An ERI Scientific Beta Publication. Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies

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1 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October 2013

2 2 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October 2013 Table of Contents 1. Introduction Performance and Risk Statistics Weight Profile Analysis Analysis of Conditional Performance Analysis of Risk Factor Exposures Analysis of Relative Risk Sector Analysis Turnover and Capacity Analysis Conclusions: How to use Scientific Beta Analytics...41 References...47 About ERI Scientific Beta...51 ERI Scientific Beta Publications...55 Printed in France, October The authors can be contacted at beta.com.

3 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Abstract The availability of an increasing variety of Smart Beta equity strategies is good news for investors, but only on the condition that they can make a fully informed choice among these alternatives. The ERI Scientific Beta platform provides rich analytics on the results of different strategies in terms of performance and risks. These advanced analytics help investors develop a clear understanding on how the different parts of the portfolio construction methodology influence the overall investment outcome. Moreover, the information conveyed by the analytics can also assist investors in making comparisons across different Smart Beta indices. The present paper describes the analytics that are available on the ERI Scientific Beta platform and illustrates how they can be used to assess Smart Beta strategies. The Scientific Beta platform offers two types of analytics. Standard analytics correspond to what we consider as the basic reporting requirements for Smart Beta indices. Those statistics are available free of charge and include Index Overview, Latest Performances, Annual Performances, Performance and Risk Statistics, Weight Profile Analysis and Holding Based Characteristics. Scientific Beta Advanced analytics provide additional tools that not only help explain the performance of Scientific Beta smart indices but also provide insights into the performance attribution, Relative Risk Analysis, CAPM Analysis, Fama-French Analysis, Carhart Analysis, Turnover and Capacity analysis, Sector and Country Allocation, Sector Attribution and Analysis of Conditional Performance in Bull/Bear or High/Low Vol markets. We provide several illustrations on analysing Smart Beta indices using these analytics, including index selection among the multitude of possible strategy specifications.

4 4 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October 2013 About the Authors Saad Badaoui is a Senior Quantitative Analyst, ERI Scientific Beta. He is a specialist in fixed income, with a focus on Sovereign Default Risk and Liquidity Risk in CDS and Bond Markets. He holds a PhD in Quantitative Finance from Imperial College London. He also holds an MSc and an MPHIL from Imperial College. Saad equally holds a BSc in Economics from Paris-Dauphine University. Prior to his PhD, Saad worked in the Quantitative Research Desk at a top tier investment bank with a focus on Credit and Interest Rate risk. Véronique Le Sourd has a Master s degree in Applied Mathematics from the Pierre and Marie Curie University in Paris. From 1992 to 1996, she worked as a research assistant in the finance and economics department of the French business school, HEC, and then joined the research department of Misys Asset Management Systems in Sophia Antipolis. She is currently a Senior Research Engineer at EDHEC-Risk Institute. Ashish Lodh is Senior Quantitative Analyst, ERI Scientific Beta. He does research in empirical finance, focusing on equity indexing strategies and risk management. He has a master s in management with a major in finance from ESCP Europe. He also has a bachelor s degree in chemical engineering from Indian Institute of Technology.

5 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Introduction

6 6 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Introduction Numerous advanced beta equity offerings try to generate outperformance over the standard market indices. These Smart Beta indices are being marketed on the basis of a number of shortcomings of cap-weighted indices, which have been documented to be overly concentrated (see Tabner, 2007; Malevergne et al., 2009) and to provide poor risk-adjusted returns (see Haugen and Baker, 1991; Grinold, 1992; Schwartz, 2000; Cochrane, 2005; Arnott, Hsu and Moore, 2005; Amenc, Goltz and Le Sourd, 2006; Goltz and Le Sourd, 2011, among others). Following such criticisms, various alternative weighting schemes have been proposed and tested to improve upon cap-weighting (see Arnott, Hsu and Moore, 2005; Choueifaty and Coignard, 2008, DeMiguel et al., 2009 ; Maillard, Roncalli and Teiletche, 2010; Meucci, 2010 ; Amenc et al., 2011a ; Amenc et al., 2011b; Lohre, Neugebauer and Zimmer, 2012, among others), and it is now commonly accepted that moving away from capweighting tends to enhance diversification and increase risk-adjusted performance over long horizons. While providers of Smart Beta strategies report the outperformance of their approaches over standard indices, this information does not provide for sufficient transparency for investors for two reasons. First, information given by strategy providers on a particular weighting scheme is often very limited when it comes to the risks of such strategies. For example, many articles on the performance of alternative beta indices have fallen short of accounting for exposures to standard equity risk factors such as value and small cap. 1 Moreover, while providers typically report long-term performance results against cap-weighted indices, little information is provided on the periodic underperformance that their strategy may suffer, and on the dependence of the performance on market conditions. Second, it is difficult to compare indices on a fair basis. More often than not, performance comparisons across these indices are published by Smart Beta providers who compare their own strategy with those of their competitors (or even with their own replication of their competitors indices). 2 Moreover, from investors perspective, it is difficult to conduct a proper analysis across different alternative beta strategies on an unbiased and comparable basis as indices are often promoted by competing providers drawing on different universes, data sets and implementation rules. In addition, the potential disparity of the choice of the analysis period across reports from different index providers renders the comparison between Smart Beta indices even more difficult as the choice of the period has a direct influence on the performance and risk statistics, in particular when considering realised returns, which are notoriously sensitive to the time period chosen. Finally, for a meaningful comparison across different Smart Beta strategies it is essential to apply the same risk and performance metrics, calculated in the same manner, to the different strategies. We therefore believe that providing an exhaustive set of analytics on our indices is a form of transparency which is essential in the area of Smart Beta indices. Moreover, we believe that investors, rather than depending only on preformatted reports supplied by promoters of Smart Beta strategies, should be able to develop their own understanding of performance and risks. 1 - For example, Arnott, Hsu and Moore (2005) did not show empirical results for the value and small cap exposure of the fundamentals-based strategy they promote. Likewise, Dash and Zheng (2010) analyse the performance of the S&P 500 equal-weighted index. While they provide evidence on style exposure to small cap and value, they do not provide any formal attribution of performance to these exposures. Demey et al. (2010) did not report any results on value and small cap exposures of the Equal Risk Contribution strategy in their foundation paper. 2 - In fact, articles published by providers of a given Smart Beta strategy often contain confusing statements about their competitors strategies. For example, in an article published by promoters of fundamentals-based equity indexation (Chow, Hsu, Kalesnik and Little, 2011), the authors, who highlight the importance of implementation rules to evaluate alternative equity indices, failed to include the turnover management rules integrated by the competitors so as to then show that the turnover they calculated themselves for these strategies was higher than that of their own index. For more details on this issue, see Amenc, Goltz, and Lodh (2012) and Chow, Hsu, Kalesnik and Little (2011).

