On the fundamental law of active portfolio management: What happens if our estimates are wrong?

The fundamental law of active portfolio management provides profound insights on the value creation process of managed funds and shows how forecasts of alphas or forecasting skills can be transformed into the value-added of an active portfolio. A key weakness of the law and its various extensions is that they ignore the estimation errors associated with the parameter inputs of the law. In this article, the author shows that the estimation errors have a substantial impact on the value-added and can easily destroy all the value promised by the law if not dealt with carefully. To minimize the impact of the estimation errors, the author proposes two methods - scaling and diversification. The scaling method scales the estimated optimal active portfolio by a suitable proportion to maximize the valued-added. The diversification approach suggests holding other portfolios along with the estimated optimal active portfolio in order to diversify away much of the estimation errors. The author shows that the two methods can be effectively used to minimize the impact of the estimation errors so as to substantially improve the valued-added.