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Full Length Article

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¸., Elmadag, 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

_

Istanbul Review

Borsa

_

Istanbul Review xxx (xxxx) xxx

http://www.elsevier.com/journals/borsa-istanbul-review/2214-8450

+MODEL

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.).

E. Tokat, A.C. Hayrullaho

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ytbxt¼et;

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:

ytyt1¼ayðyt1bxt1Þþεyt

xtxt1¼axðyt1bxt1Þþεxt;

where εytis the stationary disturbance term, and

ayðyt1bxt1Þis 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 ¼e1

e2

eigenvector ¼h11 h21

h12 h22

Normalized Hedge Ratio ¼h¼h12 =h11 :

Spread, which is expected to be stationary, is obtained as

follows:

Spread ¼yhx:

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:

Zscore 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).

E. Tokat, A.C. Hayrullaho

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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:

Returnt¼ðNhxÞt1Rtx þðNyÞt1Rty

jðNhxÞt1jþjðNyÞt1j

Nreturn ¼Return Transacion Cost

Cumulative Return ¼Y

T

t¼1ð1þNreturntÞ1

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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