Pairs trading: is it applicable to exchange-traded funds?

Abstract

Among the various statistical trading strategies, pairs trading has been widely employed as a market neutral strategy owing to its simple approach and ease of application. In this context, we develop a cointegration-based pairs trading framework with a set of pre-conditions for pair eligibility and apply it to different asset classes. The performance analysis of a portfolio of 45 pairs is considered for the period of January 2007 to January 2021, which covers the period of a full market cycle of adjacent bull and bear periods; it is studied and benchmarked against the S&P500 index, which is considered as a proxy for the general market. We find an average annual return of 15% with an average Sharpe ratio of 1.43 after considering the transaction costs; we observe that this performance does not vary significantly with a change in the transaction cost levels and does not pass below the risk-free return levels with changing market conditions. Further, the strategy is observed to perform better during bear market conditions. Considering the highly liquid trading environment of the strategy, our findings raise a call for a discussion on the semi-strong form market efficiency.

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Pairs trading: is it applicable to exchange-traded funds?
Ekin Tokat
a,
*, Ahmet Cevdet Hayrullaho
glu
b
a
TOBB University of Economics and Technology Department of Business Administration S€
o
gu
¨t€
ozu
¨Cad, No: 43, S€
o
gu
¨t€
ozu
¨, Ankara, 06560, Turkey
b
Roketsan A.S¸., Elmadag, Ankara, 06780, Turkey
Received 21 February 2021; revised 16 August 2021; accepted 18 August 2021
Available online ▪▪▪
Abstract
Among the various statistical trading strategies, pairs trading has been widely employed as a market neutral strategy owing to its simple
approach and ease of application. In this context, we develop a cointegration-based pairs trading framework with a set of pre-conditions for pair
eligibility and apply it to different asset classes. The performance analysis of a portfolio of 45 pairs is considered for the period of January 2007
to January 2021, which covers the period of a full market cycle of adjacent bull and bear periods; it is studied and benchmarked against the
S&P500 index, which is considered as a proxy for the general market. We find an average annual return of 15% with an average Sharpe ratio of
1.43 after considering the transaction costs; we observe that this performance does not vary significantly with a change in the transaction cost
levels and does not pass below the risk-free return levels with changing market conditions. Further, the strategy is observed to perform better
during bear market conditions. Considering the highly liquid trading environment of the strategy, our findings raise a call for a discussion on the
semi-strong form market efficiency.
Copyright ©2021, Borsa
_
Istanbul Anonim S¸irketi. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-
ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Pairs trading; Cointegration; Quantitative strategies; Exchange traded fund market
1. Introduction
Market practitioners have long been interested in quanti-
tative trading models. Owing to the remarkable development
in computer technology in the 1980s, the use of statistical
arbitrage strategies has increased and become popular partic-
ularly among the hedge fund strategists and investment bank
proprietary traders (Gatev et al., 2006). Specifically, pairs
trading, a strategy developed by a group of mathematicians,
physicists, and computer engineers, received particular atten-
tion in the early 1980s (Vidyamurthy, 2004). The idea behind
the pairs trading strategy is to take advantage of market in-
efficiencies; its trading rule is quite straightforward: look for
two securities whose prices have been moving together, watch
the price spread widen, and then buy the security with a
relatively lower price and sell the security with a relatively
higher price. If the securities converge to their historical
spread pattern, trading will result in profit.
Although hedge funds and investment banks have been
extensively using this strategy since the early 1980s, it has
been recently gaining increasing attention from academicians.
Previous studies related to arbitrage have primarily examined
risk-free arbitrage strategies for futures traded on various
markets to test the market efficiencies (Fung et al., 2010;
Dunis et al., 2010). Further, risk arbitrage has been relatively
less discussed while transaction costs have been rarely
considered in the existing literature (Chan, 2008,2013). An-
alyses of risk-arbitrage, particularly pairs trading, was first
introduced by Gatev et al. (1999), followed by many others
(Vidyamurthy, 2004;Clegg &Krauss, 2018;Liew &Wu,
2013;Puspaningrum et al., 2009;Rad et al., 2016). Howev-
er, the focus of prior studies has been mostly restricted to the
stock market. Although recent studies have tested the strategy
*Corresponding author.
E-mail addresses: etokat@etu.edu.tr (E. Tokat), ahayrullahoglu@etu.edu.tr
(A.C. Hayrullaho
glu).
Peer review under responsibility of Borsa
_
Istanbul Anonim S¸irketi.
