Pairs Trading

Statistical arbitrage and pairs trading

Nikos S. Thomaidis, PhD1

Dept. of Economics,
Aristotle University of Thessaloniki, GREECE

Dept. of Financial Engineering & Management
University of the Aegean, GREECE

email: nthomaid@fme.aegean.gr
Dept URL: http://labs.fme.aegean.gr/decision/
Personal web site: http://users.otenet.gr/~ ntho18

1
in collaboration with Nicholas Kondakis, Kepler Asset Management LLC, NY
(http://www.keplerfunds.com)
Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading

Outline


Outline

What is pairs trading?


Outline

Developing a pairs trading system from scratch


Outline

Empirical study: statistical arbitrage between
Dow Jones Industrial Average (DJIA) stocks


Outline

Conclusions


Outline

Conclusions
Trading risks


Outline

Conclusions
Trading risks
Opportunities


Outline

Conclusions
Trading risks
Opportunities
Future challenges


Pairs trading: the history

2
See [Pole, 2007, Vidyamurthy, 2004] and
http://www.pairtradefinder.com/forum/viewtopic.php?f=3&t=14 for
interesting facts and information on the history of the topic.


Pairs trading has at least twenty-ﬁve years of history on
Wall Street.

2


Wall Street.
Already in the mid 80’s, Morgan Stanley - and perhaps
other investment companies - have started developing
programs that could buy/sell stocks in pair combinations2 .

2


Wall Street.
These strategies were strongly quantitative (generating
trading rules using statistical/mathematical techniques,
executing trades through an automated computer-based
system).

2


Wall Street.
These strategies were strongly quantitative (generating
trading rules using statistical/mathematical techniques,
executing trades through an automated computer-based
system).
Cross-disciplinary work (mathematicians, statisticians,
physicists, computer scientists, ﬁnance experts).

2

Pairs trading: main idea



Capitalise on market imbalances between two or more
securities, in anticipation of making money when the
inequality is corrected in the future [Whistler, 2004]



Find two securities that have moved together over the
near past



near past
When the distance (spread) between their prices goes
above a threshold, short the overvalued and buy the
undervalued one



near past
When the distance (spread) between their prices goes
above a threshold, short the overvalued and buy the
undervalued one
If securities return to the historical norm, prices will
converge in the near future and you will end up with a
proﬁt


So what is pairs trading?



a market-neutral trading strategy: generates proﬁt under all
market conditions (uptrend, downtrend, or sideways
movements)



movements)
a statistical arbitrage trading strategy: proﬁt from temporal
mispricings of an asset relative to its fundamental value.



movements)
a long/short equity strategy: long positions are hedged with
short positions in the same or related sectors, so that the
investor should be little aﬀected by sector-wide events



movements)
relative-value trading,



movements)
relative-value trading, convergence trading,



movements)
relative-value trading, convergence trading, and so on...



movements)
relative-value trading, convergence trading, and so on...
Pairs trading → group trading


Why pairs work: the drunk and his dog

A humorous metaphor adapted from [Murray, 1994] to the context
of pairs trading.



of pairs trading.
A drunk customer sets out from the pub (“Gin Palace”) and
starts wandering in the streets (random walk, unit-root,
integrated stochastic process)



of pairs trading.
The accompanying dog thinks: “I can’t let him get too far oﬀ;
after all, my role is to protect him!”



of pairs trading.
The accompanying dog thinks: “I can’t let him get too far oﬀ;
after all, my role is to protect him!”
So, the dog assesses how far the drunk is and moves
accordingly to close the gap


The drunk and his dog: the story continues



Rory and Gary, two regular customers, look outside the pub’s
window and bet on the drunk’s and the dog’ s position



They observe the drunk and the dog individually but their
course looks no diﬀerent than a random walk (growing
variance in location, lack of predictability)



Suddenly, Gary throws the idea: “Well, it’s all a matter of
ﬁnding the drunk, the dog must not be far away”



He is right because the gap between the two fellows should
occasionally open and close but never being out of control
(co-integration)



(co-integration)
Rory and Gary eventually agree to play the following game:



(co-integration)
Rory and Gary eventually agree to play the following game:

“Why not betting on their relative distance rather than their
absolute positions?”