7 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Introduction ERI Scientific Beta Analytics aims to fill this gap in current Smart Beta investment practices as it provides detailed analytics and exhaustive information on Smart Beta indices to allow investors to evaluate the advanced beta strategies in terms of risk and performance. The analytic capabilities of ERI Scientific Beta include risk and performance assessment, factor and sector attribution, and relative risk assessment. The available set of tools allows investors to conduct their own analyses, select their preferred time period and choose among a wide range of analytics in order to produce their own picture of strategy performance and risk. Moreover, these analytics enable investors to compare and analyse the risk and the performance statistics of different Smart Beta strategies applied to different geographic universes leading to more than 2,400 indices. 3 The objective of this paper is to show the range of analytics ERI Scientific Beta has implemented to provide full information on Smart Beta indices. Given the rich set of the analytics available, we choose to interpret and illustrate the usefulness of these tools primarily through two selected strategy indices, namely the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. We use these strategies as they correspond to widely used methods for improving efficiency compared to cap-weighted indices. The Minimum Volatility strategy is based on Modern Portfolio Theory as it is a proxy for a portfolio that is located on the efficient frontier. 4 The literature 5 reports abundant empirical evidence of outperformance of the Minimum Volatility strategy, compared to cap-weighted indices. Additionally, Scherer (2011) has attributed this outperformance to risk-based pricing anomalies. By contrast, the Maximum Deconcentration approach is not derived from Modern Portfolio Theory, but is rather based on an ad-hoc form of diversification, as it is a generalisation of a simple equal weighting-scheme. In fact, Maximum Deconcentration indices try to get as close as possible to equal weights subject to implementation constraints (liquidity and turnover constraints) and allow adding optional constraints on risk exposures. The idea behind such ad-hoc diversification is that balancing out the weights in an index and thus increasing the effective number of assets 6 reduces the exposure to idiosyncratic risk 7 and thus leads to a better diversified portfolio. The analytics presented in the remainder of this paper can be applied to any strategy that is present on the ERI Scientific Beta platform. However, we concentrate here on results for these two strategies in order to illustrate the capabilities of these analytics. The remainder of this paper is organised as follows. Section 2 describes performance and risk statistics available for the analysis of Smart Beta strategies. Section 3 discusses the weight profile analysis (i.e. allocation of the weights to the constituents of the strategy). Section 4 explains the analysis of conditional performance, i.e. performance under different market conditions. Section 5 introduces the equity factor models (i.e. CAPM, Fama-French and Carhart Models) and their use for the analysis of the performance of Smart Beta strategies. Section 6 presents the relative risk measures. Section 7 deals with the sector analysis. Section 8 discusses the implementability issues related to the turnover and investability of the Smart Beta strategies. Finally, Section 9 presents concluding remarks on the use of the analytics on the ERI Scientific Beta platform. 3 - This point will be discussed in more detail in the conclusion, where we show an example of a comparative analysis across different Smart Beta strategies. 4 - Note that the Minimum Volatility portfolio is also the sole portfolio on the efficient frontier that can be derived without estimating individual asset expected returns. It simply requires an estimate of risk and correlations for each of the risky assets. 5 - See Haugen and Baker (1991), Chan, Karceski and Lakonishok (1999), Schwartz (2000), Jagannathan and Ma (2003), Clarke, de Silva and Thorley (2006), Geiger and Plagge (2007), Nielsen and Aylursubramanian (2008) and Poullaouec (2008), among others. 6 - The effective number of stocks is defined as the reciprocal of the Herfindahl Index, a commonly used measure of portfolio concentration. The Herfindahl index is defined as the sum of squared weights across portfolio constituents. 7 - Goltz and Sahoo (2011) also explain in details why index diversification improves portfolio performance.

8 8 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Introduction

9 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Performance and Risk Statistics

10 10 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Performance and Risk Statistics Evaluating the performance of a Smart Beta strategy requires not only considering its average return, but also evaluating the accompanying risk using suitable indicators, including measures of extreme risk. Risk-adjusted performance measures are also essential to assess if the risk of a Smart Beta index is sufficiently rewarded, as well as to compare the performance of strategies with different level of risks. ERI Scientific Beta allows investors to gain a thorough picture of performance and risk characteristics of Smart Beta strategies, by providing a large variety of indicators and a choice of time periods to compute them. It includes traditional measures based on portfolio theory as well as extreme risk measures. All indicators are displayed for a short-term period (one year), mid-term periods (three and five years) and a long-term period, using data since inception of the Smart Beta indices. 8 Annual returns are also displayed for each calendar year since This breakdown of historical performance into many different subsamples allows for a simple assessment of the robustness of long-term results. All indicators are calculated based on daily total returns (with dividends reinvested) and are annualised. The performance and risk indicators are presented both in an absolute form, considering the strategy on its own, and in a relative form, using a cap-weighted reference index that covers the broad geographic universe corresponding to the Smart Beta index. Allowing the performance and risk characteristics of each strategy to be compared with those of its cap-weighted counterpart is important, as cap-weighted indices remain the primary reference benchmarks in the investment industry. Table 1 summarises the performance and risk indicators displayed by ERI Scientific Beta, both in the absolute and relative form. 8 - All Currently available indices have the inception date of June 2002.

11 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Performance and Risk Statistics Table 1. Performance and Risk Indicators This table sums up the list of indicators displayed in ERI Scientific Beta performance and risk analysis, both in the absolute and relative perspective. Performance and risk indicators Definition 9 Absolute analysis Return Average return computations provide basic performance evaluation on various time periods. Volatility Volatility, defined as the standard deviation of returns, measures the dispersion of strategy returns around their mean. Sharpe ratio Sharpe ratio evaluates the excess return of a strategy over the risk-free rate relative to the volatility of the strategy. Sortino ratio Sortino ratio evaluates the excess returns of a strategy index over a minimum acceptable return (chosen here as the risk-free rate) relative to the downside deviation, i.e. the risk of falling under the minimum acceptable return. Historical 5% VaR VaR calculates the worst expected loss over a given horizon, at a given confidence level, under normal market conditions. Historical VaR is based on historical returns and it measures the possibility of maximum daily loss. The level of 5% means that there is only a 5% chance that the strategy will experience a loss that is greater than the calculated VaR. Cornish-Fisher 5% VaR Since the returns of portfolios are generally not normally distributed, the standard VaR calculation does not give the true 5% tail risk measure. The Cornish-Fisher VaR is computed using the Cornish-Fisher extension that adjusts the VaR for the presence of asymmetry (i.e. skewness) and or heavy tails (i.e. excess kurtosis) in the return distribution. Maximum Drawdown Maximum drawdown measures the maximum loss experienced by a strategy between a peak (i.e. the highest point) and a valley (i.e. the lowest point) over a specified period. This measure, which is quite sensitive to data frequency, is computed based on a daily price index. Relative analysis Relative return over capweighted index Relative return is defined as the strategy's return in excess of the return of a cap-weighted benchmark. Tracking-error Tracking-error is defined as the standard deviation of the difference in return between the strategy and its cap-weighted benchmark. Information ratio Information ratio compares the residual return of a strategy (i.e. the difference between the return of the strategy and the return of its cap-weighted benchmark) to its residual risk (i.e. the tracking error). Treynor ratio 10 Treynor ratio evaluates the excess returns of a strategy over the risk-free rate relative to the market risk (beta) of the strategy. Historical 5% VaTER Similar to VaR in the absolute analysis, except that VaTER (value-at-tracking-error-risk) calculates the Cornish-Fisher 5% VaTER worst expected loss of the strategy relative to the cap-weighted benchmark. Probability of Outperformance Probability of Outperformance is defined as the historical probability of outperforming the cap-weighted reference index over a given investment horizon. This measure is reported for investment horizons of 1, 3 and 5 years by using a rolling window analysis with 1-week step size. Max relative Drawdown Maximum relative drawdown measures the maximum loss relative to the cap-weighted benchmark experienced by a strategy between a peak (i.e. the highest point) and a valley (i.e. the lowest point) over a specified period. Tables 2 and 3 display the summary of performance and risk characteristics provided by ERI Scientific Beta for two indices: the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. We present the results obtained over the whole historical period, but similar computations may also be obtained over shorter periods. 9 - More detail can be found in the glossary on Note that, each indicator in the absolute analysis has an equivalent indicator computed with regard to a benchmark in the relative analysis, except the Sortino ratio. As it is not usual to compute the Sortino ratio with regard to a benchmark, we alternatively present the Treynor ratio in the relative analysis. This indicator is pertinent in this analysis, as it requires choosing a reference index to compute the beta used as the denominator in this ratio.