Available online at www.sciencedirect.com
Borsa
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Istanbul Review
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https://doi.org/10.1016/j.bir.2021.08.001
2214-8450/Copyright ©2021, Borsa
_
Istanbul Anonim S¸irketi. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: E. Tokat, A.C. Hayrullaho
glu, Pairs trading: is it applicable to exchange-traded funds?, Borsa
_
Istanbul Review, https://doi.org/10.1016/
j.bir.2021.08.001

on exchange traded funds (ETFs), prior studies initially
worked with a very limited number of pairs, and later mostly
focused on international country ETFs (see Clegg &Krauss,
2018;Schizas et al., 2011;Sipil€
a, 2013). Hence, the main
objective of this study is to examine the profitability of the
pairs trading strategy for a variety of asset classes and pair
types, such as stock only pairs, ETF only pairs, and
stockeETF pairs. Exploring the differences among the per-
formance outcomes of different asset types may provide a
better understanding of market efficiency based on asset class
or market type. Although market efficiency has long been
studied in finance literature, statistical arbitrage models have
been developed by traders to take advantage of the profit op-
portunities in the markets with different forms of efficiencies.
Therefore, this study focuses on developing a pairs trading
strategy to examine the performance of a portfolio of 46 paired
securities from different asset classes, which are traded on the
New York Stock Exchange (NYSE) and National Association
of Securities Dealers Automated Quotation (NASDAQ). The
developed strategy involves two steps: first, the cointegration
method is applied to eligible pairs whose selection is based on
a set of pre-conditions, and second, the trading rule for
opening and closing positions is set. The pairs are chosen from
the equities and ETFs representing different sectors, com-
modities, and countries. Finally, the strategy performance is
evaluated and compared to a benchmark model, which is the
buy and hold strategy in the general market, as per Standard
and Poor's(S&P) 500 index.
The remainder of the paper is organized as follows. Section
2discusses risk-free arbitrage, statistical arbitrage, and pair
trading strategies based on the existing literature. Section 3
describes the data and strategy design. The results and per-
formance are evaluated in Section 4. We conclude and discuss
the critical paths and requirements for a successful pairs
trading strategy in Section 5.
2. Pairs trading
Statistical arbitrage strategies in general involve the use of
statistical models to analyze price patterns; therefore, vari-
ants of statistical arbitrage strategies can be grouped as
mean-reverting, momentum, regime shifting, seasonal
trending, and high-frequency trading, among others (Chan,
2008). Pairs trading within this statistical arbitrage frame-
work is considered as a basis strategy and one of the simplest
approaches. Prior studies have mostly focused on risk arbi-
trage opportunities in the context of commodity futures
spread. Commodity and commodity product futures are
found to be good trading pairs for testing market efficiencies
as well as risk arbitrage opportunities (Girma &Paulson,
1999;Johnson et al., 1991). The pairs trading strategy was
first introduced to the literature of financial econometrics by
Gatev et al. (1999). The study shows that using a simple pairs
trading rule, which is called the distance method, it is
possible to generate profits over a long period of investment
time. Considering transaction costs, Do and Faff (2012) show
that the algorithm developed by Gatev et al. (1999) is largely
unprofitable and therefore inapplicable after 2002. Another
method that can be applied to a pairs trading framework is
cointegration (Puspaningrum et al., 2009;Vidyamurthy,
2004). Vidyamurthy (2004) emphasizes on the fact that se-
curity pairing is a critical step to achieve significant trading
performances. As a pairing method, it is suggested to define
pair combinations based on statistical significance, that is,
cointegration. The use of copulas in pairs trading is another
sophisticated approach relative to the distance method. Liew
andWu(2013)propose an application of copulas to pairs
trading, while Xie et al. (2016) evaluate the copula-based
pairs strategy performance by using utility stocks from the
US market. Further, Clegg and Krauss (2018) suggest the use
of partial cointegration for pair formation and generating
trading rules; their model is benchmarked against distance
and cointegration-based trading models and performs well
with at least 12% annual return after transaction costs.
Most of the previous studies have analyzed the imple-
mentation of the pairs trading strategy on stock pairs. In this
study, we focus on comparing the performance of the pairs
trading strategy for different asset types, including stocks and
ETFs. In contrast to previous studies, which mostly focus on
country ETFs, we use a wider range of ETF type in our
portfolio and consider sector index, commodity and country
ETFs. The algorithm is developed based on the cointegration
of pairs, while transaction costs are included to acquire more
realistic performance outcomes. Further, a period analysis is
conducted for the period of January 1, 2007 to January 1,
2021. Conventionally, a sub-period analysis of the varying
market conditions is conducted in studies related to pairs
trading; however, this study focuses on a sequential trading
schedule without any filtering and splitting of data. Our data
covers a full market cycle for the US stock market
1
and pro-
vides an effective performance measurement of the strategy
concerning all possible market conditions without controlling
for market disturbances.
