Efficient Indexation: An Alternative to Cap-Weighted Indices

Noël Amenc, Felix Goltz, Lionel Martellini and Patrice Retkowsky

Volume 9, Number 4, Fourth Quarter 2011

This paper introduces a novel method for the construction of equity indices that, unlike their cap-weighted counterparts, offer an efficient risk/return trade-off. The index construction method goes back to the roots of modern portfolio theory and focuses on the tangency portfolio, the portfolio that weights index constituents so as to obtain the highest possible Sharpe ratio. The major challenge is to generate the required input parameters in a robust manner. The expected excess return of each stock is estimated from portfolio sorts according to the stock’s total downside risk. This estimate uses the economic insight that stocks with higher risk should compensate their holders with higher expected returns. To estimate the covariance matrix, we use principal component analysis to extract the common factors driving stock returns. Moreover, we introduce a procedure to control turnover in order to implement the method with low transaction costs. Our empirical results show that portfolio optimization with our robust parameter estimates generates out-of-sample Sharpe ratios significantly higher than those of the corresponding cap-weighted indices. In addition, the higher risk-return efficiency is achieved consistently and across varying economic and market conditions.