12 12 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Performance and Risk Statistics Table 2. Absolute Performance and Risk Characteristics This table reports absolute performance and risk characteristics for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. The statistics are based on daily total returns (with dividend reinvested). All statistics are annualised and performance ratios that involve the average returns are based on the geometric average, which reliably reflects multiple holding period returns for investors. ERI Scientific Beta uses the yield on Secondary Market US Treasury Bills (3M) as a proxy for the risk-free rate in US Dollars. All results are in USD. Absolute Risk and Performance Statistics Scientific Beta USA Efficient Minimum Volatility Scientific Beta USA Maximum Deconcentration Return 8.58% 7.79% Volatility 18.23% 22.46% Sharpe Ratio Sortino Ratio Cornish Fisher 5% VaR 1.60% 2.05% Historical 5% VaR 1.71% 2.16% Max Drawdown 47.33% 56.43% From the results in Table 2, it appears that the two strategies post dissimilar average returns over the historical period. In fact, these two strategies are quite different in their construction, as one strategy tries to minimise volatility, while the other strategy seeks to maximise the effective number of components in the index. Differences between the two strategies clearly appear when one considers the risk indicators shown in Table 2. As expected, the volatility of the Maximum Deconcentration strategy is higher than that of the Minimum Volatility strategy. Indicators measuring the risk of loss (VaR, Max drawdown) also identify the Maximum Deconcentration strategy as more risky than the Minimum Volatility strategy. It is, therefore, clear from the analysis in Table 2 that both strategies have quite different levels of risk. Consequently, the Minimum Volatility index has higher risk-adjusted performance in terms of Sharpe ratio and Sortino ratio than the Maximum Deconcentration index. While Table 2 shows risk and return in absolute levels, investors who are judged with reference to the cap-weighted index 11 are typically concerned with relative performance. Table 3 reproduces relative performance and risk analytics available on the ERI Scientific Beta platform for the two strategies covered in this paper. Interestingly, the table shows that the excess returns of both strategies over the cap-weighted benchmark are still quite dissimilar. Furthermore, the risk of the Minimum Volatility strategy relative to a cap-weighted benchmark appears to be higher than the relative risk of the Maximum Deconcentration strategy. The VaTER (value-at-tracking-error) is also higher for the Minimum Volatility strategy than for the Maximum Deconcentration strategy. As a result, if investors are concerned by their performance in reference to a cap-weighted benchmark, the Minimum Volatility strategy will appear to be riskier than the Maximum Deconcentration strategy, while from an absolute perspective we conclude the opposite. We will see below in Section 5 that this result is likely due to the fact that the Maximum Deconcentration index is similar to the cap-weighted reference index in terms of its exposure to market risk, while the Minimum Volatility index has much lower exposure to market 11 - In order to derive risk and performance measures in relative terms, ERI Scientific Beta computes cap-weighted indices, which are used as the reference indices when evaluating performance and risks of Smart Beta strategies. The cap-weighted indices are constructed based on the following principles. First, ERI Scientific Beta constructs its universe by creating a list of all eligible securities that have passed the liquidity screen at the quarterly Review Date and ranks them in descending order of free-float market capitalisation. This list is truncated at 110% of the targeted fixed number of securities required for the US Building Block, this is called the Review List. The fixed number of securities targeted for the USA Geographic Building Block is 500 securities, resulting in a Review List of 550 potentially eligible securities at the Review Date. All Existing Securities that are also included in the new list of potentially eligible securities are automatically included in the new Underlying Universe as Surviving Securities. The ERI Scientific Beta USA cap-weighted reference benchmark will comprise the Underlying Universe with securities weighted in proportion to their free-float market capitalisation weights. For further information on the construction methodology, we refer the reader to the ERI Scientific Beta Universe Construction rules available in

13 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Performance and Risk Statistics risk. 12 In line with the outperformance numbers, the Minimum Volatility strategy shows very high outperformance probability numbers (100% for 3-year horizon) while Maximum Deconcentration shows lower but still strong numbers (89.3% for 3-year horizon). Table 3. Relative Performance and Risk Characteristics This table reports relative performance and risk characteristics over a cap-weighted benchmark for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation weights. The statistics are based on daily total returns (with dividend reinvested). All statistics are annualised and performance ratios that involve the average returns are based on the geometric average, which reliably reflects multiple holding period returns for investors. ERI Scientific Beta uses the yield on Secondary Market US Treasury Bills (3M) as a proxy for the risk-free rate in US Dollars. All results are in USD. Relative Risk and Performance Statistics Scientific Beta USA Efficient Minimum Volatility Scientific Beta USA Maximum Deconcentration Return over CW 2.59% 1.80% Tracking-Error 4.42% 3.28% Information Ratio Treynor Ratio Cornish Fisher 5% VaTER 0.44% 0.32% Historical 5% VaTER 0.41% 0.31% Probability of Outperf. (1 year) 76.7% 66.7% Probability of Outperf. (3 years) 100% 89.3% Max Relative Drawdown 7.51% 11.05% In addition to the analysis of the performance and risk statistics, investors are keen on studying the weight profile of the smart beta indices which, relates to the analysis of the allocation of the weights to the constituents of the strategy. In the following section, we discuss this point It is also interesting to note that the Minimum Volatility index has a lower Maximum Relative Drawdown than the Maximum Deconcentration index which in line with the fact that the Minimum Volatility index focuses on the defensive stocks which leads to a lower drawdown (or a lower maximum loss).