3. Model design
3.1. Cointegration
The idea of the pairs trading strategy comes from the
identification of stationary price series. Stock price series
are found to be non-stationary due to their stochastic
behavior. Following Engle and Granger (1987), if two non-
stationary price series are integrated of order one, that is
I(1), considering that the first difference of the price series
is stationary, that is I(0), then there exists a linear com-
bination of the price series, which forms a stationary
process, such that the price series are said to be cointe-
grated of order one:
1
The recent full market cycle is usually considered to have occurred be-
tween 2007 and 2013 for the US equity market; this is defined as bull, bear,
and bull periods, which are adjacent to each other and generally last from as
short as 4e5 years to as long as 20 years (see Manning &Napier, 2014;
Asymmetry Observations, n.d.).
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ytbxt¼et;
where y
t
and x
t
are the cointegrated price series, bis the
cointegration coefficient, and e
t
is the stationary cointegration
error. In this framework, the cointegrated price series will
show a long-run equilibrium relationship; any deviation from
this equilibrium will be corrected in the short-run, which can
be shown through an error correction model (ECM) of the
following form:
ytyt1¼ayðyt1bxt1Þþεyt
xtxt1¼axðyt1bxt1Þþεxt;
where εytis the stationary disturbance term, and
ayðyt1bxt1Þis the error correction term for y
t
In this
framework, the estimated coefficients of the long-run error
terms, that is ayand ax, reflect the process by which both the
price series adjust in the short-run according to their long-run
equilibrium paths or as per their speed of adjustment. This
mean-reverting property of cointegration is in line with the
idea of pairs trading, which was incorporated into the pairs
trading strategy by Vidyamurthy (2004). In this study, we
employ the cointegration framework formulated in
Vidyamurthy (2004) and use ECM to estimate the long-run
equilibrium relationship among the paired securities; further,
we detect deviations in their long-term relationship, which is
used as a sign for taking either a long or short position in
paired securities. The estimated eigenvectors from the
Johansen cointegration test (Johansen, 1995) are used as hedge
ratios to determine the portfolio weights:
eigenvalue ¼e1
e2
eigenvector ¼h11 h21
h12 h22 
Normalized Hedge Ratio ¼h¼h12 =h11 :
Spread, which is expected to be stationary, is obtained as
follows:
Spread ¼yhx:
To estimate the deviations from the spread, the Z-score,
which has a standard normal distribution and helps determine
normalized deviations from the long-run relation, is employed
as follows:
Zscore ¼ðSpread mawðSpreadÞÞ=stdwðSpreadÞ:
The pairs trading strategy relies on a mean-reverting port-
folio, and it involves taking long or short positions with
respect to Bollinger Bands. Deviation from pre-defined
threshold levels around the moving average forms the base-
line for trading decisions. The Bollinger Band approach re-
quires the optimization of threshold Z-score levels and the
window size for calculating the moving average. For the
window size, weekly (five days), monthly (20 days), semi-
annual (120 days), and annual (250 days) values are used
and tested. For the threshold levels, the tested standard de-
viations ranged between 0.1 and 3.1 with 0.2 increments,
amounting to a total of 16 threshold levels. The criterion for
closing the position requires zero standard deviation of spread
from the moving average.
3.2. Backtesting
Backtesting is a crucial component in the development of a
trading strategy; it provides the input for optimization and
performance enrichment and involves testing the algorithm via
historical data. In backtesting the performance of a trading
strategy, it is vital to use only the data that would have been
available at the time of trade. Otherwise, it is more likely to
introduce a look-ahead bias into the system. For example, if a
trade position is simulated based on the minimum and
maximum daily prices observed on the same trading day, it
will diminish the accuracy of the trade's true performance as it
is impossible to observe the minimum and maximum daily
prices before the trading day ends. A look-ahead bias can be
avoided by dividing the data frame into two sub-sets: in-
sample and out-of-sample data sets. Accordingly, the coding
for hedge ratio, spread, and other parameter calculations will
be based on different time periods. In a typical backtesting
framework, one year of formation period, during which the
hedge ratio is calculated, is followed by one year of trading
period (Figure S1, available online).
2
The use of software technology in finance, particularly for
strategy development, has created tremendous trading oppor-
tunities. Once the rules of the developed trading system are
coded, it is very likely to backtest several trading options and
analyze all the combinations of the pre-set parameters to find
the best performing rules. With an adequate number of com-
binations, several rules can be formulated to ensure a good
performance. However, an extensive search for variable
combinations with different parameters is likely to result in
data snooping bias, which is another backtesting bias. The
likelihood that a performance result obtained from pure luck
will increase with the number of combinations tested. Any
trading rule that perfectly fits to its sample data through
backtesting may not generate the same performance when it is
run against another data set, which will result in the loss of
performance persistence. To minimize the probability of
snooping bias, in-sample and out-of-sample data sets are used
for the estimation of two parameters, which are the entry level
of Z-score and window size of the moving average of spread.
