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Equity Index Research

The Impact of Risk Controls and Strategy-Specific Risk Diversification on Extreme Risk
Lixia Loh, Stoyan Stoyanov
August 2014

This paper furthers the previous analysis by examining the potential tail-risk impact of including country or sector neutrality, tracking error control and strategy-specific risk diversification in smart beta design. The analysis is performed over the ten-year period ending December 2013 for a variety of indices across developed investment universes and the full-range of diversification strategies offered by ERI Scientific Beta. The authors find no evidence that controlling for country or sector risk increases tail risk, whether in terms of absolute or relative returns. Tracking error controls and the diversification of weighting-scheme specific risk by way of equal-weighting the five basic strategies are found to reduce the total tail risk of relative returns (primarily by reducing tracking error itself). This study thus shows that it is possible to impose country or sector risk neutrality on smart beta indices with no adverse impact on tail risk and that tracking error control and the ERI Scientific Beta multi-strategy approach reduce the tail risk of relative returns.



Tail Risk of Smart Beta Portfolios: An Extreme Value Theory Approach
Lixia Loh, Stoyan Stoyanov
July 2014

This paper looks at whether the outperformance of smart beta - which typically is demonstrated by advertising a superior Sharpe ratio (i.e. a volatility-risk adjusted performance measure) - persists when one takes extreme risk (i.e. skewness and kurtosis) into account. The authors use the Smart Beta 2.0. framework and the ERI Scientific Beta platform to study the tail risk of smart beta indices for a variety of weighting schemes and factor tilts over the last ten years and across developed investment universes using a methodology which captures the tail behaviour of portfolio losses having explained away the dynamics of volatility (an extension of the GARCH-EVT model introduced in Tail Risk of Equity Market Indices: An Extreme Value Theory Approach, February 2014). Their main finding is that the total extreme risk (relative risk) of diversification strategies is primarily driven by their average volatility (tracking error), which indicates that alternative weighting schemes can deliver superior performance as evidenced by Sharpe or information ratios without increased extreme risks (left tail thickness). The authors also find that factor-tilting produces tail-risks in the total returns of equally-weighted portfolios that are in line with those of cap-weighting, but can produce economically small but statistically significant residual tail risk in relative returns. The latter caveat notwithstanding, this study shows that, at least as far as the ERI Scientific Beta indices are concerned, the over-performance of smart-beta does not come at the cost of higher extreme risk.



Risk Allocation, Factor Investing and Smart Beta: Reconciling Innovations in Equity Portfolio Construction
Noël Amenc, Romain Deguest, Felix Goltz, Ashish Lodh, Eric Shirbini
July 2014

This publication argues that current smart beta investment approaches only provide a partial answer to the main shortcomings of capitalisation-weighted (cap-weighted) indices, and develops a new approach to equity investing referred to as smart factor investing. It provides an assessment of the benefits of simultaneously addressing the two main shortcomings of cap-weighted indices, namely their undesirable factor exposures and their heavy concentration, by constructing factor indices that explicitly seek exposures to rewarded risk factors while diversifying away unrewarded risks.

The results we obtain suggest that such smart factor indices lead to considerable improvements in risk-adjusted performance. For long-term US data, smart factor indices for a range of different factor tilts roughly double the Sharpe ratio of the broad cap-weighted index. Outperformance of such indices persists at levels ranging from 2.92% to 4.46%, even when assuming unrealistically high transaction costs. Moreover, by providing explicit tilts to consensual factors, such indices improve upon many current smart beta offerings where, more often than not, factor tilts result as unintended consequences of ad hoc methodologies. In fact, this publication shows that by using consensual results from asset pricing theory concerning both the existence of factor premia and the importance of diversification, it is possible to go beyond existing smart beta approaches which provide partial solutions by only addressing one of these issues.



Index Transparency – A Survey of European Investors’ Perceptions, Needs and Expectations
Noël Amenc, Frédéric Ducoulombier
March 2014

Between August and November 2013, EDHEC-Risk Institute surveyed 109 institutional investors from across Europe, including Europe’s largest pension and reserve funds, insurance and provident institutions and their asset management subsidiaries, to document their expectations and requirements with respect to index transparency and take stock of their perceptions of, and the extent of their support for, the main directions of the ongoing regulatory debate on indexing and financial benchmarks.



