Fundamental Indexes As Proxies For Mean-Variance Efficient Portfolios

Abstract

Mean-variance efficiency was first explained by Markowitz (1952) who derived an efficient frontier comprised of portfolios with the highest expected returns for a given level of risk borne by the investor. The assumed mean-variance efficiency of the market portfolio along with the fact that it is capitalization-weighted underlies the rationale for market indexes being constructed by market capitalization weights (Mar, Bird, Casavecchia and Yeung, 2009). The pioneers of the fundamental index approach to investing, Arnott, Hsu and Moore (2005), however differ, and argue that market capitalization-weighted indexes are not mean-variance efficient due to their price-sensitivity, which leads to the overweighting of overvalued stocks and the underweighting of undervalued stocks, creating a return drag. The authors constructed an index weighted by fundamental determinants of firm value such as earnings, book value and revenue, proving that their fundamentally weighted index causes the return drag inherent in capitalization-weighted indexes to disappear. The aim of this paper is to discuss the evidence for and the arguments against fundamentally-weighted indexes as proxies for mean-variance efficient portfolios. We conclude that since the market cap-weighted index is only mean-variance efficient given the efficiency of the market, whilst the fundamental index incurs higher turnover, and may contain a value bias, its resistance to investor overreaction makes it a more valid mean-variance efficient proxy in an inefficient market.