New Method Estimates Maximum Sharpe Ratio in Massive Asset Universes Without Building the Optimal Portfolio

Researchers Mikhail Chernov, Bryan T. Kelly, Semyon Malamud, and Johannes Schwab have developed a way to estimate how good risk-adjusted performance could be in a very large universe of assets—without actually having to build the “best” portfolio.

In portfolio theory, the maximum attainable Sharpe ratio (expected excess return divided by volatility) is a key benchmark: it represents the best risk-adjusted payoff an investor could, in principle, extract from the available assets. In practice, however, finding this maximum in modern datasets is difficult because it depends on estimating a huge covariance matrix of returns. When the number of assets is large relative to the length of the return history, standard covariance estimates become unstable. The usual remedy is regularization—shrinking or smoothing the covariance estimate. But regularization comes with a cost: it tends to dampen the impact of directions in the data associated with small eigenvalues, which can mechanically understate the maximum Sharpe ratio.

The authors’ contribution is an estimator that targets the maximal Sharpe ratio directly, rather than inferring it from an estimated “efficient” portfolio. Their approach progressively restores the contribution of those small-eigenvalue components that regularization suppresses. The result is a pair of tight bounds—an upper and a lower estimate of the maximum Sharpe—that come with asymptotic confidence intervals, allowing users to quantify statistical uncertainty around the implied frontier.

The paper also revisits a common tool used to create high-Sharpe “benchmark” strategies in empirical finance: ridge-regularized Markowitz portfolios. These portfolios, which explicitly penalize extreme weights, are often treated as practical stand-ins for the theoretically optimal efficient portfolio. The researchers show that this class of ridge-regularized strategies systematically delivers out-of-sample Sharpe ratios below the true maximum—and not merely because of estimation noise. The shortfall, they argue, can be described as an explicit multiplicative factor that does not vanish even as sample sizes grow, implying an enduring gap between what these portfolios achieve and what is feasible in theory.

When the method is applied to U.S. equities, the estimated ceiling is striking. Across a broad equity universe, the authors estimate a maximal annualized Sharpe ratio of about 7.4. Excluding micro-cap stocks reduces the estimate to roughly 5.0, still well above the 1.0 to 4.0 range implied by existing portfolio-based benchmarks in the literature. Adding corporate bonds increases the estimated maximum further, although the improvement is not statistically significant, suggesting the data do not support a clear diversification-driven jump in the ceiling.

The analysis also points to how that “hidden” performance potential is expressed. Portfolios with nonlinear weights dominate those constrained to linear constructions. Meanwhile, firm characteristics proposed after 2004—often introduced as new predictors in the asset-pricing and anomalies literature—add little incremental Sharpe ratio on top of what earlier characteristics already provide.

Malamud acknowledges financial support from the Swiss Finance Institute and the Swiss National Science Foundation (Grant 100018-228042). The work also received computing support via a grant from the Swiss National Supercomputing Centre (CSCS), project ID lp46 on Alps. The authors note that the views expressed are their own and not necessarily those of the National Bureau of Economic Research.

Why it matters

If the maximum achievable Sharpe ratio in large markets is substantially higher than standard benchmarks suggest, then common yardsticks for evaluating investment skill and strategy design may be too conservative. The findings also raise questions about how much performance is being left on the table by widely used regularized Markowitz approaches. What comes next is whether these high theoretical ceilings can be approached in real trading after costs, constraints, and market impact are fully accounted for.