Log Returns

Log returns eliminate the asymmetry problem found in simple returns. For a round trip from 100 to 120 and back to 100, the log returns are equal in magnitude and opposite in sign. Log returns are time-additive across multiple periods. The sum of log returns for a no-change round trip is exactly zero. Log returns normalize for scale and support aggregation across time windows and strategies. Modeling movements makes the data more statistically reliable and reveals patterns such as mean reversion. Modeling price movements helps estimate extreme price swings for drawdown management and leverage deployment. The professional strategy operates on log returns rather than price levels. For small moves, log returns are approximately interpretable like simple percentage returns, but their additive property is unique. The model target is the close price log return. A negative log return means price fell, while a positive log return means price rose. The sum of log returns over any period equals the log of the total compound growth factor. Dividing price by its lag computes the multiplicative return between consecutive periods. Renaissance models price movements rather than absolute price lev…