14 14 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Performance and Risk Statistics

15 3. Weight Profile Analysis 15

16 16 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Weight Profile Analysis 3.1 Why use weight profile analysis? One of the objectives of an index strategy is to allow investors to seek broad exposure to the equity asset class. Therefore investing in highly concentrated indices runs counter to the investor's investment objective. In the weight profile analysis, we clearly see how well the strategy is diversified based on the distribution of constituents. If the strategy is concentrated in few stocks, it would lead to underdiversification and risk / reward inefficiency. ERI Scientific Beta uses various measures for evaluating concentration. The first measure is the effective number of stocks. It is given by the inverse of the sum of squared constituent weights. A low value represents a strategy concentrated in few stocks. We then report the nominal number of stocks in the strategy portfolio, followed by the number of stocks that comprises 90%, 75%, 50% and 25% of market capitalisation of the strategy portfolio to show the distribution of stocks in terms of market capitalisation. We also report the Deconcentration ratio, defined as the ratio of the effective number of stocks over the nominal number of stocks. Finally, we report the GLR (Goetzmann, Li and Rouwenhorst, 2005) measure which measures the diversification benefit and is the ratio of the variance of the portfolio returns to the weighted average of the variance of its constituents returns. The lower the GLR measure, the higher the diversification benefit of combining a set of stocks into a portfolio. This measure can be extended to strategies beyond the equal weighting scheme. In general, for any weighting scheme, the ratio of the variance of the portfolio returns to the weighted average variance of individual stock returns can be used to measure the extent of correlation minimisation by that weighting scheme. The idea of the minimum correlation strategy is to minimise portfolio risk by exploiting the low correlations between the stocks and not just by concentrating in low volatility stocks. The GLR measure, as opposed to portfolio level volatility measure, ignores the risk reduction through stock volatilities and reflects only on the risk reduction stemming from the combination of low correlation stocks. A portfolio that concentrates weights in stocks that have high correlation will tend to have portfolio risk which is high compared to the average standalone risk of its constituent and will thus have a high GLR measure. 3.2 Illustration Table 4 displays the summary of the weight profile analysis provided by ERI Scientific Beta for two indices: the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. The table shows that the Scientific Beta USA Efficient Minimum Volatility index has a lower effective number of stocks than the Scientific Beta USA Maximum Deconcentration index, which is in line with our expectation as the Efficient Minimum Volatility index focuses on a specific subset of the portfolio by overweighting defensive stocks. The Maximum Deconcentration index, however, aims to decrease the concentration of the portfolio by investing in a high number of stocks. This phenomenon also reflects in the number of stocks per percentage of market capitalisation, as the table shows that the

17 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Weight Profile Analysis difference in the number of stocks per market capitalisation between the Maximum Deconcentration index and Efficient Minimum Volatility index is almost double. Furthermore, while the Maximum Deconcentration index displays an impressive deconcentration ratio of 94.40%, both of the Efficient Minimum Volatility Index and the Maximum Deconcentration index show substantial improvement in the deconcentration ratio as compared to the cap-weighted reference index. Finally, both smart beta strategies have lower GLR ratios than that of the cap-weighted reference index. However, the GLR ratio of the Efficient Minimum Volatility index is lower than that of the Maximum Deconcentration index, which implies that even though the Maximum Deconcentration index has higher number of stocks than the Efficient Minimum Volatility index, there are more diversification benefits when combining defensive stocks than when combining a large number of stocks. Table 4: The table shows the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index concentration levels under various portfolio concentration measures based on the index's weight profile as of 21/12/2012, and the low correlation objective measure (GLR) based on historical returns and the index's historical weights since inception (on 21/06/2002). For sake of comparison, the table also presents the same concentration measures for the Scientific Beta USA cap-weighted benchmark. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation weights. Weight Profile/Indices Scientific Beta USA Efficient Minimum Volatility Index Maximum Deconcentration Index Cap-weighted Reference index Eff Number of Stocks Nominal Number of Stocks N.b Stocks Cumul to 90% Cap N.b Stocks Cumul to 75% Cap N.b Stocks Cumul to 50% Cap N.b Stocks Cumul to 25% Cap Deconcentration ratio 50.70% 94.40% 26.00% GLR 50.60% 56.70% 64.10% Weight profile analysis (Section 3) and unconditional performance measures (Section 2) may mask large changes related to market conditions as the analysis is done on the full sample period. The next section will thus present a conditional analysis of performance taking into account various market conditions.

18 18 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Weight Profile Analysis

19 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Conditional Performance

20 20 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Conditional Performance 4.1. Why use conditional performance analysis? Market conditions such as bullish or bearish markets, as well as periods of high or low stock market volatility, may have a considerable impact on how different portfolio strategies perform. In particular, it has been shown that the performance of Smart Beta strategies is often related to market conditions. Considering the performance of four index strategies based on alternative weighting schemes, over six month periods from January 2003 to December 2011, Amenc, Goltz, Lodh and Martellini (2012) show considerable variation of strategy performance in different sub-periods, as well as pronounced differences between strategies in terms of when they tend to outperform and underperform. Ferson and Qian (2004) note that an unconditional evaluation made for example during bearish markets will not be a meaningful estimation of forward performance if the next period was to be bullish. Conditional performance analysis provides investors with a better understanding of the performance of Smart Beta indices in various economic conditions and allows them to make a selection that takes into account their view on future market conditions. In addition, analysing the dependence of performance on market conditions also provides a view on the robustness of a strategy s outperformance. 13 Moreover, investors should carefully analyse the conditional performance of strategies to identify risk of underperformance in certain market conditions. Such a risk assessment is a first step towards managing such risks. In particular, allocating across Smart Beta strategies with contrasting conditional performance features may allow investors to diversify away the risk of ending up with a single strategy which may not deliver outperformance in the prevailing market conditions. ERI Scientific Beta considers two conditioning variables to classify market conditions and compute conditional performance: market returns (leading to a classification into bull and bear market periods) and market volatility (leading to a classification into high and low volatility regimes). Separating bull and bear market periods to evaluate performance was proposed by various authors such as Levy (1974), Turner, Starz and Nelson (1989) and, more recently, Faber (2007). In the same way, analysis of performance in high and low volatility market regimes is insightful as it is well known that the volatility of stock market returns can show important variations through years, and strategy performance may be sensitive to the levels of volatility Performance in Bull and Bear markets ERI Scientific Beta computes bull and bear returns for Smart Beta indices dividing the whole time period used for analysis into quarters and computing the corresponding returns for the cap-weighted reference index. Quarters are then classified as bull or bear quarters. Calendar quarters with positive market index returns constitute bull markets, while the rest of the quarters constitute bear markets. Table 5 below reports the conditional performance and risk statistics that result when using this definition of bull and bear markets Furthermore, because of data availability issues, the evaluation of the performance over the very long-term period (e.g. over several decades) becomes infeasible for investable indices. Thus the introduction of the conditional performance analysis is important as it can be expected to be more robust to the limitations imposed by the short length of the sample used for the risk-return analysis A related issue is that various studies have identified a relationship between the stock market volatility and the equity risk premium. Some of the findings suggest a positive relationship (French, Schwert, and Stambaugh, 1987; Baillie and DeGennaro, 1990; Campbell and Hentschel, 1992; Ghysels, Santa-Clara, and Valkanov, 2005; Guo and Whitelaw, 2006; Pastor, Sinha and Swaminathan, 2006), while others indicate a negative association between the two (Campbell, 1987; Nelson, 1991; Pagan and Hong, 1991; Whitelaw, 1994).

