In this paper we develop a statistical arbitrage trading strategy with twokey elements in hi-frequency trading: stop-loss and leverage. We consider, asin Bertram (2009), a mean-reverting process for the security price withproportional transaction costs; we show how to introduce stop-loss and leveragein an optimal trading strategy. We focus on repeated strategies using a self-financing portfolio. For everygiven stop-loss level we derive analytically the optimal investment strategyconsisting of optimal leverage and market entry/exit levels. First we show that the optimal strategy a' la Bertram depends on theprobabilities to reach entry/exit levels, on expected First-Passage-Times andon expected First-Exit-Times from an interval. Then, when the underlyinglog-price follows an Ornstein-Uhlenbeck process, we deduce analyticalexpressions for expected First-Exit-Times and we derive the long-run return ofthe strategy as an elementary function of the stop-loss. Following industry practice of pairs trading we consider an example of pairin the energy futures' market, reporting in detail the analysis for a spread onHeating-Oil and Gas-Oil futures in one year sample of half-an-hour marketprices.
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