Non-linear dependence modelling with bivariate copulas: statistical arbitrage pairs trading on the S&P 100

ABSTRACT

We develop a copula-based pairs trading framework and apply it to the S&P 100 index constituents from 1990 to 2014. We propose an integrated approach, relying on copulas for pairs selection and trading. Essentially, we fit t-copulas to all possible combinations of pairs in a formation period. Next, we trade these pairs in-sample to assess the profitability of mispricing signals derived from t-copulas. The top pairs are transferred to an out-of-sample trading period, and traded with individualized exit thresholds. In particular, we differentiate between pairs exhibiting mean-reversion and momentum effects and apply idiosyncratic take-profit and stop-loss rules. For the top 5 mean-reversion pairs, we find out-of-sample returns of 7.98% per year; the top 5 momentum pairs yield 7.22% per year. Standard deviations are low, leading to annualized Sharpe ratios of 1.52 (top 5 mean-reversion) and 1.33 (top 5 momentum), respectively.

KEYWORDS:

• Statistical arbitrage
• pairs trading
• quantitative strategies
• copula

JEL CLASSIFICATION:

• G11
• G12
• G14

Acknowledgements

We are grateful to Thomas Fischer, Ingo Klein, Benedikt Mangold, and two anonymous referees for many helpful discussions and suggestions on this topic.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Strictly speaking, the 1-month pseudo-trading period is a 1-month signal-generation period. After each signal, we monitor the cumulative return for the subsequent 120 days.

² This relaxation is introduced to ensure that we always have k pairs available for trading. However, relaxations rarely happen. On average 1–2% of all pairs exhibit a Spearman’s ${\rho }_{min}$ of at least 0.6.

³ We thank Kenneth R. French for providing all relevant data for these models on his website.

⁴ The annualized Sharpe ratio has been calculated from Table 3.