Tail Risk of Equity Market Indices: An Extreme Value Theory Approach
Lixia Loh, Stoyan Stoyanov
February 2014

Value-at-risk (VaR) and conditional value-at-risk (CVaR) have become standard choices for risk measures in finance. Both VaR and CVaR are examples of measures of tail risk, or downside risk, because they are designed to exhibit a degree of sensitivity to large portfolio losses whose frequency of occurrence is described by what is known as the tail of the distribution: a part of the loss distribution away from the central region geometrically resembling a tail. In practice, VaR provides a loss threshold exceeded with some small predened probability, usually 1% or 5%, while CVaR measures the average loss higher than VaR and is, therefore, more informative about extreme losses. An interesting challenge is to compare tail risk across different markets. Our paper differs from existing studies in a number of ways. First, we use a much larger global data set and examine left and the right tail of the market index returns in 22 developed and 19 emerging markets. Unlike previous studies, we compare the left and the right tails of different stock markets by carrying out out-of-sample analyses using both VaR- and CVaR-based tests over the full samples and in the period from Jan-2003 to Jun-2013 for which data is available for all markets. We consider three tail probability levels in the calculation of VaR and CVaR: 1%, 2.5%, and 5%.



The Local Volatility Factor for Asian Stock Markets
Lixia Loh, Lionel Martellini, Stoyan Stoyanov
August 2013

The study finds strong evidence for a very significant local volatility factor in the Asian market index returns. In particular, the analysis reveals that the relationship between the Asian equity index returns and the Asian model-free option-implied (MFOI) volatility indices is significantly stronger than the relationship between Asian equity index returns and VIX. The analysis suggests either a weaker or insignificant relationship between the Asian equity market returns and the US VIX in the presence of Asian volatilities, implying that the Asian volatility indices can absorb the information content of the VIX. This research calls into question the conclusions of previous academic studies and especially the popular idea with professionals that in a period of strong turbulence the recorrelation of the markets and their volatility would suggest the use of a very liquid contract like the VIX futures, which would thereby play a role of global protection against the strong risks of volatility, whatever the portfolios’ geographical exposure.



Tail Risk of Asian Markets: An Extreme Value Theory Approach
Lixia Loh, Stoyan Stoyanov
August 2013

This paper aims to draw inference about the tail behaviour of different markets through the fitted parameters of a GARCH-EVT model, with an emphasis on Asian markets. The empirical results indicate that the tail thickness is time-varying but there is no regional structure in the tail risk across the different regions. The comparison of the in-sample and out-of-sample tail risk measures, however, reveals higher tail risk for Asian markets indicating that the key difference over the long run is in the levels of volatility rather than in the residual tail thickness. The findings highlight the importance of volatility modelling for tail risk estimation in the time domain and across regions.



Smart Beta 2.0
Noël Amenc, Felix Goltz, Lionel Martellini
June 2013

Recent years have seen increasing interest in new forms of indexation, referred to as Smart Beta strategies. Investors are attracted by the performance of these indices compared to traditional cap-weighted indices. However, by departing from cap-weighting, Smart Beta equity indices introduce new risk factors for investors, and no sufficient attention is presently given to the evaluation of these risks. In addition, the Smart Beta market appears to be inefficient today, due to restricted access to information, as well as lack of independent analysis. This paper puts forth a new approach to Smart Beta Investment, called the Smart Beta 2.0 approach. In fact, a first important step towards a better understanding of Smart Beta strategies is to conduct proper analysis of risk and performance of Smart Beta strategies rather than relying on demonstrations of outperformance typically conducted by the providers of the strategies. Secondly, Smart Beta 2.0 allows investors to not only assess, but also to control the risk of their investment in Smart Beta equity indices. Rather than only proposing pre-packaged choices of alternative equity betas, the Smart Beta 2.0 approach allows investors to explore different Smart Beta index construction methods in order to construct a benchmark that corresponds to their own choice of risks. In particular, we discuss the following types of risk: i) exposure to systematic risk factors (which can be managed through stock selection decisions or factor constraints); ii) exposure to strategy specific risk (which can be managed by diversifying across strategies); and iii) relative performance risk with respect to traditional market cap-weighted benchmarks (which can be managed through tracking error control).




Diversifying the Diversifiers and Tracking the Tracking Error: Outperforming Cap-Weighted Indices with Limited Risk of Underperformance
Noël Amenc, Felix Goltz, Ashish Lodh, Lionel Martellini
Journal of Portfolio Management, Spring 2012

A number of quantitative or fundamental weighting schemes have been shown to produce robust outperformance with respect to standard cap-weighted equity indices over long time periods. Over periods ranging from a few months to a few years, however, such alternative weighting schemes can generate substantial downside risk relative to cap-weighted indices, which would be a source of concern for most investment managers or chief investment officers. In this article, the authors focus on two reasonable proxies for well-diversified, efficient frontier portfolios, namely, the maximum Sharpe ratio (MSR) portfolio and the global minimum volatility (GMV) portfolio. They address the question of how to use these building blocks to design an improved equity benchmark while satisfying target levels of average and extreme tracking error with respect to cap-weighted indices. The authors find that robust proxies for the GMV portfolio provide defensive exposure to equity that does well in adverse market conditions, while robust proxies for MSR portfolios provide greater access to the upside of equity markets. Because the relative performance of these two diversification approaches depends on market conditions, they expect a combination of both approaches to lead to a smoother conditional performance and higher probability of outperformance of the cap-weighted index, an intuition that is confirmed in empirical tests. Empirical analysis also suggests that “diversifying the diversifiers” still leads to high levels of relative downside risk, in particular when the performance of cap-weighted indices is unusually strong. In this context, the authors introduce an explicit relative risk control mechanism designed to reduce the consequences of severe short-term underperformance with respect to the cap-weighted index and confirm through out-of-sample empirical tests that “tracking the tracking error” would allow investors to achieve better access to outperformance per unit of extreme relative risk taken. Overall, the results reported in this article suggest that it is possible to achieve robust outperformance versus cap-weighted indices by diversifying model risk and by controlling relative risk compared to the cap-weighted indices.




