Equity Index Research
 | Does Finance Theory Make the Case for Capitalisation-Weighted Indexing?
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Proponents of cap-weighted stock market indices often argue that such indices provide efficient risk/return portfolios. This paper reviews the evidence in the academic literature and concludes that only under very unrealistic assumptions would such indices be efficient investments. In the presence of realistic constraints and frictions, cap-weighted indices cannot, according to the academic literature, be expected to be efficient investments.
The three main conclusions of the research are the following:
- A cap-weighted stock market index is not the market portfolio of financial theory (the Capital Asset Pricing Model (CAPM) theory is often evoked to show that cap-weighted stock market indices are efficient portfolios and attractive investments). That it is not is clear from the choices made in empirical studies that attempt to come up with reasonable proxies for the market portfolio. These studies attach great importance to including many more stocks than indices do, and their proxies of the market portfolio include bonds, real estate, and non-tradable assets such as human capital.
- Even if it were possible to construct and hold the market portfolio, the theory does not predict that the market portfolio is efficient unless we make highly unrealistic assumptions. In fact, the authors of the seminal academic research in the 1950s and 1960s, Harry Markowitz and William Sharpe, have themselves emphasised (Sharpe (1991) and Markowitz (2005)) that the market portfolio may not be efficient in a more realistic setting.
- In view of these arguments, financial theory alone does not justify the current practice of capweighting. In fact, from a theoretical perspective, cap-weighted stock market indices seem to offer no particular advantage.
 | Efficient Indexation: An Alternative to Cap-Weighted Indices
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The aim of efficient indexation is to improve the risk-reward ratio of a broadly diversified stock market portfolio compared to the cap-weighted index. To generate such an efficient index, we resort to mean-variance optimisation. Although our aim to maximise risk-return efficiency is fully consistent with financial theory, successful implementation of the theory depends not only on its conceptual grounds but also on the reliability of the input to the model. In our case, the results depend greatly on the quality of the parameter estimate (the covariance matrix and the expected returns of all stocks in the index).
The standard CAPM theory, as it happens, is a poor guide to the input parameters. For the CAPM, expected returns should be proportional to the stock's beta, though it has in fact been shown that such a relationship does not hold. Likewise, the single-factor nature of the CAPM would mean that there is a single (market) factor driving the correlation of stocks, whereas the consensus in both academe and business is that multifactor models do a better job capturing the common drivers behind stock comovements.
We generate proxies for tangency portfolios that rely on robust input parameters for both the covariance matrix and expected returns. One challenge is the estimation of expected return parameters. Instead of relying purely on statistics, which is known to generate poor expected return estimates, we use a common sense estimate of expected returns that relies on a risk-reward trade-off. We use the insight that the return on a given stock in excess of the risk-free rate is proportional to the riskiness of the stock. Investors are often underdiversified and averse not only to systematic risk but also the specific risk of a stock. Investors shun the volatility, negative skewness, and kurtosis of a stock's returns. We use a suitably designed risk measure that integrates these aspects and estimate expected returns by sorting stocks into high risk and low risk categories. The second central ingredient in the tangency portfolio is an estimate of the covariance of stock returns. We use a robust estimation procedure that first extracts the common factors of stock returns and then uses these factors to model the comovement of individual stocks. This efficient indexation procedure allows us to construct indices whose risk/reward ratio is significantly better than that of cap-weighted indices.
 | Towards the Design of Better Equity Benchmarks: Rehabilitating the Tangency Portfolio from Modern Portfolio Theory
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Following recent research on the relevance of idiosyncratic risk in asset pricing models, this paper proposes to use total volatility as a model-free estimate of a stock's excess expected return, and analyze the implications in terms of the design of improved equity benchmarks. It finds that maximum Sharpe ratio portfolios consistent with such expected return proxies, and built upon improved estimates of the correlation parameters, significantly outperform market cap weighted schemes on a risk-adjusted basis. This analysis, which rehabilitates the role of the tangency portfolio from modern portfolio theory, suggests that better equity benchmarks can be designed, provided that a sophisticated portfolio optimization procedure is used that relies on robust estimates of moments and co-moments of stock return distributions. This paper has important potential implications for the ongoing debate on appropriate weighting schemes for equity indices.
A revisited version of this paper was published in the Summer 2008 issue of the Journal of Portfolio Management.
 | Fundamental Differences? Comparing Alternative Index Weighting Mechanisms Noël Amenc, Felix Goltz, Véronique Le Sourd April 2008 |
While an ever increasing share of equity assets is invested in indexing strategies, the standard practice of using capitalisation weighting to construct stock market indices has been the object of much criticism. In response to this criticism, equity indices with different weighting schemes have emerged. Some indices use "fundamental" metrics (Arnott, Hsu, and Moore 2005) to weight the component stocks. In recent years, the market for such characteristics-based indices has grown tremendously, with more and more providers launching and offering them. Institutional investors have allocated significant amounts to these alternatives to value-weighted indices. Likewise, a wide range of exchange-traded funds on these new indices is now available.
 | A Comparison of Fundamentally Weighted Indices: Overview and Performance Analysis
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This paper analyses a set of characteristics-based indices that have recently been launched on the US market and have been said to outperform standard market cap-weighted indices over particular backtest samples. The EDHEC-Risk authors, Noël Amenc, Felix Goltz and Véronique Le Sourd, analyse the performance of an exhaustive list of such indices and show that the outperformance over value-weighted indices may be negative over long time periods and that characteristics-based indices do not significantly outperform simple equal-weighted indices. Furthermore, an analysis of both the style exposures and the sector exposures of characteristics-based indices reveals a significant value tilt. When properly adjusting for this tilt, these indices do not show any abnormal performance.
A revisited version of this paper was published in the February 2009 issue of European Financial Management.
 | Reactions to the EDHEC study "Assessing the Quality of Stock Market Indices"
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A recent publication by EDHEC-Risk has drawn conclusions that highlight the shortcomings of well known capitalisation- or price-weighted stock market indices and argues that the choice of benchmark for asset allocation or performance measurement is a task requiring particular care.
In a call for reactions to this publication, EDHEC-Risk finds that the answers of the more than eighty respondents (asset management firms, pension funds, insurance companies, private banks, etc.) tend to reinforce the conclusions drawn by the original publication.
Although it would at first appear that the majority of respondents are not, in general, dissatisfied with the indices they use as benchmarks (18.82% of respondents express degrees of dissatisfaction), further examination soon reveals that the shortcomings of these indices, such as inefficiency, lack of stability, and susceptibility to price bubbles, are widely recognised by the industry professionals responding to EDHEC-Risk's call for reactions. The call for reactions also shows that a considerable majority of respondents plan to review the indices they use as benchmarks, either immediately or in the future.
 | Assessing the Quality of Stock Market Indices: Requirements for Asset Allocation and Performance Measurement
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For the vast majority of European institutional investors, constructing a benchmark and measuring the performance of their portfolio in relation to the benchmark are central to their investment process. And, very often, the chosen benchmark is a market index and/or a combination of market indices.
Since their design is not affected by the securities chosen by managers and since they benefit from the sound reputation of major financial institutions, credit rating agencies and major international stock exchanges, market indices appear to be the ultimate reference not only for strategic allocation but also as a measure of investment management performance. Evaluating the quality of these indices as a benchmark is therefore a question that is essential to institutional investors.
It is the importance of this question that led Af2i (French association of institutional investors) and EDHEC-Risk to carry out research on the main market indices used by European investors.
This work received the support of BNP Paribas Asset Management and UBS Global Asset Management.