In order to minimize the probability of snooping bias, in-
sample and out-of-sample data sets are used for estimation
of two parameters, which are entry level of Z-score and
window size of moving average of spread. Sensitivity tests for
2
We tested the backtesting frameworks with formation and trading periods
of longer than one year, however, it reduced the strategy performance (see
Table 3).
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such parameters are conducted to observe the key component
of the developed strategy.
3.3. Data
The criteria for determining the assets that are potentially
suitable for pairs trading are defined. Rather than setting
various unit root tests as the first condition for an eligible pair
(Huck, 2015;Krauss &Herrmann, 2017,Clegg &Krauss,
2018), a set of pre-conditions are used to study the potential
pairs: same sector, sub-sector for stocks, weight of stock in
holdings of select sector ETF, similar investment grade for
country ETFs, geographical proximity for country ETFs, and
same commodity class such as precious metals or energy for
commodity ETFs. Previous studies (Gatev et al., 2006;Do &
Faff, 2012;Clegg &Krauss, 2018) have performed pairs
trading on a collection of stock pairs with the same sector
restriction, which is the first eligibility criterion of unit root
tests. We use the same sector restriction along with other
qualitative pre-conditions as the first criterion for pair eligi-
bility and examine stocks and ETFs. The ETFs on selected
sectors, commodities, and country indices traded in NYSE and
NASDAQ are examined in this framework. An algorithm
developed for the analysis extracted 13 years of daily price
data from the Thomson Reuters Datastream from January
2007 to January 2021.
An issue in the development of a trading strategy lies in the
short-sale constraint. We observe that it could be difficult or
impossible to sell the stock because of a small trading volume
or the restrictions imposed by the market regulator. To replicate
a practical trading environment, stocks with high market caps
and high trading volumes are selected. It is most likely for
market turmoil and crisis periods to cause structural breaks in
price series. Such structural breaks can generate jumps on price
series because of a high volatility (Fung et al., 2010). However,
the data are not filtered to avoid complications and price jumps
such as those observed repeatedly during and in aftermath of
the 2007 to 2009 global financial crisis with the aim of
imitating a realistic trading environment under uncertainty.
Therefore, this study is conducted on overlapping backtesting
frameworks, resulting in a sequential trading period analysis
with a view of the strategy performance through a full market
cycle. Accordingly, we consider the first formation period to
start from January 2007, such that the following formation
periods overlap with the trading periods, which commence from
January 2008. Prior studies on trading show that performance
varies over time (Gatev et al., 2006;Do &Faff, 2010;Clegg &
Krauss, 2018), although the studies are usually conducted on a
basis of sub-period analysis; however, our motive in this study
is to test the performance of the pairs trading strategy within a
fluctuating market atmosphere for consecutive years. Table 1
provides a summary of the data set used.
3.4. Performance evaluation
The pairs trading strategy performance is measured by
cumulative compound returns and Sharpe ratios:
Returnt¼ðNhxÞt1Rtx þðNyÞt1Rty
jðNhxÞt1jþjðNyÞt1j
Nreturn ¼Return Transacion Cost
Cumulative Return ¼Y
T
t¼1ð1þNreturntÞ1
Sharpe Ratio ¼ffiffiffiffiffiffiffiffi
252
p*meanðNreturnÞ.stdðNreturnÞ;
where Nrepresents the decision criterion, which is 1 for
short and 1 for the long position; his the normalized hedge
ratio; and Ris the asset return. Given that the strategy is
implemented on highly liquid trading venues (NYSE and
NASDAQ) with particularly high liquid stocks and ETFs, we
follow Clegg and Krauss (2018) and adjust the total return of a
closed position with 10 bps as a round-trip transaction cost.
This level is in line with other existing studies on pairs trading.
For example, Do and Faff (2012) consider institutional com-
missions of 0.1% or less between 1997 and 2009 by referring
to Jones (2002) who provided an annual time series of esti-
mated trading costs (bid-ask spreads and commission costs)
for the stocks in the Dow Jones Index to find that one-way
trading costs have consistently declined over the years and
reached approximately 0.2% in 2000. However, Prager et al.
(2012), report that the bid-ask spread declined to approxi-
mately one cent for the S&P 500 constituents. In terms of
commission rates, the trend has also been declining, such that
it is now charged as zero for the online trading of stocks and
ETFs by many trading platforms (Fidelity, n.d.;TD
Ameritrade, n.d.).
