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

According to widely referenced applications of the Grinold (1989) “Fundamental Law” theory, simply adding more securities to an optimization universe, adding more factors to a forecast return model, trading more frequently, or reducing more constraints can add investment value to an optimized investment strategy. We show with intuitive discussion followed by a novel simulation study that applications of the Grinold theory for optimized portfolio design are often unreliable and self-defeating. Critical limitations 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