An actual traded pair

1.05
GT
1 HPQ
0.95

0.9

0.85

0.8

0.75

0.7

0.65

Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12

Figure 1: Normalised price paths of Goodyear (GT) and Hewlett Packard
(HPQ).


Why pairs trading is successful?

A behavioural-finance explanation:
New information is rapidly impounded in stock prices through
investment activity (market efficiency)
Stock price movements reflect all publicly available
information (future earnings prospects, corporate news,
political events)
Two securities that are close substitutes for each other
respond similarly to incoming news
Overreaction and herding behaviour of uninformed and
“noisy” investors often drives prices apart
But, any deviation is temporary and rational traders are
expected to close the “gaps” in the long run


Basic steps in developing a pairs trading system


Group formation
Pick closely-related stocks and detect stable relative price
relationships


Group formation
relationships
Group trading
Determine the direction of the relationship (divergence,
re-convergence)
Find suitable trade-open and trade-close points


Group formation
relationships
Group trading
Determine the direction of the relationship (divergence,
re-convergence)
Find suitable trade-open and trade-close points
Risk management
Minimise divergence risk (the gap between stocks further
widens)
Fine-tune parameters with respect to a trading performance
criterion (maximise expected return, maximise a reward-risk
ratio, etc)


Group formation strategy


Maximum price correlation (MPC)

1 Choose a charting time-frame
2 Compute the correlation of historical price series, e.g.

Correlation coeﬃcient
Pair 1 Stock 1 Stock 3 0.91
... ... ...

3 Pick the top 20% of pairs (i.e 4 pairs) with the highest
historical correlation
4 Formed groups: {1, 3, 5}, {2, 4}, {8, 10}

Minimum normalised price distance (MNPD)

Popular in literature [Gatev et al., 2006, Andrade et al., 2005]
Construct a cumulative total return index for each stock over
the formation period
t
crt,i ≡ (1 + rτ,i ), t = 1, 2, ..., T
τ =1

where cr0,i = 1 and rt,i is the t-period’s return on stock i .
Introduce a “distance” measure:
e.g. Euclidean distance
T
d(i , j) ≡ |cr ,i − cr ,j | ≡ (crt,i − crt,j )2
t=1

Rank stock pairs based on increasing values of d - pick the
top a% of the list for group formation

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 vector
Pt = (Pt1 , Pt2 , . . . , PtN ) satisfy the relationship

Pt1 = c + β2 Pt2 + · · · + βn PtN + Zt
where Zt is the mispricing index (captures temporal deviations
from equilibrium)
The coeﬃcients of the relationship can be estimated using
Ordinary Least Squares (OLS)


Identify stationary relationships (2/5)

Construct a portfolio as follows:

Stocks 1 2 3 ··· N
Positions +1 ˆ
-β2 ˆ
- β3 ··· ˆ
- βN

ˆ
where βi is the OLS estimate of βi and “+” (“-”)
indicates a long (short) position
ˆ ˆ
The portfolio value Zt ≡ β · Pt , where
ˆ ˆ ˆ ˆ
β ≡ (1, −β2 , −β3 , . . . , −βN )

is by construction mean-reverting (ﬂuctuates around c ,
ˆ
the OLS estimate of c)


Identify relationships with OLS (3/5)

15
Stock 1
Stock 2
Prices

10

5
0 50 100 150 200 250
Group formation sample



14.5
actual price pairs
Equilibrium relationship:
equilibrium relationship
14 −−−−−−−−−−−−−−−−−−
P2 = 14.843 − 0.257 P1

13.5 positive
mispricing
13
Stock 2

12.5 negative
mispricing
12

11.5

11
5.5 6 6.5 7 7.5 8 8.5
Stock 1



16.5
Stock 2 overpriced relative to Stock 1
16

15.5
Relative mispricing

15

14.5

14
Zt=P2 + 0.257 P1
13.5
Stock 2 underpriced relative to Stock 1
13
0 50 100 150 200 250
Group formation sample


Conditions for meaningful capital allocations

The average capital invested on each stock
(average price × number of shares) must be
below 80% and above 5%
The ratio between the maximum and the
minimum number of shares held from each asset
should not exceed 10.
etc

These place restrictions on the beta coeﬃcients
(stock holdings) → restricted OLS estimation


Group trading


Trading strategya
a
See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012]


Trading strategya
a

Open a position in a group, over the trading period, when the
mispricing index diverges by a certain threshold
ˆ
Buy the portfolio, if Zt < ZtL,α
ˆtH,α
Sell the portfolio, if Zt > Z
where ZtL,α , ZtH,α is a 100 × (1 − 2α)% conﬁdence
ˆ ˆ
“envelope” on the value of the mispricing.