3
Although the assumption of 10 bps trans-
action cost seems reasonable, the strategy is also tested for
higher transaction cost levels.
Table 1
Summary of the data set.
Pairs group Number
of stocks
Number
of ETFs
Number of
STCKeSTCK
pairs
Number of
ETFeSTCK
pairs
Number of
ETFeETF
pairs
Financials 4 1 3 4 e
Technology 5 1 3 3 e
Healthcare 3 1 2 3 e
Consumer
Goods
723 6 e
Energy 3 1 2 2 e
Industrial 3 1 1 3 e
Utilities 2 1 1 2 e
Commodities e5ee3
Regional e7ee4
All 27 20 15 23 7
Note: STCK: equity stock, ETF: exchange traded fund.
3
Markets in Financial Instruments (MiFID II) Directive introduced by the
European Union aiming to enhance investor protection is seen as another
source of impact on significant declines in commission rates (Reuters, 2019).
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4. Results
The pairs trading strategy is tested on a wide range of se-
curities from different sectors, commodity markets, and
country indices (see Table S1, available online); 20 ETFs and
27 stocks are used to test the performance of 45 pairs. The
portfolio is composed of 15 stock only pairs, 7 ETF only pairs,
and 23 stockeETF pairs.
We aim to explore the effectiveness of cointegration-based
pairs trading together with our set of pre-conditions, which are
used for selecting the potential pairs. As the cointegration
relation and corresponding hedge ratios are calculated for a
period of 13 years for each pair, only the statistics of the
cointegrated series are reported in Table 2
4
. The results sup-
port the rolling cointegration relationship among the pairs
(Kutan &Zhou, 2003), that is, the pairs show a changing co-
movement behavior with time. Out of the 45 pairs studied, we
observe 15 and 28 cointegrated pairs in the first and second
year of the hedge ratio formation, respectively, and the number
changes over time. Following Clegg and Krauss (2018),itis
possible to observe profitable results for partially cointegrated
data using a cointegrating pairs trading strategy. For trading
applications, we not only use cointegration-based pairs, but
also consider the pairs without a significant cointegration
relation and use their corresponding hedge ratios. Table 2
shows the percentage of cointegrated pairs in the portfolio
together with the corresponding annualized mean returns. The
results do not provide evidence of a correlation between the
density of cointegrated pairs and trading performance.
The results are based on an optimum parameter, which
provides the highest cumulative compound return. One of the
parameters is the Z-score, which is tested for the range be-
tween 0.1 and 3.1; window size is another parameter that is
tested based on its weekly (five days), monthly (20 days),
semi-annual (120 days), and annual (250 days) values.
Therefore, a total of 64 different parameter combinations are
tested to evaluate the best performance, which is the highest
cumulative compound return. A sensitivity test is further
conducted to detect the parameter with the highest impact on
our strategy. The mean of the standard deviations are used to
conduct a comparison. Table 3 summarizes the trading sta-
tistics for each trading period. In all the periods, majority of
the pairs are traded; for example, there are only two out of 45
pairs without any open trading positions during the first year of
trading. Although it is observed that the average number of
positions is relatively higher for the global financial crisis
period and the preceding year (trading period of 2008e2009
and 2009e2010), respectively, it does not lead to a poorer
cumulative return performance due to the accumulation of
transaction costs; further, over these years, the annual mean
returns have attained their highest levels. Maximum drawdown
is another trade statistic, which observes the highest loss
incurred among the open positions for any pair. The average
maximum drawdown is the highest but limited to 11% in the
trading year of the global financial crisis. Parameter sensitivity
tests consider window size as the critical parameter. Across all
sub-periods, the minimum proportion of pairs with window
size sensitivity is 70%, suggesting its significance in strategy
irrespective of the market condition.
Table 4 summarizes annualized risk and return character-
istics of the strategy for the observed data from January 2007
to January 2021. Here, S&P 500 index, with the ticker symbol
^
GSPC, is considered as the proxy for the general market, and
its annualized mean return and Sharpe ratio are taken as the
benchmark criteria for performance evaluation. The annual-
ized mean return for the pairs portfolio is 15% with a Sharpe
Table 2
Cointegration test statistics.
