The Profitability of Pairs Trading in an Emerging Market Setting

The Empirical Economics Letters, 8(5): (May 2009)
ISSN 1681 8997
The Profitability of Pairs Trading in an Emerging Market
Setting: Evidence from the Istanbul Stock Exchange
Alovsat Muslumov
Department of Mathematics, Istanbul Bilgi University
Dolapdere, Istanbul, Turkey
Email: [email protected]
Asli Yuksel
Department of Business Adminstration, Bahcesehir University
Besiktas, Istanbul, Turkey
Email: [email protected]
Aydin Yuksel
Isik University, Department of Management, Sile, Istanbul, Turkey.
Email: [email protected]
Abstract: This study measures the performance of the pairs trading strategy in an
emerging stock market setting, using the methodology of Gatev et al. (2006). Distancebased pairs trading methodology gives an average excess return of 5.4 % for the top 20
best pairs portfolios. Although statistically significant, these results for the selffinancing portfolios lack economic significance considering transaction and shortselling costs.
Keywords: Pairs Trading; Statistical Arbitrage
JEL Classification Number: G11
1.
Introduction
Capital market equilibrium requires the absence of arbitrage in the financial market.
However, statistical arbitrage methods which are used to uncover risky arbitrage strategies
that benefit from temporary price deviations of securities from their historical expected
values are reporting positive returns for investors. One of the most frequently referred to
statistical arbitrage tools is the “pairs trading” strategy, which involves the simultaneous
purchase of a security and sale of another security which have historically moved together
with the expectation that deviations from their historical relationship will be reversed.
Although the pairs trading strategy is commonly used by hedge funds and investment
banks, empirical studies testing the profitability of this strategy are scarce. Pairs trading
profitability tests have been part of methodological studies (Engle and Smith, 1999) or part
The Empirical Economics Letters, 8(5): (May 2009)
496
of case studies (Froot and Dabora, 1999). Among the others, the most significant and
extensive study testing the profitability of pairs trading is that of Gatev et al. (2006), which
focuses on the US market. Our study applies pairs trading methodology of Gatev et al.
(2006) to an emerging stock market setting.
Following this section, section two explains this study’s methodology, and section three
presents the empirical results and conclusions.
2. Methodology
Our study used daily adjusted closing prices of the stocks listed on the Istanbul Stock
Exchange (ISE) between January 1, 1990 and April 20, 2007. The source of data is
Datastream. In the 12 months pair formation (training) period all stocks traded on the ISE
are selected, except those with more than five non-traded days. The price series of each
stock are then normalized by setting the starting value on the first day of the pair formation
period to one. Later, all possible pairs from the set of stocks are constructed, and then, for
each pair of stocks, the sum of the squared deviations between their normalized stock
prices are calculated. Finally, all pairs were sorted in ascending order of the sum of the
squared deviations. Our reference to pairs subset preserves the order in this sorted pairs set.
For example, the top 20 pairs means the top 20 pairs in this minimum historical distance
order, whereas 101-120 pairs means the subset of pairs in the sorted pairs set that starts
with the 101st pair and ends with the 120th pair. In the pairs formation process, no
restriction (such as industry, size etc.) was imposed. By considering only minimum
distance criteria, any stock could be paired with any other stock.
The trading period immediately followed the pairs formation period. During the trading
(testing) period, which lasted as six months, the trading was started when the difference
between normalized prices of stocks forming a pair diverged by more than two historical
standard deviations calculated using the price deviations during the pair formation period.
We went 1 TL (Turkish Lira) short in the high priced stock and 1 TL long in the low priced
stock. If the trading position was still open the next day, we followed buy-and-hold strategy
that marked our position to the market daily. We closed our position when the normalized
prices crossed. In the case of a stock delisting, we closed our position at the last available
price. If the trading position was still open at the end of the trading period, we closed our
position at the prices of the last day of the trading period.
