Beyond Point Forecasts: Tail Information and Equity Portfolio Formation

We propose a directional tail-based stock-selection method using conditional return distributions to examine how distributional information revealed by machine learning prediction models can be translated into investment value for long–short portfolios, and why this value may persist despite arbitrage competition. Existing research on machine learning asset pricing primarily focuses on conditional mean prediction. Although recent studies incorporate quantiles, predictive probabilities, and uncertainty information, they have not fully established how different parts of the return distribution should inform long and short decisions separately, or how the incremental value of distributional information arises through portfolio returns and joint risk. To address these limitations, we aggregate quantile endpoints calibrated using historical errors across multiple coverage levels to construct separate upperand lower-tail measures, and combine them with the cross-sectional ranks of point forecasts to form directional stock-selection signals. In a sample of U.S. stocks from 1992 to 2024, the method increases full-sample gross Sharpe ratios for both equal- and value-weighted portfolios across ten machine learning prediction models: the model averages rise from 2.411 to 2.781 and from 0.902 to 1.251, respectively. Further leg-level analysis shows that improvements in equal-weighted portfolios arise primarily from covariance-based risk offsets between the long and short legs, whereas improvements in value-weighted portfolios more strongly reflect the combined effects of directional returns and risk matching. Our economic mechanism analysis finds that the method jointly uses conventional return characteristics and information related to idiosyncratic volatility, liquidity, and trading frictions, linking directional selection of high-risk stocks to overall portfolio risk management. Realizing these investment opportunities often requires specialized resources, including securities-lending supply, financing capacity, risk capital, and trade execution capabilities. Thus, even when market participants can identify the relevant return information, implementation constraints may limit the speed with which arbitrage capital eliminates its investment value. These findings reveal the portfolio decision value of conditional return distributions and provide new empirical evidence on return predictability and limits to arbitrage in machine learning asset pricing.