An Evaluation of Alternative Equity Indices - Part 1: Heuristic and Optimised Weighting Schemes

Abstract

There is now a dazzling array of alternatives to the market-cap approach to choosing constituent weights for equity indices. Using data on the 1,000 largest US stocks every year from 1968 to the end of 2011 we compare and contrast the performance of a set of alternative indexing approaches. The alternatives that we explore can be loosely categorised into two groups. First, a set of weighting techniques that Chow et al (2011) describe as “heuristic.” The second set are based upon “optimisation techniques,” since they all require the maximisation or minimisation of some mathematical function subject to a set of constraints to derive the constituent weights. We find that all of the alternative indices considered here would have produced a better risk-adjusted performance than could have been achieved by having a passive exposure to a market capitalisation-weighted index. However, the most important result of our work stems from our ten million Monte Carlo simulations. We find that choosing constituent weights randomly, that is, applying weights that could have been chosen by monkeys, would also have produced a far better risk-adjusted performance than that produced by a cap-weighted scheme.

Keywords: Alternative equity indices, risk-adjusted performance, Monte Carlo simulation

JEL Classification: G11,12