Figure 1 illustrates the two stages of pair formation and testing with the example of two
stocks, Pinar Sut and Tukas. In the pair formation period, starting on February 1, 2000 and
ending on January 31, 2001, we calculated the standard deviation of the normalized price
deviations of the two stocks as 0.0608. In the trading period between February 1, 2001 and
July 31, 2001, we started trading when the normalized price series of the two stocks
The Empirical Economics Letters, 8(5): (May 2009)
497
diverged more than two standard deviations, i.e. when the price deviations exceeded
0.1216. The trading position opened first on the tenth trading day when we went short 1 TL
on Pinar Sut, whose price series had risen and long 1 TL on Tukas whose price series had
fallen. Figure 1 shows that the number of round trips in the trading period was six, and that
in the first four round trips, we went short on Pinar and long on Tukas, and vice-versa in
the last two round trips. The total gain over the six-month trading period for the TukasPinar Sut pair is 103.81%.
Figure 1: Daily Normalized Prices: Pinar Sut and Tukas
Pair Formation Period
PINAR SUT
TUKAS
N orm aliz ed R eturns
1
0.8
0.6
0.4
0.2
0
50
100
150
200
250
Trading Period
N orm aliz ed R eturns
2
1.5
1
0.5
0
20
40
60
80
100
120
Days
Note: Pair Formation Period: February 2000 - January-2001 and Trading Period: February 2001 –
July 2001. Grey shaded areas refer to the no-trade periods.
Excess returns of the pair portfolios were calculated using return on fully invested capital
and committed capital. Fully invested portfolio return was scaled to the number of open
pairs, whereas committed capital portfolio return (which is a more conservative measure)
was scaled to all pairs in the portfolio, even if these pairs had not been traded. The
The Empirical Economics Letters, 8(5): (May 2009)
498
inclusion of the initial investment (that is 1 TL) for the pairs not traded can be considered
as the opportunity cost of capital.
Our pairs trading strategy resulted in overlapping six-month trading periods. That is, with
the exception of the first 18 months, which included our pair formation and first trading
periods, we traded six different pair portfolios in the same month which were initiated one
month apart. The monthly averages of the overlapping portfolios were calculated to correct
for correlation. These monthly averages resulted in the time-series of monthly excess pairs
portfolio returns.
3.
Empirical Results
The results of the pairs trading strategy are presented in Table 1. Panel A summarizes the
findings for ‘no-waiting’ portfolios. These are portfolios where we close our position in the
trading period using the prices on the convergence day. According to the findings, the top
five pairs fully invested portfolio earned 0.64% (t-statistic, 17.43), whereas excess returns
gradually declined as we moved to lower distance pairs portfolios. The top 20 pairs fully
invested portfolio gave a statistically significant 0.45% excess return. The return was
0.53% for the 101-120 portfolio. The fully invested portfolio for all pairs produced a 0.33%
excess return. The more conservative committed capital portfolios gave similar results.
Interestingly, for the top five, ten and fifteen pair portfolios, committed capital portfolios
gave higher excess returns than fully invested portfolios. This is understandable, since for
some months when there were negative excess returns, the committed capital portfolios
experienced less loss than fully invested portfolios. The excess return for the top five pair
committed capital portfolios was 0.65%, whereas the top 20 committed capital pairs
portfolio earned 0.44%. These results are significantly lower than those of Gatev et al.
(2006), who reported monthly excess returns of 1.31% for the top five pairs fully invested
portfolio, and 1.43% for the top 20 pairs fully invested portfolio.
Panel B of Table 1 presents the results when the positions were closed one day after the
convergence day. On convergence day (opening day), if investors were buying at the ask
(bid) quotes and selling at the bid (ask) quotes, the returns of pairs trading would be biased
upward. However, if the prices were equally likely to be at bid or ask on the next day of the
convergence, closing the position having waited for one day (after the convergence) would
reduce the excess returns by as much as half the sum of the spreads (round trip transaction
costs). Therefore, in our top five pairs committed capital (fully invested) portfolio, the
excess return with one day waiting for trading declined to 0.44% (0.44%). Although
statistically significant, our excess returns were not large in financial terms considering
transaction and short-selling costs.