Formation
period (FP)
Trading
period (TP)
Percentage of
cointegrated pairs
Annualized mean
return of pairs
trading strategy
2007e2008 2008e2009 35% 41%
2008e2009 2009e2010 62% 28%
2009e2010 2010e2011 96% 8%
2010e2011 2011e2012 20% 13%
2011e2012 2012e2013 47% 9%
2012e2013 2013e2014 44% 8%
2013e2014 2014e2015 47% 8%
2014e2015 2015e2016 47% 13%
2015e2016 2016e2017 71% 11%
2016e2017 2017e2018 51% 8%
2017e2018 2018e2019 49% 10%
2018e2019 2019e2020 27% 9%
2019e2020 2020e2021 64% 25%
Note: Formation period considers the hedge ratio calculation. Trading period
considers running the pairs trading strategy based on the hedge ratio calculated
in the formation period.
Table 3
Trading statistics.
Trading period Proportion
of pairs
traded
Average
number
of positions
per pair
Average
maximum
drawdown
Proportion
of pairs
with
Z-score
sensitivity
Proportion
of pairs
with
window
size
sensitivity
2008e2009 1.00 41 0.113 0.3 0.7
2009e2010 1.00 30 0.095 0.2 0.8
2010e2011 0.91 16 0.042 0.13 0.87
2011e2012 1.00 20 0.053 0.23 0.77
2012e2013 0.98 12 0.048 0.11 0.89
2013e2014 0.98 12 0.044 0.11 0.89
2014e2015 1.00 12 0.036 0.07 0.93
2015e2016 1.00 13 0.051 0.11 0.89
2016e2017 1.00 16 0.054 0.2 0.8
2017e2018 0.93 16 0.035 0.11 0.89
2018e2019 1.00 18 0.051 0.18 0.82
2019e2020 1.00 12 0.049 0.25 0.75
2020e2021 1.00 21 0.087 0.09 0.91
Note: Formation period considers the hedge ratio calculation. Trading period
considers running the pairs trading strategy based on the hedge ratio calculated
in the formation period.
4
ADF stationarity test statistics, trace statistics of Johansen cointegration
test, and the corresponding hedge ratios calculated for each pair for each
period can be provided upon request.
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ratio of 1.41. Considering the total amount of transaction costs
for a portfolio of 45 pairs as compared to the buy and hold
strategy for the benchmark, this result is not disappointing. For
the same period,
^
GSPC provides an 8% mean return and 0.82
Sharpe ratio on an annualized basis. One interesting obser-
vation is the relatively stable performance of the pairs port-
folio among all the years studied except during the 2007 to
2009 global financial crisis period. In contrast to the highly
volatile behavior of the general market, which fluctuates from
38% drawdown to 29% annual peak through the years, pairs
trading produces a minimum of 8% to a maximum of 25%
annualized returns, except during the 2007 to 2009 financial
crisis. Such a relatively steady performance supplies a close
analogy to the portfolio hedging with index futures, such that
the return is higher than the risk-free rate (Hull, 2009). The
results also confirm the findings of previous studies (Clegg &
Krauss, 2018;Do &Faff, 2010;Jacobs &Weber, 2015)on
pairs trading at times of financial distress; the strategy exhibits
a strong performance in the times of market turmoil; it shows
its peak during the global financial crisis with an annualized
return of 41% and Sharpe ratio of 1.85. Although the strategy
mostly underperforms in the bull markets, it still produces a
minimum of 8% annualized returns. This outcome with better
Sharpe ratios than that of a benchmark is remarkably satis-
fying, considering the poor performance of many trading
strategies that are used in the bull markets (Clegg &Krauss,
2018;Green et al., 2017).
Table 5 presents results of the sub-group performance anal-
ysis. All the group settings result in a better performance than
the benchmark in terms of annual mean return and Sharpe ratio.
Among the selected ones, the pairs from the regional country
ETFs seem to perform the best in terms of annualized risk and
return figures, which are 1.73 and 20%, respectively. Another
interesting result is the better performance of emerging country
pairs in contrast to the developed country ETF pairs. This might
be attributable to a relatively high volatility and less newswire or
Table 4
Performance evaluation of the pairs trading strategy.
