0.04 0.03 0.03 0.03 0.01 -0.02(0.00) (0.00) (0.00) (0.00) (0.09) (0.30)
Consumer Durables 0.04 0.04 0.04 0.03 0.04 0.15(0.00) (0.00) (0.00) (0.01) (0.00) (0.00)
Manufacturing 0.00 0.00 0.00 -0.01 -0.01 0.03(0.95) (0.96) (0.88) (0.69) (0.61) (0.56)
HiTec 0.03 0.03 0.03 0.03 0.03 0.09(0.03) (0.03) (0.05) (0.08) (0.14) (0.04)
Health 0.02 0.02 0.02 0.02 0.02 0.03(0.04) (0.04) (0.06) (0.10) (0.14) (0.20)
Other 0.01 0.01 0.01 0.01 0.04 0.14(0.39) (0.36) (0.44) (0.55) (0.10) (0.00)
Table 4 : OLS estimates of the regression equation (t-statistics inparentheses).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
It involves
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
It involves
Frequent rebalancing of trading positions
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
It involves
Frequent rebalancing of trading positionsMultiple openings and closings of trades
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
It involves
Frequent rebalancing of trading positionsMultiple openings and closings of tradesShort-selling
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
It involves
Frequent rebalancing of trading positionsMultiple openings and closings of tradesShort-selling
Transaction costs, margin requirements, etc
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
It involves
Frequent rebalancing of trading positionsMultiple openings and closings of tradesShort-selling
Transaction costs, margin requirements, etc
How are the strategies expected to perform in a more realisticmarket environment?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading costs
Pairs trading is a cost-sensitive investment strategy
It involves
Frequent rebalancing of trading positionsMultiple openings and closings of tradesShort-selling
Transaction costs, margin requirements, etc
How are the strategies expected to perform in a more realisticmarket environment?
Can generated profits offset trading costs?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Descriptive statistics (1/2)
Top-10% (IR) portfolio of strategiesSample period
Total days in sample: 4065Total trading days in sample: 3865.7Total number of traded stocks: 35
Group formationTotal number of formed groups: 71.43Average size of groups: 4.51
(1.59)Group trading
Total number of group openings during study: 195.76Number of groups that never open: 4.19Average number of active groups per trading day: 1.17
(0.45)Fraction of trading time groups are open: 0.88Average number of times a group is opened over the trading period: 3.32
(2.24)Average duration of positions (days): 27.59
(28.94)Average duration of long positions (days): 24.50
(30.66)Average duration of short positions (days): 30.15
(27.05)
Notes: (1) Averages over all parametrisations, (2) Standard deviation in parentheses.
See also [Sullivan et al., 1999, Andrade et al., 2005, Gatev et al., 2006] for descriptive
measures of trading performance.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Descriptive statistics (2/2)
Top-10% (IR) portfolio of strategiesDivergence risk
Percentage of groups that are inac-tive (never open): 3.21Percentage of active groups with asingle divergent trade: 26.31Percentage of active groups thatare opened and closed many time,though the final trade is divergent: 57.13Percentage of active groups with nofinal divergent trade: 13.34
Note: Averages over all 360 parametrisations (see also
[Andrade et al., 2005, Do and Faff, 2010]).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The impact of transaction costs (1/2)
Transaction cost6 0 bps 10 bps
Strategies Best at Zero Cost Best Best at Zero Cost Best
Mean(%) 5.93 5.93 5.38 5.78Stdev(%) 4.31 4.31 4.34 4.30DStdev(%) 2.55 2.55 2.54 2.54
IR 1.37 1.37 1.24 1.35DIR 2.32 2.32 2.12 2.27
Transaction cost 50 bps Buy & hold
Strategies Best at Zero Cost Best
Mean(%) 4.93 5.34 5.92Stdev(%) 4.33 4.28 22.00DStdev(%) 2.55 2.55 16.54
IR 1.14 1.25 0.27DIR 1.93 2.10 0.36
Table 5 : Top-10% (IR) portfolio.
6Fixed cost per unit of trading volume.Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
The impact of transaction costs (2/2)
Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12−20
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0 bps10 bps50 bps
Figure 8 : Historical performance of the top-10% (IR) portfolioassuming different levels of transaction costs.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (1/2)
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (1/2)
Statistical arbitrage strategies are highly parametrised.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (1/2)
Statistical arbitrage strategies are highly parametrised.
Given a particular sample period and suppose we have enoughtime to experiment with alternative parametrisations of thesystem.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (1/2)
Statistical arbitrage strategies are highly parametrised.
