Optimizing Statistical Arbitrage with Stop-Losses and Leverage

Summary

This paper extends a mean-reversion trading framework with stop-loss rules and leverage. It models security prices as an Ornstein–Uhlenbeck process and evaluates repeated trades through a self-financing portfolio, accounting for proportional transaction costs. For each chosen stop-loss level, it derives optimal leverage and market entry and exit thresholds.

The analysis links strategy returns to the chances of reaching those thresholds, expected first-passage times, and expected times for the process to leave a price interval. It gives analytical expressions for exit times under the Ornstein–Uhlenbeck assumption and expresses long-run returns as a function of the stop-loss. An example examines a Heating Oil and Gas Oil futures spread using half-hourly prices over a one-year sample. The findings are model-based and tied to that specific example; the document provides no broader evidence that the strategy will remain profitable in other markets or after implementation frictions beyond the modeled transaction costs.

Key ideas

• The framework adds stop-loss levels and leverage to a mean-reverting statistical arbitrage strategy.
• Optimal leverage and entry and exit thresholds depend on the selected stop-loss level.
• The return analysis uses threshold-reaching probabilities and expected first-passage and first-exit times.
• An Ornstein–Uhlenbeck model allows analytical treatment of interval exit times and long-run returns.
• A Heating Oil and Gas Oil futures spread illustrates the method on half-hourly data from a one-year sample.

Tags

# Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market


# Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market









In this paper we develop a statistical arbitrage trading strategy with two key elements in hi-frequency trading: stop-loss and leverage. We consider, as in Bertram (2009), a mean-reverting process for the security price with proportional transaction costs; we show how to introduce stop-loss and leverage in an optimal trading strategy. We focus on repeated strategies using a self-financing portfolio. For every given stop-loss level we derive analytically the optimal investment strategy consisting of optimal leverage and market entry/exit levels. First we show that the optimal strategy a' la Bertram depends on the probabilities to reach entry/exit levels, on expected First-Passage-Times and on expected First-Exit-Times from an interval. Then, when the underlying log-price follows an Ornstein-Uhlenbeck process, we deduce analytical expressions for expected First-Exit-Times and we derive the long-run return of the strategy as an elementary function of the stop-loss. Following industry practice of pairs trading we consider an example of pair in the energy futures' market, reporting in detail the analysis for a spread on Heating-Oil and Gas-Oil futures in one year sample of half-an-hour market prices.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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