Comparing Raw Stock Returns with PCA Residuals as Reversal Signals

Summary

The document raises a question about a common cross-sectional mean-reversion approach: remove market-related components from each security’s return, often by projecting returns onto principal components, then trade the residuals as a reversal signal. The author compares this idea with using raw returns directly and reports that, in their analysis, raw returns had a higher cross-sectional correlation with future returns than the residuals did.

The observation challenges the assumption that removing shared variation necessarily improves a reversal signal. The author asks whether the result is generally known and whether it holds throughout the trading day or only at particular times. No dataset details, sample period, statistical estimates, or controls are provided, and the post offers no explanation or resolution. The comparison is therefore a research question rather than evidence that raw returns are generally superior; its result may depend on the assets, measurement choices, market regime, and return horizon.

Key ideas

• A standard mean-reversion approach removes market-related return components before treating residuals as a signal.
• The author reports stronger cross-sectional correlation with future returns for raw returns than for residuals.
• The post asks whether this relationship varies by time of day.
• The observation lacks methodological details and does not establish a general result.

Tags

# Correlation between idiosyncratic residuals and forward returns


# Correlation between idiosyncratic residuals and forward returns












The classic mean-reversion strategy is to calculate an "expected return" (alpha) by computing the raw return for each security and then remove the part which you think is market driven. Statistically you just do a PCA and remove the projection of the return over the sum of eigenspaces. Then you will trade the residuals as a reversion signal.

Today I looked at cross sectional correlation (every stock every day in the same vector) of stock return against the forward returns (return of the stock in the future) and realized that the correlation was better than the correlation between residuals and forward returns.

My question is then: is this fact well known, is that the case all day or just around particular moments? I have a personal explanation but I am curious to see what you think of it.

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