Beyond pooling: The role of correlation structures for contemporaneous and lagged cross-asset stock prediction

We examined whether the correlation structure of the training universe affects cross-asset prediction of daily equity returns. Market-neutral residual returns were constructed for 75 S&P 500 stocks across five sectors by regressing daily stock returns against SPY, with market betas estimated using only training-fold data to prevent look-ahead bias. Four training regimes were defined for each target stock using quartiles of pairwise residual correlations: high-correlation, medium-correlation, anti-correlation, and same-sector, plus a pooled baseline. Two pipelines were evaluated: one based on contemporaneous residual correlation and another based on lagged predictive correlation, Corr(εᵢ(t), εₜₐᵣᵠᵉₜ(t+1)), estimated exclusively within each training fold. Ridge regression, Random Forest, and XGBoost were evaluated using three-fold walk-forward TimeSeriesSplit across 10 target stocks and 10 random seeds (9,000 total model fits). BCa bootstrap confidence intervals clustered by target stock showed that no pairwise regime differences were significant under contemporaneous construction, whereas under lagged construction the medium-correlation regime significantly outperformed the high- and anti-correlation regimes despite all regimes producing near-zero or negative out-of-sample R². This pattern is consistent with unstable training-fold predictive correlations that fail to generalize out of sample rather than robust lead-lag structure. Together, both pipelines converge on the same conclusion: correlation structure does not reliably improve cross-asset forecasting performance for daily large-cap U.S. equities, consistent with the Efficient Market Hypothesis.