Trading strategya
a

ˆ
ˆtH,α
ˆ ˆ
Unwind the position after h periods of time


Trading strategya
a

ˆ
ˆtH,α
ˆ ˆ
Unwind the position after h periods of time unless


Trading strategya
a

ˆ
ˆtH,α
ˆ ˆ
Unwind the position after h periods of time unless the
mispricing index continues to diverge (does not cross up the
lower bound or cross down the upper bound)


Trading strategya
a

ˆ
ˆtH,α
ˆ ˆ
Close the position earlier and open a new position if the
synthetic re-converges and crosses the opposite bound


Trading strategya
a

ˆ
ˆtH,α
ˆ ˆ
Close the position earlier and open a new position if the
synthetic re-converges and crosses the opposite bound
ZtL,α , ZtH,α is of the form c ± zα σZ , where c , σZ are the
ˆ ˆ ˆ ˆ ˆ ˆ
sample mean and standard deviation of the synthetic value
over the formation period and zα is the critical value from a
N(0, 1) distribution.

Example: trading a group of 2 stocks (1/2)

GOODYEAR (GT) vs HEWLETT PACKARD (HPQ)
42 20

GT
40 HPQ 18
Price ($)

Price ($)
38 16

36 14

34 12
0 20 40 60 80 100 120
Trading period

24

23

22
Mispricing

21

20

19 Zt=PGT −1.06 PHPQ Mispricing index Confidence bounds Long positions Short positions

18
0 20 40 60 80 100 120
Trading period

Figure 3:Mispricing index: Zt = PGT − 1.06PHPQ , Trading parameters:
HOP = 1day , αL = 10%, αH = 5% .



24

23

22
Mispricing

21

20

19 Mispricing index Confidence bounds Long positions Short positions

18
0 20 40 60 80 100 120
Trading period

8
Cumulative return (%)

6

4

2

0

−2
0 20 40 60 80 100 120
Trading period

Figure 4: HOP=1 day, αL = 10%, αH = 5% .



1.6

AA AXP CAT IBM Long positions Short positions
Normalised prices

1.4

1.2

1

0.8
0 50 100 150 200 250
Trading period

0

−1
Mispricing

−2

−3
Mispricing index Confidence bounds Long positions Short positions
−4
0 50 100 150 200 250
Trading period



Example: trading a group of 4 stocks(2/2)

0

−1
Mispricing

−2

−3
Mispricing index Confidence bounds Long positions Short positions
−4
0 50 100 150 200 250
Trading period
30

20

10

0

−10
0 50 100 150 200 250
Trading period



System performance measurement
Are there truly successful rules that deliver consistent return or
risk-adjusted return?
Performance indicators (mean, std, downside std, information ratio
(IR), downside IR)
How does performance vary with different market conditions?
Can high returns be explained by specific exposure to industry and
other systematic risk factors?
Are we capturing other patterns of stock movements (price
reversals)?
How skillful is our system in terms of picking the right pairs/finding
price equilibriums?
How able is our system to early detect price divergence and predict
re-convergence points?
Do our strategies require too much trading?
Do our strategies maintain their performance ranking over time? Do
the best remain the best and the worst remain the worst?