21 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Conditional Performance Table 5. Bull / Bear Market Performance Statistics 15 This table reports general absolute and relative performance and risk statistics for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index in the periods of bull and bear market regimes respectively as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. The statistics are based on daily total returns (with dividend reinvested). All statistics displayed in this table are quarterly values and performance ratios that involve the average returns are based on the geometric average, which reliably reflects multiple holding period returns for investors. ERI Scientific Beta uses the yield on Secondary Market US Treasury Bills (3M) as a proxy for the risk-free rate in US Dollars. All results are in USD. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation weights. Calendar quarters with positive market index returns comprise bull markets and the rest constitute bear markets. Bull / Bear Market Performance Statistics Scientific Beta USA Efficient Minimum Volatility Scientific Beta USA Maximum Deconcentration Bull Market Bear Market Bull Market Bear Market Absolute Analysis Return 6.54% -5.39% 7.68% -7.70% Volatility 6.36% 12.61% 7.99% 15.38% Sharpe Ratio Relative Analysis over a Cap-weighted index Relative Return -0.28% 2.10% 0.86% -0.20% Tracking-Error 1.75% 2.84% 1.43% 1.95% Information Ratio From Table 5, we can see that both the Minimum Volatility strategy and the Maximum Deconcentration strategy exhibit positive returns during bull markets and negative returns during bear markets. Looking at relative returns, we observe that during bull markets, the Minimum Volatility Index underperforms the cap-weighted index, while the Maximum Deconcentration Index outperforms the cap-weighted index. During bear markets, we have the opposite result, with an outperformance of the Minimum Volatility Index and an underperformance of the Maximum Deconcentration Index. Moreover, on one hand, the Sharpe ratio of the Minimum Volatility index is higher than that of the Maximum Deconcentration index for both market conditions due to Minimum Volatility index reduced volatility as it concentrates in low volatility or defensive stocks. On the other hand, for both bull and bear market conditions the tracking errors of the Minimum Volatility index are also higher than those of the Maximum Deconcentration index due to a lower market risk exposure. 16 From these results, it appears that the two strategies display quite dissimilar relative returns over both bull and bear market conditions. Thus, the conditional analysis gives useful insights to help investors choose between two strategies depending on future market conditions they may anticipate. In particular, the Minimum Volatility index is suitable for equity investors with a cautious outlook while the Maximum Deconcentration index is suitable for investors with a more optimistic outlook on market returns. Moreover, the differences in conditional performance of these two indices suggests that investors may benefit from combining both strategies in a portfolio, which will capture the average level of long-term outperformance while smoothing outperformance across market conditions (see Amenc, Goltz, Lodh and Martellini (2012) for an analysis of diversifying across strategies with diverging conditional performance characteristics) Note that for methodology reasons, the conditional values displayed on Tables 5 and 6 are quarterly values, which differs from all other tables where the values displayed are annualised This equity risk exposures will be discussed in Section 5.

22 22 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Conditional Performance 4.3. Performance in High and Low Volatility Markets In a similar fashion to analysing bull and bear market performance, ERI Scientific Beta separates high and low volatility regime returns, where high volatility quarters are those with a higher volatility than the median reference index volatility across all quarters, and low volatility quarters are those with a lower volatility than the median reference index volatility across all quarters. The series of daily returns of the index across all the high volatility (respectively low volatility) quarters are consolidated into a single synthetic high volatility (respectively low volatility) time series. The two resulting sets of daily returns are then used to compute quarterly risk and performance statistics. Table 6 reports the performance statistics observed in these different market conditions. Table 6. High / Low Volatility Market Performance Statistics This table reports general absolute and relative performance and risk statistics for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index in the periods of high and low volatility regimes respectively as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. The statistics are based on daily total returns (with dividend reinvested). All statistics displayed in this table are quarterly values and performance ratios that involve the average returns are based on the geometric average, which reliably reflects multiple holding period returns for investors. ERI Scientific Beta uses the yield on Secondary Market US Treasury Bills (3M) as a proxy for the risk-free rate in US Dollars. All results are in USD. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation weights. High Volatility market comprises the top 50% of quarters sorted on the quarterly cap-weighted benchmark s volatility and the Low Volatility market comprises the rest. High/ Low Volatility Market Performance Statistics Scientific Beta USA Efficient Minimum Volatility Scientific Beta USA Maximum Deconcentration High Vol Regime Low Vol Regime High Vol Regime Low Vol Regime Absolute Analysis Return -0.18% 4.47% -0.90% 4.81% Volatility 11.91% 4.91% 14.76% 5.87% Sharpe Ratio Relative Analysis over a Cap-weighted index Relative Return 0.85% 0.43% 0.13% 0.89% Tracking-Error 2. 81% 1.35% 2.20% 1.29% Information Ratio From Table 6, we observe that during high volatility regime, both Minimum Volatility Index and Maximum Deconcentration Index post a negative performance, while during low volatility regime, these two strategies both have a positive performance. Looking at relative returns over a cap-weighted index, it appears that both strategies outperform their cap-weighted counterpart, whatever the volatility regime. Unlike the performance evaluation conditional on bull and bear markets that clearly showed which strategy was most favourable depending on market conditions, on a relative perspective, the performance evaluation conditional on volatility regimes does not give such a clear picture, as neither of the two strategies clearly dominates the other in one particular regime. However, closer examination of information ratios show that the Minimum Volatility strategy displays quite similar risk-adjusted relative performance under the two volatility regimes, while the information ratio of the Maximum Deconcentration strategy becomes very low during the high volatility regime, because the tracking error of the strategy is higher compared to the low volatility regime, while its excess

23 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Conditional Performance return is lower. Until now, we have assessed the risk associated with the performance of these Smart Beta strategies using risk-adjusted performance ratios, such as the Sharpe ratio or the information ratio. Another approach to measure the performance relative to the risk taken is to separate the total return of each strategy into (a) the normal return due to the rewards from systematic risk factor exposures and (b) the abnormal return (alpha) that is not explained by the exposure to systematic risk factors. The next section will illustrate the analytics provided by ERI Scientific Beta for analysing such systematic risk factor exposures.

24 24 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Conditional Performance

25 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Risk Factor Exposures

26 26 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Risk Factor Exposures As part of its effort to introduce more transparency in the area of Smart Beta indices, ERI Scientific Beta provides information on factor risk exposures 17 for all of its Smart Beta indices. Such factor risk exposures matter because they are often implicit results of portfolio construction and investors would want to know how exposed they are to certain factors. In fact, many studies have underlined the importance of such exposures in explaining part of the outperformance over cap-weighted indices (see Jun and Malkiel, 2007; Kaplan, 2008; Blitz and Swinkels, 2008; Amenc, Goltz and Le Sourd, 2009). Of course, a conclusion on risk factor exposures, and any related conclusion on separating the part of performance that comes from such exposures from additional alpha generated by a strategy, depends on how one defines the factor model. ERI Scientific Beta offers a range of different factor models, which are well documented in the finance literature, to allow investors to conduct such an analysis. Below, we will briefly describe the available factor models and then turn to an illustration of their use based on the Scientific Beta US Minimum Volatility and Maximum Deconcentration indices. In what follows, we intend to briefly describe the factor risk models and for further details on the regression methodology we refer the reader to the glossary in Equity Factor Models It is crucial for investors to be aware of the factor tilts that result (explicitly or implicitly) from the construction methodology of a Smart Beta index so that they can assess if such factor tilts are consistent with their investment objectives; or if the performance of the strategy is driven solely by certain factor tilts. As the consensus in academic finance and among practitioners suggests that the simple single market factor used in the Capital Asset Pricing Model (CAPM) model (Sharpe, 1964) does not fully capture the cross sectional variation of expected stock returns, there has been a development of multi-factor models that account for a range of priced risk factors. Fama and French (1993), who provided an important contribution in this area, have highlighted two important factors, a value factor associated with the book-to-market ratio and a size factor associated with a company s market capitalisation. The Fama-French three-factor model has been extended by Carhart (1997) to include the momentum factor (see Jegadeesh and Titman, 1993). To provide insights into the relevant risk factor exposures of its strategies, ERI Scientific Beta provides information on factor exposures using the three different factor models (i.e. the CAPM, Fama-French and Carhart models). Thus investors can get a complete picture of the exposure of the Smart Beta strategies to the market factor, value factor, small cap factor and momentum factor, and can use one or several factor models to analyse these risk exposures and the residual performance of Smart Beta indices depending on their own preference and judgement. 5.2 Illustration In order to illustrate how ERI Scientific Beta analytics for the equity risk factor exposures can be used to analyse Smart Beta strategies, Table 7 shows the factor analysis for the Scientific Beta USA 17 - Deviation from standard cap-weighting approach potentially leads to exposure to equity risk factors that are different from those of cap-weighted references.

