Statistical Arbitrage with Pairs Trading

• DOI: http://doi.org/10.1111/irfi.12074
• Date: 01 June 2016
• Author: Ahmet Göncü,Erdinç Akyıldırım
• Published date: 01 June 2016

Statistical Arbitrage with Pairs

Trading

AHMET GÖNCÜ

†,‡

AND ERDİNÇ AKYILDIRIM

§,¶

†

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

ABSTRACT

We analyze statistical arbitrage with pairs trading assuming that the spread of

two assets follows a mean-reverting Ornstein–Uhlenbeck 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 filtering

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.

I. INTRODUCTION

In today’sfinancial markets, there is an increasing tendency to utilize algorith-

mic trading in the presence of large number of assets and rapid flow 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

profits asymptotically via trading signals generated from quantitative models,

whereas pure arbitrage is a special case of statistical arbitrage that generates al-

most sure profits in finite 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 first generation of statistical arbitrage

strategies that are used to exploit financial 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. 307–319

DOI: 10.1111/irfi.12074