Elsevier

Economics Letters

Volume 202, May 2021, 109842
Economics Letters

Systematic risk in pairs trading and dynamic parameterization☆

https://doi.org/10.1016/j.econlet.2021.109842Get rights and content

Highlights

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    Statically parameterized pairs trading has undesirable systematic risk.

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    Kalman Filter is used to estimate cointegration coefficients and adjust ASR-thresholds.

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    Stochastic discount factors are used for construction of dynamic ADF-thresholds.

  • •

    Dynamic parameterization promotes performance and reduces systematic risk.

  • •

    Dynamic thresholds minify effects of initial settings.

Abstract

In statistical arbitrage, pairs trading is usually considered a risk-neutral strategy. However, the methodologies in existing literature on choosing thresholds and calibrating cointegration coefficients could be arbitrary and insensitive to market changes. This research discovers that static parameterization in pairs trading could result in undesirable systematic risk and potential losses. We apply Kalman Filter to intertemporally estimate cointegration coefficients and the absolute standardized residual (ASR) threshold, and relate the ADF-threshold with stochastic discount factors. Backtests confirm our superiority in attaining better risk-to-reward ratios and lower systematic risk.

Introduction

Pairs trading is a relative value arbitrage strategy that has almost two decades’ history on Wall Street (Gatev et al., 2006). The essence of pairs trading is to long-short two co-moving stocks, whose spread is abnormally large. There is rich literature on pairs trading. Pioneered by Gatev et al. (2006), the distance approach is most intensively studied. Vidyamurthy (2004) apply the cointegration approach to build more reliable equilibrium relationship, which is empirically testified by Caldeira and Moura (2013).

Recent studies have come up with more approaches for optimal trading rules. For example, the time series approach (Elliott et al., 2005) and the stochastic control approach (Jurek and Yang, 2007). Chen et al. (2014) use a TAR-GARCH (three-regime threshold autoregressive GARCH) for return spreads, and take the upper and lower regimes as trading signals. In a more recent work, Chen and Lin (2016) propose nonparametric tolerance limits to generate trading signals. Little work has been devoted to ADF (augmented Dickey–Fuller) threshold in cointegration-based pairs trading.

Motivated by Law et al. (2018) on the idea of a single-stage cointegration approach to avoid excessive risk, this paper discovers that static parameterization (rolling regressions and arbitrary thresholds) leads to systematic risk. We propose dynamic parameterization to accommodate different market conditions so that its choice is no longer arbitrary but with sound economic intuition. Empirical evidence shows superior performance of our methods.

Section snippets

Necessary condition for risk-neutral pairs trading

We suppose an arbitrageur formulates a pairs trading portfolio in a d-asset market. Each asset is assumed to be cointegrated with at most one asset. Let Xt denote the n×n pair-position matrix, with row and column indexes corresponding to different assets available. For example, element at the ith row and the jth column is βtij⋅1A⋅−11+1εt>0, if asset i and j are cointegrated with relationship: lnpit=αt+βtijlnpjt+εt,where pit=SitSi0 is the standardized price and Sit is the price of asset i at

Dynamic parameterization for pairs trading

We apply Kalman Filter to dynamically calibrate cointegration coefficients and adjust ASR-thresholds. Furthermore, we use stochastic discount factors (SDF) inferred from rolling panels to design ADF-thresholds.

Data description and assumptions

We take the constituents of TPX100 (the 100 largest Japanese stocks) as trading universe, and a 15-year backtest period from 1-Jan-2006 to 31-Dec-2017 is chosen. According to Law et al. (2018), the former 10 years is already long enough to cover different financial cycles. Our sample further includes more recent market events. For example, the Fed’s rate hike during 2017–2018, the global financial market crash due to COVID-19 in 2020, etc. Borrow cost and transaction cost are assumed to be 0,

Conclusion

In this research, we find that pairs trading entails undesirable systematic risk under static parameterization. We propose dynamic parameterization methods to tackle this problem: dynamic ADF-threshold, adjusted ASR-threshold, and conditional cointegration coefficients obtained from Kalman Filter. Backtests witness both robust improvements in terms of performance and remarkable reduction in systematic risk. Besides, our methods also reduce the effects of initial values of thresholds, making the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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