27 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Risk Factor Exposures Efficient Minimum Volatility and the Scientific Beta USA Maximum Deconcentration indices for the CAPM, Fama-French and Carhart models. Table 7. Analysis of Risk Factor Exposures with three Different Factor Models The table shows the coefficient estimates and R-squared of the regression of the excess returns (over the risk-free rate) for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index as of 31/12/2012 using the CAPM single factor model, the Fama-French model and the Carhart Four Factor model over the whole period (since inception-21/06/2002). The coefficient estimates are also reported and values significant at the 95% confidence level are shown in bold. We use simple OLS regression and the t-statistic is computed using paired difference testing on the OLS estimates of betas. SMB factor (small size factor) is the daily return series of a portfolio that is long the top 30% of stocks (small market-cap stocks) and short the bottom 30% of stocks (large market-cap stocks) sorted on market capitalisation in ascending order. HML factor (value factor) is the daily return series of a portfolio that is long the top 30% of stocks (value stocks) and short the bottom 30% of stocks (growth stocks) sorted on book-to-market value in descending order. MOM factor (momentum factor) is the daily return series of a portfolio that is long the top 30% of stocks (winner stocks) and short the bottom 30% of stocks (loser stocks) sorted on past returns in descending order. Factors/Indices CAPM Model Fama French Model Carhart Four Factor Model Scientific Beta USA Efficient Min Volatility Scientific Beta USA Max Deconcentration Scientific Beta USA Efficient Min Volatility Scientific Beta USA Max Deconcentration Scientific Beta USA Efficient Min Volatility Scientific Beta USA Max Deconcentration Coeff Coeff Coeff Coeff Coeff Coeff Alpha/Unexplained 2.85% 1.66% 2.31% 0.13% 2.22% 0.10% Market Small-Big High-Low Momentum R-Squared The factor analysis reveals that both Scientific Beta USA Efficient Minimum Volatility Index and Scientific Beta USA Maximum Deconcentration Index are significantly exposed to the Market, SMB, HML and MOM risk factors as shown by the bold values, though the magnitude of their exposures are quite different. For instance, the Scientific Beta Minimum Volatility index shows a lower exposure to the market risk factor than the Scientific Beta Maximum Deconcentration index due to a stronger deviation from the cap-weighted reference index. 18 Furthermore, based on both the Fama French and the Carhart analysis, it appears that both Smart Beta strategies have a significant small cap bias, but this bias is stronger for the Scientific Beta USA Maximum Deconcentration index than for the Scientific Beta USA Efficient Minimum Volatility index, as shown by their Small minus Big (SMB) coefficients. This result is not surprising, as the Maximum Deconcentration strategy reduces concentration away from the largest cap stocks in the cap-weighted index, and thus mechanically tilts towards the smaller capitalisation stocks in the universe. The negative exposure of the indices to the High minus Low factor (which represents the value premium of buying stocks with high book-to-market ratios and selling stocks with low book-to-market ratios) and their positive exposure to the momentum factor (which represents the premium for buying past winner stocks and selling past loser stocks) are quite small, in fact the magnitude of the coefficients is very weak compared to those of the market and SMB factors which constitute the main risk exposures. While the factor risk analysis helps investors assess the performance of the strategy that is due implicitly or explicitly to certain factor tilts, another approach to analyse the performance is 18 - This result is in line with the high tracking errors of the Scientific Beta Minimum Volatility index presented in Table 5 and Table 6.

28 28 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Risk Factor Exposures to measure the risk of deviation from the performance of a cap-weighted reference index. Such deviations will be a crucial issue for investors who are evaluated against the performance of capweighted benchmarks which constitute their peer group. In the following section, we describe the relative risk indicators that are available on the Scientific Beta platform.

29 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Relative Risk

30 30 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Relative Risk 6.1. Methodology Alternative index construction schemes lead a priori to an exposure to risk of substantial deviations with respect to cap-weighted reference indices. This is not surprising as it is widely known that Smart Beta strategies lead to factor exposure choices that are different from those of cap-weighted indices. Indeed, the illustration of Scientific Beta analytics on factor exposures in Section 5 above has confirmed this general finding for the specific example of Maximum Deconcentration and Efficient Minimum Volatility Indices. As a result of such factor exposures, investment professionals who deviate from cap-weighted indices take on considerable risk of periodic underperformance, and thus a clear reputational risk as cap-weighted indices represent a common reference for their peer group of investment professionals. Given its importance in practice, it is crucial to properly analyse this relative risk. Average measures of relative risk and return are not enough for investors who also need to pay attention to extreme relative risk, i.e. to occurrences of extreme underperformance relative to cap-weighted indices. ERI Scientific Beta proposes a rolling window analysis of Smart Beta index returns relative to the cap-weighted reference index in order to capture the variation of return and risk through time. 19 Trailing one-year relative return series and trailing one-year tracking-error series are computed using data for the whole historical period. This analysis provides a complete description of the variation of the spread between the strategy and its cap-weighted benchmark through time. For example, the tracking error could vary significantly during the analysis period. In order to summarise this information, we then report the extreme occurrences of tracking error (the threshold for the highest 5% of trailing one year tracking error) and relative returns (the threshold for the lowest 5% of one year trailing relative returns). Table 8 below provides the definitions of the statistics we report in Table 9. Table 8. Relative Risk Indicators This table sums up the list of indicators displayed in ERI Scientific Beta relative risk analysis. Relative risk indicators Average Relative Return Extreme Relative Return (5%) Average Tracking-error Extreme Tracking-error (95%) Maximum Relative Drawdown Maximum Time under Water Definition Average relative return is obtained as the arithmetic mean of the trailing relative return series. Extreme relative return (5%) measures the maximum expected amount of the relative annual loss that the strategy can suffer at a 95% confidence level. It is computed as the 5th percentile of the one year rolling relative returns. Average trailing tracking error is the arithmetic mean of the trailing tracking error series. Extreme tracking error (95%) measures the maximum amount of the tracking error that the strategy can experience at a 95% confidence level. It is computed as the 95th percentile of the one year rolling trackingerror. Maximum relative drawdown measures the maximum relative loss experienced by a strategy between a peak and a valley over a specified period (similar to Section 2). The time under water is calculated for each drawdown period to measure how long it takes investors to recover their relative loss with respect to the cap-weighted reference index. The maximum time under water is the highest value of time under water over the analysis period The rolling window analysis is done using a window size of one year (52 weeks) and a step size of one week or 5 business days (from Monday to Friday), using daily return series.

