Systematic risk in pairs trading and dynamic parameterization☆
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 denote the pair-position matrix, with row and column indexes corresponding to different assets available. For example, element at the th row and the th column is , if asset and are cointegrated with relationship: where is the standardized price and is the price of asset 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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