Statistical Arbitrage with Pairs Trading

Date01 June 2016
AuthorAhmet Göncü,Erdinç Akyıldırım
Published date01 June 2016
Statistical Arbitrage with Pairs
Institute of Quantitative Finance, Xian Jiaotong Liverpool University, Suzhou, China,
Bogazici University, Center for Economics and Econometrics, Istanbul, Turkey,
Department of Banking and Finance, Akdeniz University, Antalya, Turkey, and
Bogazici University, Center for Applied Research in Finance, Istanbul, Turkey
We analyze statistical arbitrage with pairs trading assuming that the spread of
two assets follows a mean-reverting OrnsteinUhlenbeck process around a
long-term equilibrium level. Within this framework, we prove the existence
of statistical arbitrage and derive optimality conditions for trading the spread
portfolio. In the existence of uncertainty in the long-term mean and the vola-
tility of the spread, statistical arbitrage is no longer guaranteed. However, the
asymptotic probability of loss can be bounded as a function of the standard er-
ror of the model parameters. The proposed framework provides a new ltering
technique for identifying best pairs in the market. Backtesting results are given
for some of the pairs of stocks that are studied in the literature.
In todaysnancial markets, there is an increasing tendency to utilize algorith-
mic trading in the presence of large number of assets and rapid ow of informa-
tion. The existing trend of algorithmic trading forces the investors to use
advanced quantitative techniques in order to generate trading signals. In the gen-
eral sense, statistical arbitrage refers to trading strategies that generate almost sure
prots asymptotically via trading signals generated from quantitative models,
whereas pure arbitrage is a special case of statistical arbitrage that generates al-
most sure prots in nite time. In this study, we consider one of the most com-
monly used statistical arbitrage techniques known as pairs trading.
Pairs trading can be considered as the rst generation of statistical arbitrage
strategies that are used to exploit nancial markets that are out of equilibrium.
Pairs trading assumes that while markets may not be in equilibrium, over time
they move to a rational equilibrium, and the trader has an interest to take max-
imum advantage of the deviations from the equilibrium. For interested readers,
more detailed description of pairs trading can be found in Vidyamurthy (2004),
© 2016 International Review of Finance Ltd. 2016
International Review of Finance, 16:2, 2016: pp. 307319
DOI: 10.1111/ir.12074

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