Given a particular sample period and suppose we have enoughtime to experiment with alternative parametrisations of thesystem.
We will most likely be able to detect a strategy that beats themarket, no matter what the performance measure is.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (1/2)
Statistical arbitrage strategies are highly parametrised.
Given a particular sample period and suppose we have enoughtime to experiment with alternative parametrisations of thesystem.
We will most likely be able to detect a strategy that beats themarket, no matter what the performance measure is.
But, what can we say about the trading performance on awider dataset?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (1/2)
Statistical arbitrage strategies are highly parametrised.
Given a particular sample period and suppose we have enoughtime to experiment with alternative parametrisations of thesystem.
We will most likely be able to detect a strategy that beats themarket, no matter what the performance measure is.
But, what can we say about the trading performance on awider dataset?
Data snooping(“dredging” or “fishing”):
The practice of overfitting a trading strategy to a particular sampleperiod [Sullivan et al., 1998, Sullivan et al., 1999, White, 2000].
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (2/2)
Is the observed good performance of a StatArbsystem
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (2/2)
Is the observed good performance of a StatArbsystem
→ due to genuine superiority?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (2/2)
Is the observed good performance of a StatArbsystem
→ due to genuine superiority?or...
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping (2/2)
Is the observed good performance of a StatArbsystem
→ due to genuine superiority?or...
→ due to a few lucky trades?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Data snooping quotations
“Given enough computer time, we are sure that we can find a mechanical
trading rule which ‘works’ on a table of random numbers, provided of
course that we are allowed to test the rule on the same table of numbers
which we used to discover the rule.”[Jensen and Bennington, 1970].
“Even when no exploitable [trading] model exists, looking long enough
and hard enough at a given set of data will often reveal one or more
[trading strategies] that look good, but are in fact useless.”[White, 2000].
“If you have 20,000 traders in the market, sure enough you’ll have
someone who’s been up every day for the past few years and will show
you a beautiful P&L. If you put enough monkeys on typewriters, one of
the monkeys will write the Iliad in ancient Greek. But would you bet any
money that he’s going to write the Odyssey next?” [Taleb, 1997]7.
7Random Walk: Taleb on Mistakes that Market Traders can make,
http://equity.blogspot.com/2008/11/taleb-on-mistakes-that-market-traders.html
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to eliminate data snooping biases?
8See also [Lai and Xing, 2008], ch.11, for a discussion.Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to eliminate data snooping biases?
Using an estimation and validation (test) data set8
Helps measuring model performance beyond known dataSensitive with respect to the particular choice of sampleperiods (training and testing)Sensitive to market conditions
8See also [Lai and Xing, 2008], ch.11, for a discussion.Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to eliminate data snooping biases?
Using an estimation and validation (test) data set8
Helps measuring model performance beyond known dataSensitive with respect to the particular choice of sampleperiods (training and testing)Sensitive to market conditions
Using multiple estimation/validation periods
Performance assessments are more fairProblems arise if these periods are consecutiveThe choice of periods can introduce further bias
8See also [Lai and Xing, 2008], ch.11, for a discussion.Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to eliminate data snooping biases?
Using an estimation and validation (test) data set8
Helps measuring model performance beyond known dataSensitive with respect to the particular choice of sampleperiods (training and testing)Sensitive to market conditions
Using multiple estimation/validation periods
Performance assessments are more fairProblems arise if these periods are consecutiveThe choice of periods can introduce further bias
Statistical techniques
Little sensitivity to market conditionsHelps exploring new market scenarios (beyond those present inthe dataset)
8See also [Lai and Xing, 2008], ch.11, for a discussion.Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How would you choose your sample periods?
Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12−50
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19941995
1996
1997
1998
1999
20002001
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20052006
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2008
2009
2010
Buy & hold strategy
Cum
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rn (
%)
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading performance comparisons (1/2)
Splitting the data set into estimation and validation periods
Sample 1 Sample 2 Sample 3 Sample 4
Estimationperiod
1994- 96 1997-99 2000-02 2003-06
Validation pe-riod
1997- 99 2000-02 2003-05 2006-10
Number ofobservations(validationset)
756 days 756 days 756 days 1041 days
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Trading performance comparisons (2/2)
Jun96 Jan97 Jul97 Feb98 Sep98 Mar99 Oct99 Apr00
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0
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100
150
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Top−10% (IR)Buy & holdIR=0.27
IR=1.28
Oct99 Apr00 Nov00 May01 Dec01 Jul02 Jan03−5
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Validation set 2
−30
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IR=−0.17
IR=1.21
Jul02 Jan03 Aug03 Feb04 Sep04 Mar05 Oct05 May06−5
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Validation set 3
−50
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Top−10% (IR)Buy & hold
IR=0.05
IR=0.52
Oct05 May06 Nov06 Jun07 Dec07 Jul08 Jan09 Aug09 Mar10−10
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%)
Validation set 4
−100
−50
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Top−10% (IR)Buy & hold
IR= −0.55
IR= 0.78
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Statistical techniques
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Statistical techniques
Random portfolios [Burns, 2006, Gatev et al., 2006]How skillful is our strategy in terms of picking the right stocks
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Statistical techniques
Random portfolios [Burns, 2006, Gatev et al., 2006]How skillful is our strategy in terms of picking the right stocksat the right combination?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Statistical techniques
Random portfolios [Burns, 2006, Gatev et al., 2006]How skillful is our strategy in terms of picking the right stocksat the right combination?
“Monkey” trading [Perlin, 2009]Is our trading system superior to a “monkey”, which opensand closes trading positions at random points?
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Statistical techniques
Random portfolios [Burns, 2006, Gatev et al., 2006]How skillful is our strategy in terms of picking the right stocksat the right combination?
“Monkey” trading [Perlin, 2009]Is our trading system superior to a “monkey”, which opensand closes trading positions at random points?
Other more sophisticated approaches
Reality Check [White, 2000]Test of Superior Predictive Performance [Hansen, 2005]False discovery rate [Bajgrowiczy and Scailletz, 2009]
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Skillful vs lucky stock picking
Dec95 Sep98 May01 Feb04 Nov06 Aug09
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ills
Median
90th percentile
10th percentile
months of consecutive underperformarnce
months of consecutive outperformarnce
Top−10% (IR) strategy
Figure 9 : Skillful-picking days9.
9See also [Burns, 2006] for a probabilistic performance analysis.Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Group-selection skills: interesting statistics
Based on the probability of “superiority”
Percentage of skilled months: 63.10%
Percentage of unskilled months: 36.90%
Average number of consecutive skillful-picking months: 2.51
Average number of consecutive unskilled-picking months: 1.47
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Do stock-picking benefits accumulate over time?
Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12−100
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Top−10% (IR) strategy
Probability of outperformance: 98.20%
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Is my trading system as smart as a monkey?
10
10This particular monkey-trader was recruited from
http://www.free-extras.com/images/monkey_thinking-236.htm .
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Skillful vs lucky trading
Dec95 Sep98 May01 Feb04 Nov06 Aug090
0.2
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ills
Dec95 Sep98 May01 Feb04 Nov06 Aug09−0.2
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urn
months of consecutive underperformarnce
months of consecutive outperformarnce
Top−10% (IR) strategy
10th percentile
90th percentile
Median
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Group-trading skills: interesting statistics
Percentage of skilled months: 66.31%
Percentage of unskilled months: 32.62%
Average number of consecutive skilled months: 2.88
Average number of consecutive unskilled months: 1.49
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Beating the monkey in terms of cumulative return
Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12−100
−50
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300
Cum
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Top−10% (IR) strategy
Probability of outperformance: 98.20%
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to improve your pairs trading system
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to improve your pairs trading system
Use firm fundamentals to select stocks with similar elasticityto risk factors.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to improve your pairs trading system
Use firm fundamentals to select stocks with similar elasticityto risk factors.
Trade at higher frequencies (possibly using microstructureinformation).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to improve your pairs trading system
Use firm fundamentals to select stocks with similar elasticityto risk factors.
Trade at higher frequencies (possibly using microstructureinformation).
Select stocks with similar response patterns to marketdisturbances
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to improve your pairs trading system
Use firm fundamentals to select stocks with similar elasticityto risk factors.
Trade at higher frequencies (possibly using microstructureinformation).
Select stocks with similar response patterns to marketdisturbances→ Event-response analysis ([Pole, 2007], section 2.4).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
How to improve your pairs trading system
Use firm fundamentals to select stocks with similar elasticityto risk factors.
Trade at higher frequencies (possibly using microstructureinformation).
Select stocks with similar response patterns to marketdisturbances→ Event-response analysis ([Pole, 2007], section 2.4).
Incorporate any type of prior domain knowledge (e.g. industryor value/growth classifications).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Event-response analysis
0 20 40 60 80 100 120 1400.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
Group formation period (days)
Nor
mal
ised
pric
e
local maxima
local minima
.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Pairs trading is a statistical arbitrate trading strategy.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Pairs trading is a statistical arbitrate trading strategy.