The Empirical Economics Letters, 8(5): (May 2009)
499
Table 1: Excess Returns of Two Unrestricted Pairs Trading Strategies (Standard
Deviation – 2.0)
Pairs Portfolio
Top 5 Top 10
A. Excess Return Distribution (no waiting)
Average excess return (fully
invested)
0.00642 0.00608
Standard error (Newey-West)
0.00037 0.00030
t-Statistic
17.43
20.19
Excess return distribution
Median
0.00775 0.00976
Standard deviation
0.06706 0.06014
Skewness
-0.78
-0.79
Kurtosis
5.98
5.38
Minimum
-0.28759 -0.25751
Maximum
0.20632 0.15457
Observations with excess
return < 0
44%
41%
Average excess return on
committed capital
0.00648 0.00631
Median excess return on
committed capital
0.00763 0.01002
B. Excess Return Distribution (one day waiting)
Average excess return (fully
0.00438 0.00519
invested)
Standard error (Newey-West)
0.00029 0.00024
t-Statistic
15.08
21.61
Excess return distribution
Median
0.00495 0.00675
Standard deviation
0.06697 0.05608
Skewness
-0.28
-0.54
Kurtosis
5.84
5.09
Minimum
-0.26655 -0.23942
Maximum
0.29002 0.18103
Observations with excess
return < 0
46%
42%
Average excess return on
committed capital
0.00443 0.00537
Median excess return on
committed capital
0.00110 0.00623
Top 15 Top 20 101-120
All
0.00567 0.00451 0.00530 0.00335
0.00021 0.00022 0.00015 0.00011
26.75 20.73
35.54
30.75
0.00645 0.00484
0.05567 0.05425
-0.31
-0.45
4.15
4.91
-0.18452-0.21727
0.15090 0.15348
0.00623
0.05026
-0.19
4.45
-0.16952
0.15433
0.00471
0.05439
0.09
6.05
-0.20216
0.23632
42%
45%
46%
44%
0.00571 0.00442 0.00468 0.00151
0.00687 0.00580 0.00534 0.00076
0.00521 0.00448 0.00653 0.00467
0.00019 0.00018 0.00014 0.00009
27.99 24.43
46.85
49.53
0.00537 0.00354
0.05221 0.05030
-0.13
-0.15
3.91
4.82
-0.17125-0.19737
0.14447 0.17017
0.00713
0.04744
-0.13
4.29
-0.16700
0.14150
0.00351
0.05177
0.29
6.10
-0.18539
0.24053
44%
42%
46%
47%
0.00527 0.00439 0.00572 0.00219
0.00523 0.00369 0.00429 0.00078
The Empirical Economics Letters, 8(5): (May 2009)
500
When we diversified the portfolio by including more pairs to the portfolio, we reduced the
standard deviation and range of the returns and increased the skewness coefficient. One of
the notable findings here was negative skewness (greater than normal probability of large
losses) as opposed to the positive skewness in Gatev et al. (2006). This finding is also
reflected in the median excess return which is higher than mean value. The top five pairs
portfolio experienced negative returns in 84 months out of a total 191 months, compared to
88 months out of 191 months for the all pairs portfolio.
Our results should be interpreted carefully. Though they indicate that the profit from pairs
trading strategy using two historical standard deviation, 12 month pairs formation and 6
month pairs trading windows is not economically significant in the ISE stocks, it doesn’t
allow us to completely reject the profitability of the pairs trading strategy using the ISE
stocks. The search for optimal trigger points (historical standard deviations) and optimal
pairs formation and trading windows may produce more profitable pairs trading strategies.
These should be the topics for future research.
Summary statistics of the monthly excess returns on portfolios of pairs between January
1990 and April 2007 (191 observations) are also discussed. We traded according to the
rule that opened a position on a pair at the end of the day during which prices of the stocks
in the pair diverged by two historical standard deviations (Panel A). The results in Panel B
correspond to a strategy that delayed the opening of the pairs position by one day. All pairs
are ranked according to least distance in historical price space. The ‘top n’ portfolios
include the n pairs with least distance measures, and the portfolio ‘101–120’ studied the 20
pairs below the top 100. The t-statistics were computed using Newey-West standard errors
with six-lag correction. Absolute kurtosis is reported.
References
Engle, R.F. and A.D. Smith, 1999, Stochastic Permanent Breaks, The Review of
Economics and Statistics 81 (4), 553-574.
Froot, K.A. and E.M. Dabora, 1999, How Are Stock Prices Affected By The Location of
Trade, Journal of Financial Economics 53(2), 189-216.
Gatev, E.G., Goetzmann, W. and K.G. Rouwenhorst, 2006, Pairs Trading: Performance of
a Relative Value Arbitrage Rule, Review of Financial Studies 19(3), 797-827.