31 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Relative Risk 6.2. Illustration Table 9 displays the summary of relative risk and return characteristics of two strategies: Scientific Beta USA Efficient Minimum Volatility Index and Scientific Beta USA Maximum Deconcentration Index. Table 9. Relative Risk Characteristics This table, based on a rolling window analysis, reproduces relative average and extreme return and risk statistics for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. The statistics are based on daily total returns (with dividend reinvested). All statistics are annualised and performance ratios that involve the average returns are based on the geometric average, which reliably reflects multiple holding period returns for investors. All results are in USD. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float marketcapitalisation weights. Relative Risk Characteristics Scientific Beta USA Efficient Minimum Volatility Scientific Beta USA Maximum Deconcentration Extreme Relative Return (5%) -2.67% -3.53% Average Tracking-Error 3.94% 3.08% Extreme Tracking-Error (95%) 8.25% 5.61% Max Relative Drawdown 7.51% 11.05% Max Time Under Water The indicators presented on Table 9 are rarely displayed by traditional providers of Smart Beta strategy indices, who typically do not put much emphasis on analysing periods of underperformance. However, these results bring complementary information to traditional average indicators, such as those displayed in Table 3. Extreme relative returns show that in the extreme case, both strategies may encounter up to 3% of daily underperformance relative to the cap-weighted benchmark, though both of them post an annualised excess performance of about 2% over the whole historical period. The table also shows the extreme occurrences of tracking-error figures, which is valuable information for investors who are sensitive to the risk of large performance deviations from their cap-weighted reference benchmark. Clearly, following the Minimum Volatility index which already has high levels of average tracking error of the order of 3.94%, leads to a very high tracking error of about 8% in the extreme case. Finally, the evaluation of the maximum relative drawdown and the maximum time under water respectively shows the maximum relative loss and the maximum number of days a strategy needed to recover from a relative loss with regard to a cap-weighted benchmark. In our examples, we see that the Maximum Deconcentration strategy, despite its lower levels of tracking error and extreme tracking error, actually had more pronounced and longer relative drawdowns than the Minimum Volatility strategy. Until now, all performance measures presented were computed globally without differentiating the strategy according to its country or sector exposures. The next section explores the features of the Scientific Beta platform that allows users to evaluate how country and sector allocation contribute to the performance.

32 32 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Analysis of Relative Risk

33 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Sector Analysis

34 34 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Sector Analysis For equity investors quantifying the country exposure has always been an important aspect of understanding the exposures of their portfolios. Furthermore, sector analysis is also an important factor in the decision making process as investors may want to avoid volatile sectors that are the most sensitive to business cycles. In addition to this, investors may be keen on understanding the source of outperformance of the strategy portfolio with respect to its cap-weighted reference index. To this end, ERI Scientific Beta provides the user with the ability to analyse sector and country allocations. To stay consistent with the previous sections, we discuss and illustrate the sector analysis in the context of the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. For further information on the country analysis, we refer the reader to where one can find information on the absolute and relative country allocation with respect to the reference cap-weighted index for multi-regional Smart Beta strategy indices Sector Allocation Sector allocation separates the investment weights of the strategy portfolio into various sectors, enabling investors to gain insight into the effect of the strategy's methodology on sector exposure. ERI Scientific Beta provides information about sector exposures (in terms of percentage weights) of the strategy, based on its stock weight profile at the last rebalancing date. It shows the distribution of absolute sector weights across sectors as well as the relative sector weights of the strategy with respect to those of the cap-weighted reference index. The sector classification used is the Thomson Reuters Business Classification. For the sake of illustration, Table 10 shows the sector allocation of the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. We present the absolute industry exposures as well as the relative industry exposures with regard to the capweighted reference index. The table reveals that for both the Scientific Beta USA Efficient Minimum Volatility and the Scientific Beta USA Maximum Deconcentration indices, the distribution of the weights is spread out over all the sectors which imply that the Smart Beta indices are well diversified across all sectors. Interestingly, while both indices have the largest underweight and the largest overweight relative to the cap-weighted index in the same sector, these differences are more pronounced for the Minimum Volatility index. For instance, relative to the cap-weighted index, the exposure to the Technology sector is 7.90% lower for the Minimum Volatility index and 5.20% lower for the Maximum Deconcentration Index respectively. Likewise, relative to the cap-weighted index, the exposure of the Minimum Volatility index to the Utilities sector is 9.40% higher, while that of the Maximum Deconcentration index is 2.80% higher. For investors, the fact that the Scientific Beta USA Efficient Minimum Volatility Index leads to greater sector shifts, with regard to the cap-weighted reference index than the Scientific Beta USA Maximum Deconcentration Index, is potentially useful information when they evaluate the suitability of such strategies for their investment purposes. However, the analysis of sector exposures does not provide any insights on the relevance of these exposures for the performance of the index. In particular, an

35 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Sector Analysis investor may be keen to understand whether the performance of a strategy is explained mainly by sector tilts or by stock-level weighting decisions. We now turn to the discussion of a performance attribution analysis that provides answers to these questions. Table 10. Sector Allocation. The table shows (1) top absolute industry exposures (in terms of percentage weight) and (2) top relative industry exposures (in terms of percentage weight) with regard to the cap-weighted reference index for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index, based on the weight profile of each index at the last rebalancing time (21/12/2012). The Scientific Beta USA capweighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation. Sector/Indices Sector Allocation Scientific Beta USA Efficient Min Volatility Scientific Beta USA Max Deconcentration Absolute Relative Absolute Relative Energy 6.50% -5.30% 10.3% -1.40% Basic Materials 4.40% 1.00% 6.3% 2.90% Industrials 7.90% -3.10% 13.1% 2.20% Cyclical Cons. Goods & Services 13.1% 0.60% 15.70% 3.10% Non Cyclical Cons. Goods & Services 17.20% 7.30% 7.80% -2.00% Financials 11.80% -5.00% 18.20% 1.40% Healthcare 15.50% 4.30% 9.60% -1.50% Technology 8.3% -7.90% 10.90% -5.20% Telecommunication services 2.50% -1.40% 1.60% -2.20% Utilities 12.90% 9.40% 6.30% 2.80% 7.2. Sector Performance Attribution Sector attribution is one of the most important ways of understanding the drivers of outperformance of the strategy portfolio with respect to its cap-weighted reference index. ERI Scientific Beta uses the Menchero (2004) Multi-period attribution framework to disaggregate the outperformance of a strategy with respect to its benchmark on a sector basis. This attribution method breaks down the outperformance of the strategy portfolio with regard to the cap-weighted reference index into three effects. The stock effect accounts for the share of outperformance attributable to the ability of the strategy to select outperforming stocks, the sector effect accounts for the share attributable to the ability of the strategy to overweight sectors that outperform the reference index and the interaction effect accounts for the combination of sector and stock effects. For more details, we refer the reader to Menchero (2004) and to scientificbeta.com 20. This methodology consists of two steps: (1) computing sector weights for the Smart Beta strategy portfolios; and (2) attributing sector-wise excess returns of these portfolios to the three components: sector effect, stock effect and interaction effect. The stock universe is divided into 10 industry sectors. For the sake of illustration, Table 11 shows the sector attribution of the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. The table displays the breakdown of index s performance with regard to its cap-weighted reference index into returns attributed to stock effect, sector effect and interaction effect from Menchero Multi-period Attribution model In particular, see Documentation / Glossary / Menchero Multi-period Performance Attribution.

