Comparing Historical Trade Returns with a Lognormal Projection

Summary

This indicator estimates the expected value of a long trade held for a fixed number of bars in two ways. Its empirical engine repeatedly samples overlapping historical trades, optionally applying take-profit and stop-loss rules, then calculates average return, dispersion, win rate, and an annualized Sharpe ratio. Its theoretical engine estimates drift and volatility from recent log returns and uses the resulting lognormal distribution to calculate expected simple return, standard deviation, and probability of gain directly.

The document explains how differences between the estimates can reveal trends or distribution shapes that a random-walk model misses. It also describes the endpoint projection and the annualization settings needed for Sharpe calculations. The historical samples overlap heavily, so the effective number of independent observations is much smaller than the raw sample count; the historical win rate and Sharpe should be treated as uncertain. The theoretical estimate assumes independent normally distributed log returns, and the projection is an endpoint distribution rather than a forecast path.

Key ideas

• The indicator compares repeated historical trade outcomes with a lognormal model calibrated on recent returns.
• Closed-form lognormal formulas provide expected return, standard deviation, and win probability without random path simulation.
• Take-profit and stop-loss settings affect the historical replay, which checks the stop before the target when both are touched in one bar.
• Overlapping historical trades are dependent, making apparent sample sizes overstate the amount of independent evidence.
• The lognormal model assumes independent normal log returns and does not capture clustering, fat tails, or persistent trends.

Tags

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