FP TP Annual
average
return of
PT
Annual return
of S&P 500
Average Sharpe
ratio of PT
Sharpe Ratio
of S&P 500
FP: 1 Year
TP: 1 Year
2007e2008 2008e2009 41% 38% 1.85 0.94
2009e2009 2009e2010 28% 20% 1.64 0.80
2009e2010 2010e2011 8% 11% 1.22 0.67
2010e2011 2011e2012 13% 1% 1.39 0.07
2011e2012 2012e2013 9% 12% 1.43 0.94
2012e2013 2013e2014 8% 26% 1.30 2.23
2013e2014 2014e2015 8% 12% 1.53 1.09
2014e2015 2015e2016 13% 1% 1.47 0.03
2015e2016 2016e2017 11% 11% 1.34 0.89
2016e2017 2017e2018 8% 18% 1.33 2.59
2017e2018 2018e2019 10% 7% 1.31 0.34
2018e2019 2019e2020 9% 29% 1.28 2.09
2019e2020 2020e2021 25% 15% 1.47 0.59
Average of annual returns and Sharpe ratios from 2007e2021 15% 8% 1.43 0.82
Alternative backtesting framework:
FP: 1 Year
TP: 4 Year
2010e2011 2011e2015 2% 15% 1.56 0.86
FP: 4 Year
TP: 4 Year
2010e2014 2014e2018 2% 11% 1.21 0.84
Alternative transaction costs:
FP: 1 Year
TP: 1 Year
Transaction Cost: 20 bps
2007e2008 2008e2009 39% 38% 1.60 0.94
2016e2017 2017e2018 7% 18% 1.19 2.59
FP: 1 Year
TP: 1 Year
Transaction Cost: 30 bps
2007e2008 2008e2009 33% 38% 1.45 0.94
2016e2017 2017e2018 6% 18% 1.08 2.59
Alternative sequence of formation and trading periods:
FP: 1 Year
TP: 1 Year
01.2008e01.2009 01.2009e01.2010 38% 20% 1.61 0.80
03.2008e03.2009 03.2009e03.2010 29% 59% 1.73 2.12
06.2008e06.2009 06.2009e06.2010 14% 14% 1.45 0.79
09.2008e09.2009 09.2009e09.2010 13% 8% 1.50 0.51
Note: Formation period (FP) considers the hedge ratio calculation. Trading period (TP) considers running the pairs trading (PT) strategy based on the hedge ratio
calculated in the formation period.
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Tab l e 5
Performance evaluation based on group classifications.
Trading Years 2008e2009 2009e2010 2010e2011 2011e2012 2012e2013 2013e2014 2014e2015 2015e2016 2016e2017 2017e2018 2018e2019 2019e2020 2020e2021 2007e2021
Average
Average annualized return
S&P500 38% 20% 11% 1% 12% 26% 12% 1% 11% 18% 7% 29% 15% 8%
Financials 73% 88% 5% 20% 14% 8% 8% 14% 4% 6% 7% 5% 10% 20%
Technology 49% 28% 3% 24% 11% 7% 13% 9% 16% 7% 9% 14% 16% 16%
Healthcare 39% 33% 9% 5% 6% 5% 7% 14% 8% 5% 8% 13% 34% 14%
Consumer Goods 51% 14% 10% 10% 7% 6% 7% 7% 10% 8% 8% 8% 16% 12%
Energy 12% 17% 7% 9% 10% 5% 13% 11% 10% 4% 13% 9% 32% 12%
Industrial 15% 22% 3% 18% 10% 7% 5% 17% 12% 5% 4% 6% 22% 11%
Utilities 65% 8% 8% 5% 3% 5% 3% 5% 5% 3% 3% 0% 21% 10%
Commodities 13% 24% 19% 12% 17% 21% 8% 17% 20% 15% 9% 13% 45% 18%
Regional 53% 17% 12% 14% 8% 7% 13% 19% 17% 20% 31% 16% 27% 20%
Portfolio Average 41% 28% 8% 13% 9% 8% 8% 13% 11% 8% 10% 9% 25% 15%
Average Sharpe ratio
S&P500 0.94 0.80 0.67 0.07 0.94 2.23 1.09 0.03 0.89 2.59 0.34 2.09 0.59 0.82
Financials 1.73 1.67 0.96 1.48 1.68 1.27 1.75 1.66 0.98 1.49 1.27 1.04 1.35 1.41
Technology 2.14 1.90 0.54 1.68 1.20 0.58 1.93 0.88 1.37 1.09 1.30 1.53 1.31 1.34
Healthcare 1.52 1.82 1.55 0.85 1.44 0.91 1.23 1.49 0.71 1.09 1.11 1.71 2.35 1.37
Consumer Goods 2.15 1.30 1.48 1.52 1.19 1.42 1.41 0.98 1.32 1.42 1.34 1.51 1.38 1.42
Energy 1.02 1.57 1.04 1.21 1.84 1.62 2.23 1.29 1.31 0.78 1.64 1.49 1.55 1.43
Industrial 1.10 2.19 0.62 2.06 1.86 1.29 1.60 2.02 1.82 1.13 0.86 0.66 1.09 1.41
Utilities 3.18 1.22 1.51 1.29 1.14 1.33 0.85 1.62 1.38 1.22 1.25 0.28 1.47 1.36
Commodities 1.01 1.58 1.32 1.15 1.28 2.01 1.42 1.44 1.32 2.27 0.80 1.39 1.00 1.39
Regional 2.78 1.55 1.97 1.28 1.26 1.30 1.38 1.80 1.88 1.45 2.20 1.90 1.71 1.73
Portfolio Average 1.85 1.64 1.22 1.39 1.43 1.30 1.53 1.47 1.34 1.33 1.31 1.28 1.47 1.43
Note: The last column shows the 13 year average of each related row.
