Equity Index Research
 | Performance of Socially Responsible Investment Funds against an Efficient SRI Index: The Impact of Benchmark Choice when Evaluating Active Managers
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Performance measurement of socially responsible investment (SRI) has been the subject of numerous studies in various countries. However, the conclusions of performance assessments always depend on the choice of the reference index one uses. SRI criteria lead to a reduction of the stock universe. Typical SRI indices respect such screenings and then simply weight the acceptable stocks by market cap, or alternatively by sustainability scores. They thus ignore the risk/return properties of stocks and in particular the correlations. Consequently, they do not necessarily reflect the performance available from a well-diversified portfolio of SRI-compliant stocks. Efficient SRI indices on the other hand, apply an optimal weighting scheme to the screened universe. They thus constitute a relevant proxy for the performance that is achievable through a sole focus on improving diversification within an SRI universe. In that sense they constitute a useful yardstick for active SRI funds from which investors would at least expect improved diversification, if not additional value added through stock picking. Given that such efficient SRI indices are also easy to replicate at low cost, they constitute investable alternatives to actively managed funds, and are thus relevant for practical comparisons of performance.
This paper conducts a performance measurement of SRI funds and assesses the impact of changing the reference from a standard SRI index to an efficient SRI index. The analysis of fund performance shows that an efficient SRI index raises the bar for actively managed SRI funds. While about 60% of funds have a positive information ratio when compared to the cap-weighted EuroStoxx Sustainability Index, only about 25% of funds do so with respect to the Efficient SRI Index. It is also interesting to note that the median information ratio across funds is slightly positive (0.05) when using the standard SRI index, but it is clearly negative (-0.22) when using the Efficient SRI index.
 | What Drives the Performance of Efficient Indices? The Role of Diversification Effects, Sector Allocations, Market Conditions, and Factor Tilts
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Capitalisation-weighted indices are known to suffer from problems associated with high concentration; they fail to take full advantage of the diversification opportunities offered by equity markets. Efficient indices draw on portfolio construction techniques to provide risk/return tradeoffs better than those of their cap-weighted counterparts. Efficient indices provide significant improvements of risk/return properties across different regions and various economic and market conditions. This paper, then, provides a detailed comparison of the performance of efficient indices and that of the respective cap-weighted indices to account for the sources of this outperformance.
The efficient index is built on the concept of finding a proxy for the tangency portfolio by maximising the Sharpe ratio, and better diversification is a major contributor to the performance of efficient indexation. Efficient indices are at their best when market conditions reward optimal diversification strategies, that is, when cap-weighted indices tend to be most heavily concentrated and when correlations are stable. In addition, we look at the way sector performance contributes to the overall performance of both efficient and cap-weighted indices. Unlike that of the cap-weighted index, the performance of efficient indices is driven more by better diversification across stocks than by shifts in sector weights. Finally, an analysis of the equity risk factor exposures for both efficient and cap-weighted indices confirms that—though exposures of efficient indices are obviously different from those of cap-weighted indices—the performance of efficient indices cannot be explained entirely by simple factor tilts. On the whole, our results suggest that improved diversification is a key source of the outperformance of efficient indexing.
 | Scientific Diversification in Practice: Reactions to EDHEC-Risk Efficient Indices
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Capitalisation weighting in equity index construction has come in for harsh criticism of late. Our research into efficient indexation returns to the roots of modern portfolio theory to provide an alternative to current methods of constructing equity indices. In 2010, as it happens, EDHEC-Risk Institute launched a set of efficient equity indices as an alternative to cap-weighted indices. The aim of these indices is to be more risk/reward efficient than cap-weighted indices (see Amenc et al. 2010 for a description of the method). The constituent weights in the index are obtained from a formal Sharpe ratio maximisation, thus taking into account expected returns, volatilities, and the correlation of constituent stocks. The index series is based on all constituent securities in the FTSE All-World Index Series. The recent launch of a worldwide index series using the efficient weighting includes indices on the main countries (US, Japan, UK) and regions (Europe, Asia Pacific, etc.); it also includes worldwide indices (All World, Emerging Markets, etc). To assess industry views of this initiative, we surveyed asset managers and investors. This document begins with an overview of efficient indexation and then outlines the reactions received from survey respondents.
 | Improved Beta? A Comparison of Index-Weighting Schemes
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This paper analyses a set of equity indices whose aim is to improve on capitalisation weighting and thus to provide “improved beta”. Four main weighting schemes are analysed: efficient indices, fundamental indices, minimum-volatility indices, and equal-weighted indices. Empirical results for US and Developed World data on these indices show that the average returns of all four alternative index construction methods are superior to those of cap-weighted equity indices in both universes and that, by several measures of risk-adjusted performance, they are likewise superior. We also analyse factor exposures of alternative weighting schemes. Only the fundamental index has a value exposure that is substantially greater than that of the equal-weighted index. Other non-cap-weighted indices such as efficient indexation and minimum volatility have value exposures that are comparable to that of equal weighting. Since the indices studied here are made up of large-cap stocks, none of these indices shows any economically meaningful bias towards small caps. Interestingly, the minimum-volatility index, similar to the cap-weighted indices, shows a negative small-cap exposure since it favours the largest stocks.
 | 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.