Performs better under limiting conditions:
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Pairs trading is a statistical arbitrate trading strategy.
Performs better under limiting conditions:
⊲ infinitely-dimensional asset universe.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Pairs trading is a statistical arbitrate trading strategy.
Performs better under limiting conditions:
⊲ infinitely-dimensional asset universe.⊲ infinite amount of trading time, etc.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Pairs trading is a statistical arbitrate trading strategy.
Performs better under limiting conditions:
⊲ infinitely-dimensional asset universe.⊲ infinite amount of trading time, etc.
Computational challenges (processing huge amounts ofinformation, asset selection, fine-tuning, model estimation).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Pairs trading is a statistical arbitrate trading strategy.
Performs better under limiting conditions:
⊲ infinitely-dimensional asset universe.⊲ infinite amount of trading time, etc.
Computational challenges (processing huge amounts ofinformation, asset selection, fine-tuning, model estimation).
Implementation challenges facing a real market environment(high portfolio turnover, market frictions).
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
Epilogue
Pairs trading is a statistical arbitrate trading strategy.
Performs better under limiting conditions:
⊲ infinitely-dimensional asset universe.⊲ infinite amount of trading time, etc.
Computational challenges (processing huge amounts ofinformation, asset selection, fine-tuning, model estimation).
Implementation challenges facing a real market environment(high portfolio turnover, market frictions).
If benefits (marginally) exceed costs your system is a hit!
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
References I
Andrade, S., Vadim, P., and Seasholes, M. (2005).Understanding the profitability of pairs trading.working paper.
Bajgrowiczy, P. and Scailletz, O. (2009).Technical trading revisited: False discoveries, persistence tests,and transaction costs.working paper.
Burgess, N. (2000).Statistical arbitrage models of the FTSE 100.In Abu-Mostafa, Y., LeBaron, B., Lo, A. W., and Weigend,A. S., editors, Computational Finance 1999, pages 297–312.The MIT Press.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
References II
Burns, P. (2006).Random portfolios for evaluating trading strategies.working paper.
Do, B. and Faff, R. (2010).Does simple pairs trading still work?Financial Analysts Journal, 66(4):83–95.
Engle, R. F. and Granger, C. W. J. (1987).Co-integration and error correction: Representation,estimation, and testing.Econometrica, 55:251–276.
Gatev, E., Goetzmann, W., and Rouwenhorst, K. (2006).Pairs trading: performance of a relative-value arbitrage rule.The Review of Financial Studies, 19(3):797–827.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
References III
Hansen, P. (2005).A test for superior predictive ability.Journal of Business & Economic Statistics, 23(5):365–380.
Jensen, M. and Bennington, G. (1970).Random walks and technical theories: some additionalevidence.The Journal of Finance, 25:469 – 482.
Lai, T. and Xing, H. (2008).Statistical Models and Methods for Financial Markets.Springer.
Murray, M. (1994).A drunk and her dog: An illustration of cointegration and errorcorrection.The American Statistician, 48(1):37–39.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
References IV
Perlin, M. (2009).Evaluation of pairs trading strategy at the braziliannancial market.Journal of Derivatives & Hedge Funds, 15:122–136.
Pole, A. (2007).Statistical arbitrage: algorithmic trading insights and
techniques.John Wiley and Sons, Inc.
Sullivan, R., Timmermann, A., and White, H. (1998).Dangers of data-driven inference: The case of calendar effectsin stock returns.CSD Economics Discussion Paper 98-16.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
References V
Sullivan, R., Timmermann, A., and White, H. (1999).Data-snooping, technical trading model performance and thebootstrap.The Journal of Finance, 54:1647–1691.
Thomaidis, N. S. and Kondakis, N. (2012).Detecting statistical arbitrage opportunities using a combinedneural network - GARCH model.Working paper available from SSRN.
Thomaidis, N. S., Kondakis, N., and Dounias, G. (2006).An intelligent statistical arbitrage trading system.Lecture Notes in Artificial Intelligence, 3955:596–599.
Vidyamurthy, G. (2004).Pairs trading: quantitative methods and analysis.John Wiley and Sons, Inc.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
References VI
Whistler, M. (2004).Trading pairs: capturing profits and hedging risk with
statistical arbitrage strategies.John Wiley and Sons, Inc.
White, H. (2000).A reality check for data snooping.Econometrica, 68(5):1097–1126.
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading