Managing Portfolios Across the Return Distribution

We develop a dynamic portfolio-choice framework in which investors target the region of the payoff distribution that the portfolio is designed to improve. Out of sample, the estimated policies form an ordered frontier: the policy focused on the downside delivers the strongest left-tail protection and the highest Sharpe ratio, while the policy focused on the upper quantile earns the highest mean return. The gains over volatility-managed portfolios are concentrated in periods when downside-tail dispersion is high. Evidence from fund flows in income, growth and downside protection products supports the interpretation of the quantile index as a reduced-form mandate measure.