Retrospective Brownian Bridge Simulation for Strategy Robustness

Summary

The article proposes retrospective simulation as a way to test whether a trading strategy depends too heavily on one realized market path. It generates alternate histories with a non-parametric Brownian bridge approach: daily returns are resampled with replacement, while the first and final prices are held fixed and geometric smoothing brings the paths to the endpoint. The example uses SENSEX data, optimizing an exponential moving average crossover on the in-sample period before evaluating it out of sample and across simulated paths.

The reported crossover beats buy-and-hold in sample but performs poorly out of sample, illustrating the danger of selecting parameters on one history. The article also compares the distributions of simulated returns with observed extremes and estimates VaR and CVaR, noting fat tails and slight negative skew. This is an exploratory framework, not proof that simulated histories represent all plausible markets: endpoint choice and resampling assumptions matter, the sample is finite, and the author notes that the in-sample and out-of-sample periods lack an embargo despite possible residual dependence.

Key ideas

• Resampling historical returns with replacement creates alternate paths while geometric smoothing fixes the terminal price.
• The example optimizes short and long EMA periods on the realized in-sample path, then tests them on later data.
• The selected crossover performs worse out of sample, demonstrating the risk of path-specific parameter fitting.
• Running strategies across many simulated histories can reveal parameter combinations that succeed more consistently.
• The simulated return distribution is used to examine tail risk with VaR and CVaR.
• The method depends on its resampling and endpoint assumptions and does not eliminate model uncertainty.

Tags

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