Experimental set-up

Daily prices of 30 stock members of Dow Jones Industrial
Average (DJIA) index (with dividends reinvested)
Sample period: 3 Jan 1994 to 24 Feb 2010
Group formation:
Window length (WL) {125, 250} days
Screen out DJIA stocks with one or more days without a trade
(identify relatively liquid stocks and facilitate pairs formation)
Choose matching stocks based on MNPD and MPC criteria
(form groups from the 5%, 20% or 50% highest-ranking pairs
of the list)
Trading strategy
Trading period: subsequent {50, 125, 150} days
Hold-out period (HOP): {1, 5, 10, 25} days
αL , αH ∈ {1, 5, 10, 20, 40}%
A total of 3, 600 parametrisations


Best trading strategies

Design parameters3 Best strategy (Mean return) Best strategy (IR)
Sample: 1994-2010
WL 125 125
TP 150 150
GFC MPC - 5% MPC - 20%
HOP 25 25
αL (%) 40 10
αH (%) 1 1

3
WL: Length of moving window, TP: Trading period, GFC: Group formation criterion, HOP: Position holdout
period.

Performance of best trading strategies

Trading measures Best strategy Best strategy (IR) Buy & hold portfolio
(Mean return)
Sample: 1994-2010 (784 observations)
Mean(%) 11.65 7.78 5.92
Stdev(%) 26.44 9.94 22.00
DStdev(%) 23.75 6.48 16.54
IR 0.44 0.78 0.27
DIR 0.49 1.20 0.36

Table 1: Average weekly performance (annualised measures).


Portfolios of good strategies



No investor would risk putting all his money in a single
strategy



strategy
Mixing-up diﬀerent parameter combinations



strategy
Mixing-up diﬀerent parameter combinations
“Bundles” of trading strategies:

“Distribute your capital evenly between the top-a % of the
parameterisations”


Performance of mixtures - Mean return

Percentage of trading strategies Best Buy &
Strategies
100 90 65 35 10 strategy hold
Mean(%) 1.98 2.46 3.42 4.64 6.48 11.65 5.92
Stdev(%) 3.65 3.63 3.69 4.00 6.19 26.44 22.00
DStdev(%) 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 0.27
DIR 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).


Performance of mixtures - Information ratio (1/2)

Percentage of trading strategies Best Buy &
Strategies
100 90 65 35 10 strategy hold
Mean(%) 1.98 2.46 3.42 4.43 5.93 7.78 5.92
Stdev(%) 3.65 3.63 3.66 3.65 4.31 9.94 22.00
DStdev(%) 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 0.27
DIR 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).


Performance of mixtures - Information ratio (2/2)

IR−maximising strategies
350

top−100
300 top−90
top−65
top−35
250
top−10
best strategy

200 buy & hold

150

100

50

0

−50
Dec95 Sep98 May01 Feb04 Nov06 Aug09


Systematic risk exposure

200
Market
SMB
HML
Top−10%(IR)
150
cumulative return (%)

100

50

0

−50

Figure 7: Historical performance of the top-10% portfolio (IR) and
systematic factors of risk.


Systematic risk exposure

Percentage of trading strategies
Strategies Best strategy
100 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.


Trading costs


Trading costs

Pairs trading is a cost-sensitive strategy


Trading costs

It involves


Trading costs

It involves
Frequent re-balancing of trading positions


Trading costs

It involves
Multiple openings and closings of trades


Trading costs

It involves
Short-selling


Trading costs

It involves
Short-selling
Transaction costs, margin requirements, etc


Trading costs

It involves
Short-selling
How the strategies are expected to perform in a more realistic
market environment?


Trading costs

It involves
Short-selling
How the strategies are expected to perform in a more realistic
market environment?
Can generated proﬁts oﬀset trading costs?


Descriptive statistics (1/2)

Top-10% (IR) portfolio of strategies
Sample period
Total days in sample: 4065
Total trading days in sample: 3865.7
Total number of traded stocks: 35
Group formation
Total number of formed groups: 71.43
Average size of groups: 4.51
(1.59)
Group trading
Total number of group openings during study: 195.76
Number of groups that never open: 4.19
Average number of active groups per trading day: 1.17
(0.45)
Fraction of trading time groups are open: 0.88
Average 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.


Descriptive statistics (2/2)

Top-10% (IR) portfolio of strategies
Divergence risk
Percentage of groups that never
open: 3.21
Percentage of groups opened once
but never converging in the trading
period: 26.31
Percentage of groups that have mul-
tiple round-trip trades and a ﬁnal di-
vergent trade: 57.13
Percentage of groups with no ﬁnal di-
vergent trade: 13.34

Note: Averages over all 360 parametrisations.