EDHEC-Risk Asian Index Survey 2011
Noël Amenc, Felix Goltz, Masayoshi Mukai, Padmanaban Narasimhan, Lin Tang
May 2012

This is the first comprehensive survey of Asian investment professionals that identifies the criteria investors use to assess and select stock and bond indices, measures satisfaction of Asian investors with existing indices, and documents their segmentation practices. It includes comparisons with results from sister surveys of European and North-American investors.

The 127 Asian investment professionals, representing asset managers, institutional investors, investment consultants, and private wealth managers, who responded to the survey are principally from the three asset management hubs in the Asia Pacific region (Australia, Singapore and Hong Kong), but a wide range of other countries are represented, including India, China, Japan and New Zealand.

This new survey-based evidence will be useful to Asian investors who wish to benchmark their indexation practices to research advances as well as to the practices of their peers in the region and globally. It will also provide much-needed information to providers of investment solutions who want to better address the needs of Asian investors.




EDHEC-Risk North American Index Survey 2011
Noël Amenc, Felix Goltz, Lin Tang, Vijay Vaidyanathan
April 2012

As the choice of an index is a crucial step in both asset allocation and performance measurement, it is useful to investigate index use and perceptions about indices. The EDHEC-Risk North American Index Survey 2011 aims to analyse the current uses of and opinions on stock, bond and equity volatility indices. While information on index vehicles is widely available, particularly in the case of exchange-traded vehicles, the objective of the survey is to provide unique insight into the users’ perspective in the index industry, not only including a description of the current practices, but also user perceptions on different indices and on benefits and drawbacks of index construction methodologies. Furthermore, there is a growing body of research on index construction and index use. Recent studies assess current indices and also propose alternative approaches to construct indices. This survey also serves as a tool to explore views of institutional index users on the conclusions of the literature in financial research.

The survey elicited responses from 139 North American investment professionals. Overall, the respondents represent approximately $12 trillion worth of assets under management (AUM). This, in turn, represents around one third of all AUM in the North American asset management industry.




Performance of Socially Responsible Investment Funds against an Efficient SRI Index: The Impact of Benchmark Choice when Evaluating Active Managers - An Update
Véronique Le Sourd
March 2012 (previous version: September 2011)

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 62% of funds have a positive information ratio when compared to the cap-weighted EuroStoxx Sustainability Index, only about 36% 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 (0.04) when using the standard SRI index, but it is more clearly negative (-0.12) when using the Efficient SRI index.




EDHEC-Risk European Index Survey 2011
Noël Amenc, Felix Goltz, Lin Tang
October 2011

As the choice of an index is a crucial step in both asset allocation and performance measurements, it is useful to investigate index use and perceptions about indices. The EDHEC-Risk European Index Survey 2011 analyses the current uses of and opinions on stock, bond and equity volatility indices with the aim of providing unique insight into the users’ perspective in the index industry.

Furthermore, there is a growing body of research on index construction and index use. Recent studies assess current indices and also propose alternative approaches to construct indices. This survey also serves as a tool to explore views of institutional index users on the conclusions of the literature.

This survey enabled opinions from 104 institutional investment managers to be gathered, which represent approximately seven trillion Euros of assets under management. This represents more than half of all assets under management by the European asset management industry. The respondents are from asset management companies, pension funds and insurance firms located all over Europe.

The opinions collected reflect investors’ overall judgement on index quality, on the key issues they see with current indices, and the likely future trends for the index landscape.




Improved Beta? A Comparison of Index-Weighting Schemes
Noël Amenc, Felix Goltz, Lionel Martellini, Shuyang Ye
First version: September 2010; This version: September 2011

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?
Felix Goltz, Véronique Le Sourd
January 2010

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
Noël Amenc, Felix Goltz, Lionel Martellini, Patrice Retkowsky
January 2010

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
Lionel Martellini
2008

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
Noël Amenc, Felix Goltz, Véronique Le Sourd
March 2008

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 March 2009 issue of European Financial Management.




Reactions to the EDHEC study "Assessing the Quality of Stock Market Indices"
Felix Goltz, Guang Feng
September 2007

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
Noël Amenc, Felix Goltz, Véronique Le Sourd
September 2006

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.