Optimal Sharpe Ratio Portfolios and the Role of Perfect Foresight into Returns, Volatilities, and Correlation

Using CRSP daily returns for the 1,000 largest U.S. equities from 1968 to 2017, we examine which forecasting task matters most for Sharpe-optimal portfolio construction: returns, volatilities, or correlations. We introduce the Optimal Sharpe Ratio (OSR) portfolio, an expost boundary condition that selects portfolio weights to maximize the Sharpe ratio over the next calendar year, using that year's realized daily return path and realized covariance matrix, subject to long-only and concentration constraints (including a 5% maximum weight per stock). OSR is not investable and is used only to map what is theoretically achievable under the stated constraints. Comparing OSR to counterfactual portfolios with perfect foresight of only one input at a time and to a return-foresight "Top 20" selection benchmark, we find that correlation and covariance information account for most of the attainable improvement in Sharpe efficiency. Even with perfect foresight of next year's best-performing stocks, return-first selection often reduces diversification and imposes a selection penalty (the Sharpe loss from concentrating in highly correlated names). We define the efficiency gap as the difference between OSR efficiency and the efficiency delivered by common allocation approaches under the same constraints. The practitioner implication is that the highest payoff for improving risk-adjusted outcomes typically comes not from marginally better winner identification but from correlation-aware portfolio construction, including covariance modeling and correlation-sensitive constraints that preserve diversification while pursuing return opportunities.