The impact of transaction costs (1/2)

Transaction cost4 0 bps 10 bps
Strategies Best at Zero Cost Best Best at Zero Cost Best
Mean(%) 5.93 5.93 5.38 5.78
Stdev(%) 4.31 4.31 4.34 4.30
DStdev(%) 2.55 2.55 2.54 2.54
IR 1.37 1.37 1.24 1.35
DIR 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 5.92
Stdev(%) 4.33 4.28 22.00
DStdev(%) 2.55 2.55 16.54
IR 1.14 1.25 0.27
DIR 1.93 2.10 0.36

Table 5: Top-10% (IR) portfolio.

4
Fixed cost per unit of trading volume.

The impact of transaction costs (2/2)

160
0 bps
140 10 bps
50 bps
120

100

80

60

40

20

0

−20

Figure 8: Historical performance of the top-10% (IR) portfolio assuming
diﬀerent levels of transaction costs.


Data snooping (1/2)


Data snooping (1/2)

Statistical arbitrage strategies are highly parametrised


Data snooping (1/2)

If we experiment with enough parameter settings, some of
them are likely to beat the benchmark under any performance
measures, by chance alone


Data snooping (1/2)

For example, strategies that went short in DJIA stocks during
the period Apr 2008 - Oct 2008, would possibly outperform
the market portfolio in a longer sample


Data snooping (1/2)

Simply because of the special characteristics of this single
period


Data snooping (1/2)

Simply because of the special characteristics of this single
period

Data snooping(“dredging” or “ﬁshing”):
The practice of hand-tailoring the trading strategy to the data
under consideration [Sullivan et al., 1999, White, 2000]


Data snooping (2/2)

Is the seemingly outstanding performance


Data snooping (2/2)

→ due to genuine superiority?


Data snooping (2/2)

or...


Data snooping (2/2)

or...
→ due to luck?


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]5

5
Random Walk: Taleb on Mistakes that Market Traders can make,
http://equity.blogspot.com/2008/11/taleb-on-mistakes-that-market-traders.html

How to eliminate data snooping biases?



Using an estimation and validation (test) data set
Helps observing model performance beyond the training sample
Sensitive with respect to the particular choice of sample
periods (training and testing)
Sensitive to market conditions



Using multiple estimation/validation periods
Reported performance is less prone to data-snooping biases
Problems arise if these periods are consecutive
The choice of periods can introduce further bias



Using multiple estimation/validation periods
Reported performance is less prone to data-snooping biases
Problems arise if these periods are consecutive
The choice of periods can introduce further bias
Statistical techniques
Little sensitivity to market conditions
Helps exploring new market scenarios (beyond those present in
the dataset)


How would you choose your sample periods?

Buy & hold strategy
350

300 2007
2001
2000
250 2004

1999 2006
2002 2005
200
2003
1998
150 2008

100 1997

2010
50 1996 2009
1995
0 1994

−50


Trading performance comparisons (1/2)

Splitting the data set into estimation and validation periods

Sample 1 Sample 2 Sample 3 Sample 4
Estimation
1994- 96 1997-99 2000-02 2003-06
period
Validation pe-
1997- 99 2000-02 2003-05 2006-10
riod
Number of
observations
756 days 756 days 756 days 1041 days
(validation
set)


Trading performance comparisons (2/2)

Validation period 1 Validation set 2
10 150 25 30
Top−10% (IR) IR=1.21
IR=0.27 Buy & hold
20 20



100 15 10
5

10 0

50 5 −10
0 Top−10% (IR) IR=−0.17
IR=1.28 Buy & hold
0 −20

0 −5 −30
Jun96 Jan97 Jul97 Feb98 Sep98 Mar99 Oct99 Apr00 Oct99 Apr00 Nov00 May01 Dec01 Jul02 Jan03

Validation set 3 Validation set 4
5 50 20 50
IR=0.52 Top−10% (IR) IR= −0.55 Top−10% (IR)
Buy & hold Buy & hold
IR= 0.78



10 0

0 0

0 −50
IR=0.05

−5 −50 −10 −100
Jul02 Jan03 Aug03 Feb04 Sep04 Mar05 Oct05 May06 Oct05 May06 Nov06 Jun07 Dec07 Jul08 Jan09 Aug09 Mar10



Random portfolios [Burns, 2006]
How skillful is our strategy in terms of picking the right stocks



at the right combination?



“Monkey” trading
Is our trading system superior to a “monkey”, which opens
and closes trading positions at random points?



“Monkey” trading
Is our trading system superior to a “monkey”, which opens
and 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]


Skillful vs lucky stock picking

1
months of consecutive out
performarnce
0.8
group formation skills
Probability of superior

0.6

0.4

0.2
months of consecutive under
performarnce
0
0.3
90th percentile Top−10% (IR) strategy
0.2

0.1
Monthly return

0

−0.1

Median
−0.2 10th percentile



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


Do stock-picking beneﬁts accumulate over time?

300

Top−10% (IR) strategy
250

Probability of outperformance:
98.20%
200

150

100

50

0

−50

−100


Is my trading system as smart as a monkey?

6

6
This particular monkey-trader was recruited from
http://www.free-extras.com/images/monkey_thinking-236.htm .

Skillful vs lucky trading

1
months of consecutive out
performarnce
0.8
group formation skills
Probability of superior

0.6

0.4

0.2
months of consecutive under
performarnce
0
0.2
90th percentile

0.1
Monthly return

0

−0.1
Median
10th percentile
−0.2


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


Beating the monkey in terms of cumulative return

300

250

Probability of outperformance:
98.20%
200

150

100

50

0

−50

−100


How to improve your pairs trading system



Use ﬁrm fundamentals to select stocks with similar factor risk
exposure



exposure
Trade at higher frequencies (microstructure information)



exposure
Select stocks with similar response patterns to market
disturbances



exposure
disturbances
→ Event-response analysis [Pole, 2007]



exposure
disturbances
Incorporate any type of prior expert knowledge



exposure
disturbances
Achieve the right balance between automation and human
intervention



exposure
disturbances
intervention
Is it possible to select the best-performing rules ex ante?



exposure
disturbances
intervention
Historical (in-sample) performance



exposure
disturbances
intervention
Historical (in-sample) performance
Economic conditions (picking those rules that perform better
with a particular state of the business and market cycle)


Event-response analysis

1.35

1.3

1.25 local maxima

1.2
Normalised price

1.15

local minima
1.1

1.05

1

0.95
0 20 40 60 80 100 120 140
Group formation period (days)
.


Epilogue


Epilogue

Pairs trading is a statistical arbitrate trading strategy


Epilogue

Performs better under limiting conditions


Epilogue

inﬁnitely-dimensional asset universe


Epilogue

inﬁnite amount of trading time, etc


Epilogue

Computational challenges (processing huge amounts of
information, asset selection, ﬁne-tuning, model estimation)


Epilogue

Implementation challenges (high portfolio turnover, trading
costs, execution risk)


Epilogue

Implementation challenges (high portfolio turnover, trading
costs, execution risk)
If beneﬁts exceed costs your system is a hit!


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.


References II

Burns, P. (2006).
Random portfolios for evaluating trading strategies.
working paper.
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.
Hansen, P. (2005).
A test for superior predictive ability.
Journal of Business & Economic Statistics, 23(5):365–380.


References III

Jensen, M. and Bennington, G. (1970).
Random walks and technical theories: some additional
evidence.
The Journal of Finance, 25:469 – 482.
Murray, M. (1994).
A drunk and her dog: An illustration of cointegration and error
correction.
The American Statistician, 48(1):37–39.
Pole, A. (2007).
Statistical arbitrage: algorithmic trading insights and
techniques.
John Wiley and Sons, Inc.


References IV

Sullivan, R., Timmermann, A., and White, H. (1999).
Data-snooping, technical trading model performance and the
bootstrap.
The Journal of Finance, 54:1647–1691.
Thomaidis, N. S. and Kondakis, N. (2012).
Detecting statistical arbitrage opportunities using a combined
neural 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.


References V

Whistler, M. (2004).
Trading pairs: capturing proﬁts and hedging risk with
statistical arbitrage strategies.
White, H. (2000).
A reality check for data snooping.
Econometrica, 68(5):1097–1126.


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