Optimizing Entry and Exit Thresholds for an Ornstein–Uhlenbeck Strategy

Summary

This document describes an analytical method for choosing entry and exit levels in a statistical arbitrage strategy whose log price follows an exponential Ornstein–Uhlenbeck process. The trade cycle runs from an entry level to an exit level and back to the entry level. The method uses first-passage-time results to derive the expected duration and its variance, then relates these to return and risk per unit of time.

Bertram’s framework optimizes thresholds for either expected return or Sharpe ratio, accounting for transaction costs and, for the Sharpe objective, a risk-free rate. It gives a symmetry condition around the process’s long-term mean, reducing the two-threshold search to one variable, and includes parameter fitting and metric calculation procedures. The document also provides example outputs and plots, but these are illustrative rather than evidence of out-of-sample performance. Results depend on the assumed mean-reverting process and its parameter estimates; transaction costs, model fit, and real-world trading frictions can limit practical applicability.

Key ideas

• The model assumes log price follows an Ornstein–Uhlenbeck process around a long-term mean.
• A completed trade cycle moves from an entry threshold to an exit threshold and back.
• First-passage-time formulas estimate the expected cycle duration and its variance.
• Thresholds can be optimized for expected return or Sharpe ratio per unit of time.
• The optimal exit level is symmetric to the entry level around the long-term mean under the stated model.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.