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Tail Risk of Smart Beta Portfolios: an Extreme Value Theory Approach

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Tail Risk of Smart Beta Portfolios: an Extreme Value Theory Approach An EDHEC-Risk Institute Publication Tail Risk of Smart Beta Portfolios: An Extreme Value Theory Approach July 2014 Institute 2 Printed in France, July 2014. Copyright EDHEC 2014. The opinions expressed in this study are those of the authors and do not necessarily reflect those of EDHEC Business School. Tail Risk of Smart Beta Portfolios: An Extreme Value Theory Approach — July 2014 Table of Contents Executive Summary .................................................................................................5 1. Introduction ............................................................................................................9 2. Smart Beta Indices .......................................................................................... 15 3. A Conditional EVT Model .................................................................................21 4. Empirical Analysis ............................................................................................31 Conclusion ...............................................................................................................43 Appendix ..................................................................................................................47 References ...............................................................................................................57 About EDHEC-Risk Institute ................................................................................61 EDHEC-Risk Institute Publications and Position Papers (2011-2014) ........65 An EDHEC-Risk Institute Publication 3 Tail Risk of Smart Beta Portfolios: An Extreme Value Theory Approach — July 2014 About the Authors Lixia Loh is a senior research engineer at EDHEC-Risk Institute–Asia. Prior to joining EDHEC Business School, she was a Research Fellow at the Centre for Global Finance at Bristol Business School (University of the West of England). Her research interests include empirical finance, financial markets risk, and monetary economics. She has published in several academic journals, including the Asia-Pacific Development Journal and Macroeconomic Dynamics, and is the author of a book, Sovereign Wealth Funds: States Buying the World (Global Professional Publishing, 2010). She holds an M.Sc. in international economics, banking and finance from Cardiff University and a Ph.D. in finance from the University of Nottingham. Stoyan Stoyanov is professor of finance at EDHEC Business School and head of research at EDHEC Risk Institute–Asia. He has ten years of experience in the field of risk and investment management. Prior to joining EDHEC Business School, he worked for over six years as head of quantitative research for FinAnalytica. He has designed and implemented investment and risk management models for financial institutions, co-developed a patented system for portfolio optimisation in the presence of non-normality, and led a team of engineers designing and planning the implementation of advanced models for major financial institutions. His research focuses on probability theory, extreme risk modelling, and optimal portfolio theory. He has published over thirty articles in leading academic and practitioner-oriented scientific journals such as Annals of Operations Research, Journal of Banking and Finance, and the Journal of Portfolio Management, contributed to many professional handbooks and co-authored three books on probability and stochastics, financial risk assessment and portfolio optimisation. He holds a master in science in applied probability and statistics from Sofia University and a PhD in finance from the University of Karlsruhe. 4 An EDHEC-Risk Institute Publication Executive Summary An EDHEC-Risk Institute Publication 5 Tail Risk of Smart Beta Portfolios: An Extreme Value Theory Approach — July 2014 Executive Summary Cap-weighted indices, although widely used the comparison. Under this hypothesis, the as passive investment vehicles, have two improved performance may be at the cost important drawbacks with far-reaching of an increase in tail thickness. consequences for investors — they represent concentrated portfolios and they are To study the tail risk systematically across also exposed to risk factors that are not different weighting schemes and stock well rewarded. Both drawbacks indicate selection criteria, we need a solid indexing significant inefficiencies for long-term methodology that can produce diversified investors. factor-tilted indices consistently across different geographical universes. The Smart Index providers offer factor indices that Beta 2.0. methodology — as put forward by aim at tilting the portfolio towards better EDHEC Risk Institute and applied for the rewarded factors. Although clearly an production of the ERI Scientific Beta indices improvement over cap-weighting, the — allows the challenges affecting the industry index solutions are often based smart beta indices provided by traditional on ad-hoc stock-selection and weight industry vendors to be addressed.2 It allocation criteria prone to data-mining separates two main steps in the index 1 - See Amenc et al. (2012) risks. Because of the dangers of data-mining, construction process and offers investors and the references therein. 2 - See Amenc and Goltz investors are advised to stick to simple factor the chance to make an informed decision (2013) for further details. An implementation of definitions rather than rely on proprietary about the factor tilt and the diversification the methodology with and complex factors (see Gelderen and method. The diversification method deals complete and transparent documentation is available Huij (2013)). with the over-concentration issue and at http://www.scientificbeta. com. the factor tilt method leads to exposure Empirical research1 has demonstrated to better rewarded factors. Thus, the two that smart beta indices offer improved main components in the construction performance and also sometimes process of factor indices are: (i) achieving lower volatility than the cap-weighted a factor tilt through stock selection and benchmarks. It is, thus, of practical and (ii) efficiently extracting the risk premia also of theoretical interest to check if through improved diversification, via the smart beta indices exhibit higher extreme application of a smart weighting scheme. risk or similar extreme risk as that of the The two components are distinct; investors cap-weighted indices. The importance of can explicitly choose which factor to tilt this question stems from the fact that the towards, while the diversification method superior risk-adjusted performance of smart reduces the impact of specific or unrewarded beta indices is usually demonstrated by risks. The stock-selection criteria considered comparing their Sharpe ratios to that of are size, liquidity, momentum, volatility, the corresponding cap-weighted index. If, value, and dividend yield and the weighting however, it turns out that smart beta schemes are Efficient Minimum Volatility, returns have a substantially heavier left Efficient Maximum Sharpe Ratio, Maximum tail unaccounted for by volatility, then Deconcentration, Maximum Decorrelation Sharpe ratios may be misleading when and Diversified Risk Weighted. We examine comparing risk-adjusted performance the tail risk of these strategies with and because a dimension of risk would be lost in without a factor tilt for the following 6 An EDHEC-Risk Institute Publication Tail Risk of Smart Beta Portfolios: An Extreme Value Theory Approach — July 2014 Executive Summary Scientific Beta universes: USA (500 stocks), Autoregressive Conditional Heteroskedastic Eurozone (300 stocks), UK (100 stocks), (GARCH) model and, second, the remaining Japan (500 stocks), Developed Asia-Pacific tail risk is estimated from the residual ex-Japan (400 stocks), and World Developed process using EVT. From a risk management (2,000 stocks). The data used cover the full perspective, it is important to segregate the sample period from June 2003 to December two components because the dynamics of 2013 and also two sub-sample periods, the volatility contributes to the unconditional pre-crisis period from June 2003 to June tail thickness phenomenon. Generally, the 2007 and the turbulent period from July GARCH part is responsible for capturing the 2007 to December 2013. dynamics of volatility while EVT provides a model for the behaviour of the extreme To compare extreme risk across different tail of the distribution. smart beta indices, we use a statistical methodology based on extreme value We carry out the comparison by, first, looking theory (EVT) and conditional value-at-risk at the differences in tail risk of absolute and (CVaR) at 1% tail probability as a downside relative returns by varying the weighting risk measure. EVT has been used for a long scheme using all stocks in the corresponding 3 - Relative returns are time in areas other than finance to study universe.3 Our main finding is that the defined as the difference between the returns of the the probabilities of extreme events, and in CVaR across strategies is primarily driven strategy and the returns of the corresponding the area of risk measurement it has been by the average volatility or the average cap-weighted benchmark. used to describe the probabilistic behaviour tracking error for the case of absolute and of tail losses. On the other hand, both the relative returns, respectively. The results more common value-at-risk (VaR) and show that adopting a different weighting CVaR are risk measures used to estimate scheme
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