Estimation Error and the Fundamental Law of Active Management: Is Quant Fundamentally Flawed?

Abstract

According to widely referenced applications of the Grinold (1989) Fundamental Law theory, simply adding securities to an optimization universe, adding factors to a forecast return model, trading more frequently, or reducing constraints can add investment value to an optimized investment strategy. The authors show with intuitive discussion followed by Monte Carlo simulation that many applications of Grinold theory for optimized portfolio design are often unreliable and self-defeating. Critical limitations of the theory are due to ignoring estimation error (Michaud 1989) and constraints required in practical applications. A substantial fraction of professional actively managed funds may be negatively impacted.

This article was originally published as “Estimation Error and the Fundamental Law of Active Management” Is Quant Fundamentally Flawed: by Richard Michaud, PhD, David Esch, PhD, and Robert Michaud, and is available at https://www.newfrontieradvisors.com/media/1798/fundamental-law-march-2020.pdf.

TOPICS: Portfolio theory, portfolio construction

Key Findings

• • Estimation error cannot be ignored as a dangerous source of underperformance for quantitative managers, especially when mean-variance optimizers are used to construct portfolios. A substantial proportion of actively managed funds may be impacted by neglecting estimation error.

• • The four implied principles of management often taught as corollary to Grinold’s Fundamental Law of Active Management—(1) more assets in the investment universe, (2) more factors used in forecasting, (3) more frequent trading, and (4) removing constraints from optimizations—are not necessarily additive in the presence of estimation error and can harm out-of-sample performance when applied aggressively, contrary to the guidance of the Fundamental Law formulas.

• • Grinold’s formulation of the Fundamental Law is often taught as fact by many institutional education programs. The real-world failure of many of the necessary conditions for the mathematical proof are seldom included in finance curricula but should be noted.