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analysts'coverage on the ETFs of an emerging country. Jacobs
and Weber (2015) observe low pair visibility (less newswire or
analysts’coverage) and limits to arbitrage (volatility) as the two
parameters that make pairs trading more profitable. Their
finding also explains the superior performance of the regional
ETF pairs among the selected groups. Among the various in-
dustry sets, the financial sector together with the healthcare and
technology sectors perform well. Financial pairs work well
during the global crisis period as majority of the financial stocks
collapse together owing to a significant amount of systematic
risk; additionally, the pairs from the healthcare sector perform
well during the COVID-19 pandemic for similar reasons.
Moreover, pairs trading performance analysis suggests that
performance does not vary significantly according to the asset
type. Finally, our findings provide a ground to question the semi-
strong form of market efficiency, considering the level of returns
pairs trading produced from 2007 to 2021 in a highly liquid
stock and ETF environment.
We re-examine certain parameters of the model as they had
consistently achieved higher than risk-free return levels. The
strategy is first tested with higher transaction cost levels. We
assume a round-trip transaction cost per trade of 20 and 30
bps. The strategy appears to be robust to transaction cost as-
sumptions, that is, it is common for statistical pairs trading
strategies as the performance does not change dramatically for
higher transaction cost levels. Among the outliers, during the
trading year of 2017e2018 in which the trading strategy ex-
hibits a poor performance, the annualized mean return de-
creases by 1% with a 10 bps increase in transaction costs and
Sharpe ratio changes from 1.11 to 1.08 with the transaction
cost level at 30 bps (see Table 4). Another outlier is the trading
year with the highest average number of positions per pair
where we expect to see a diminishing impact of higher
transaction costs on strategy performance. In this particular
period, which coincides with the 2007 to 2008 global financial
crisis considered as the best performing trading year, return
performance decreases by 2% with a 10 bps increase in the
transaction costs. An addition of 10 bps decreases the annual
mean return to 33%; however, the outcome is still fairly
satisfying. Additionally, the strategy is tested with a disrupted
sequence of formation and trading periods. We replace the first
formation period of January 2007 for hedge ratio calculation
with different months of the year and employ the backtesting
framework accordingly. A sample of the formation and trading
periods with the strategy performance results is shown in
Table 4. Although the annualized mean return and Sharpe
ratios vary according to different period settings, the strategy
still performs better than the risk-free market return with
satisfying Sharpe ratio levels. However, the variation in the
performance bears the potential to construct a dynamically
adaptive pairs trading strategy for future studies.
5. Conclusion
Pairs trading has long been one of the most popular hedge
fund strategies. This study focuses on developing the strategy
with a cointegration approach and a set of pre-conditions for
pair eligibility. The portfolio of 45 pairs achieves a 15%
annual mean return after transaction costs; its performance
does not change much in a negative direction with fluctuating
markets, suggesting a casual hedging strategy for market
participants. Performance is particularly strong during times
of market turmoil. This finding together with a moderate
level of return and risk figures for the bull market conditions
can help us to draw a conclusion on potential arbitrage op-
portunities and question the semi-strong form of market ef-
ficiency. Another outcome of the study is the high
dependency of strategy performance on the model parame-
ters. This result leads us to study parameter optimization,
which has the potential to improve the strategy performance
for the next trading period. Two parameters that are found to
be critical for strategy performance and need to be optimized
are the Z-score value and window size of moving average;
window size proves to be the most critical parameter based
on sensitivity tests. The finding on the lack of a strong
relationship between the cumulative returns and degree of
cointegration implies that there exists a possibility to gain
profits in the absence of a strong cointegration property and a
possible change in the cointegration relation among the pairs.
This may be attributed to the change in the dynamics of the
environment that provides the strength of cointegration be-
tween the two securities, such as a change in marketing tar-
gets, one of the company's management, financial market
structure, or the country's economic prospect. Further, a
steady return performance among fluctuating market condi-
tions draws our attention to the set of qualitative pre-
conditions used for pair eligibility. Therefore, fine-tuning
the set of pre-conditions and the further development of a
dynamically adaptive algorithm to optimize the hedge ratio
should be the focus of future studies.
Funding
This work was supported by the Scientific and Techno-
logical Research Council of Turkey (TU
¨B
_
ITAK).
Declaration of competing interest
There is no conflict of interest.
Appendix A. Supplementary data
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.bir.2021.08.001.
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