We decompose market return variance into a component that covaries with the

stochastic discount factor (SDF) and one that does not. The SDF-orthogonal component—conditional excess volatility—contributes to variance but cannot

earn a risk premium. The ratio γt ≡ μt/σ2t identifies the excess volatility share through γt = eγt(1 − ψt), where ψt is the fraction of variance orthogonal to the

SDF and eγt prices the remaining. Using three distinct estimates of γt across 20

equity markets, we find that γt does not rise in recessions and often declines.

Because standard models uniformly predict countercyclical eγt, this finding

requires the excess volatility share to increase substantially in bad times. Our

empirical results implies that excess volatility constitutes at least half of the

total market volatility in recessions. We show that this mechanism provides a unified explanation for (i) why optimal portfolio weights do not increase in downturns despite rising Sharpe ratios, (ii) why the term structure of Sharpe ratios on dividend claims is downward-sloping, and (iii) why option portfolios with fixed risk quantities earn lower returns at longer horizons.

We study whether a hierarchical vision transformer applied to candlestick-chart images improves cross-sectional return prediction in U.S. equities. Using CRSP data from 1993–2024, we train the model on chart images and evaluate it under an out-

of-sample portfolio protocol. The hierarchical model delivers a stronger and more

stable return ranking than a convolutional benchmark, with gains that persist in a

post-2019 holdout, among large-cap stocks, and after transaction costs. Spanning

regressions show the signal is not subsumed by standard technical indicators or

traded factor portfolios. Synthetic probes and occlusion maps reveal that predictive

content concentrates in recent, reversal-related price structure.

The alpha from a characteristic-sorted top-minus-bottom portfolio is not automatically evidence that the sorting characteristic predicts expected returns. We show that the standard factor-model regression used to estimate the sort alpha is numerically identical to a weighted pooled firm-level OLS regression. Because the pooled OLS estimator combines within-firm and between-firm variation, our Generalized Portfolio Sorts (GPS) framework decomposes the sort alpha exactly into a within-firm prediction alpha and a permanence wedge capturing persistent between-firm composition. For book-to-market, an insignificant sort alpha of 27 bp/month masks a prediction alpha of 142 bp/month (t=4.53) offset by a permanence wedge of -115 bp/month. Across 171 anomalies, 36--42% change significance status when the sort alpha is replaced by the prediction alpha; the permanence wedge is near-invariant across benchmark factor models, with cross-model correlations above 0.99.