36 36 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Sector Analysis Table 11. Sector Attribution. The table shows the results of Menchero Multi-period attribution, in which the outperformance of each strategy index with regard to its cap-weighted reference index is broken down into stock effect, sector effect and interaction effect. The reported returns are annualised and geometrically averaged over all quarters from 21/06/2002 to 31/12/2012 (see Menchero, 2004). The analysis is displayed for the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation weights. Sector/Indices Sector Attribution Scientific Beta USA Efficient Min Volatility Scientific Beta USA Max Deconcentration Perf Perf Stock Selection 6.94% 2.11% Sector Allocation -0.96% 0.57% Interaction -3.30% -0.83% The table reveals some commonality between the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index, as stock selection effect contributes positively to the performances of the Smart Beta strategies. However, the Scientific Beta USA Efficient Minimum Volatility Index shows a relatively larger negative interaction effect as the index overweights/underweights the appropriate stocks but not always within the appropriate sectors. 21 Interestingly, the sector attribution analysis reveals that for both Scientific Beta USA indices, improved weighting across stocks as opposed to simple sector tilts, is the main driver of the outperformance with respect to their cap-weighted reference index. This information is interesting as it suggests that although both Smart Beta indices use different weighting schemes, their outperformance is driven by the effectiveness of the diversification process across stocks. This is perhaps not surprising as the methodologies of both strategies do not explicitly aim to capitalise on their exposure to the right sectors, but rather have an explicit objective of improving diversification across stocks, away from the heavily concentrated cap-weighting scheme. While the sector analysis provides investors with a sound understanding of the sector allocation and thus sheds some light on the diversification benefit of the index, there are two issues that may prevent investors from investing in a smart beta strategy which are related to the investability and transaction costs. To this end, ERI Scientific Beta provides investors with measures that could help them assess the implementability These results are consistent with the pronounced sector underweights/overweights observed in the sector allocation (Table 10) of the Scientific Beta Efficient Minimum Volatility index.

37 8. Turnover and Capacity Analysis 37

38 38 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Turnover and Capacity Analysis 8.1 Why use turnover and capacity analysis? Turnover, which leads to higher transaction costs than those of buy-and-hold strategies and which may make it harder to invest in and replicate the index, is of concern to index investors. Turnover analysis refers to the measurement of how frequently, and in which relative proportions, the constituents of an equity strategy index are traded over a specific period. Cap-weighted indices can, in principle, be viewed as a buy-and-hold strategy that involves no turnover. In practice, they involve a residual turnover due to index constitution changes resulting from periodic review and specific corporate events. Alternatively weighted indices, by contrast, may exhibit a higher level of turnover as they involve some rebalancing of constituent weights too, due to the fact the weights depend on different characteristics than the market capitalisation. Turnover varies greatly from one index to another, depending on the inputs entering the weighting mechanism, hence the importance of measuring and reporting the turnover of alternative indices. ERI Scientific Beta reports the annualised historical one-way turnover for each index, after each quarterly review date. We use a standard measure for turnover, which is the sum of absolute deviations of individual weights between the end of a quarter and the beginning of the following quarter. This results in a two-way quarterly turnover, which is then annualised and set to a one-way figure. As far as the capacity analysis is concerned, it allows the level of investability of an equity index to be assessed and it can be defined as the absolute or relative amount one can invest into the index in order to keep its investment objective and/or style intact, without adding additional constraints on liquidity that would force a deviation from the stated objective of the index. The capacity of a fund or an index is tightly linked to the liquidity of its constituents: the more liquid they are, the higher the capacity. To this end, Deuskar and Johnson (2011) show that the liquidity of on an overall equity index is a crucial concern for investors who perform their due diligence and choose their index, partly because it allows them to know whether reviewing their real-life portfolio will be done at minimal costs when the underlying index is reviewed. Thus, measuring and reporting a proxy for liquidity are crucial steps in alternative indexing. The definition of capacity depends on a set of mostly arbitrary and dynamically updated assumptions, notably the conditions under which the fund will have to deviate from its strategy in order to avoid illiquidity issues. Those conditions are often expressed as a portion of current float and/or trading volume. ERI Scientific Beta proxies the capacity of an index using the weighted average market capitalisation of its constituents. This metric has the advantage of providing a clear and systematic comparison with the cap-weighted reference.

39 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Turnover and Capacity Analysis 8.2 Illustrations Table 12: The table shows the turnover level of the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index in % as of 21/12/2012. It also shows the capacity of the same indices as measured by the average market capitalisations, in $m. For sake of comparison, the table presents the same measures for the Scientific Beta USA cap-weighted benchmark. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation weights. Turnover and Capacity /Indices Scientific Beta USA Efficient Minimum Volatility Maximum Deconcentration Cap-weighted Reference index Index Index One Way Turnover (annualised) 29.50% 27.20% 4.30% Average Capacity ($m) Latest Capacity ($m) The table shows that the turnover of the Scientific Beta Efficient Minimum Volatility index and that of the Scientific Beta Maximum Deconcentration index are higher than that of the cap-weighted reference. This is to be expected as alternative weighting schemes involve substantial weight deviations from the cap-weighted reference index, which has a residual turnover. However, it is interesting to see that both strategies respect the target turnover of 30%, which is quite manageable in terms of trading costs. Secondly, the turnover of the Efficient Minimum Volatility index is higher than that of the Maximum Deconcentration index, which is in line with our previous results on the risk factor exposures as the Efficient Minimum Volatility index deviates strongly from the cap-weighted reference index and thus requires a stronger weight rebalancing. The capacity of both smart beta strategies is about 1/4th that of the cap weighted index, which means that, as opposed to the widely cited criticism, the smart beta strategies can be made quite liquid. Furthermore, the table reveals that the Efficient Minimum Volatility index has higher average capacity than the Maximum Deconcentration index, implying that the former has higher investability than the latter. As seen in the factor risk analysis, the Maximum Deconcentration strategy shows higher exposure to the small cap factor which results in lower investment capacity compared to the Efficient Minimum Volatility strategy.

40 40 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Turnover and Capacity Analysis

41 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Conclusions: How to use Scientific Beta Analytics

42 42 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Conclusions: How to use Scientific Beta Analytics There is an increasing variety of Smart Beta strategies. This choice is good news for investors, but only on the condition that they can make a fully informed choice among these alternatives. ERI Scientific Beta provides rich analytics on the different weighting schemes as well as their results in terms of risk-adjusted performance and risks. These advanced analytics will help the user develop a clear understanding on how the different parts of the methodology influence the overall investment outcome. Moreover, the information provided by the analytics can also assist investors in making comparisons across different Smart Beta indices, while drawing on a set of indices that reflect different Smart Beta strategies and share a common framework and database. The Scientific Beta platform offers two types of analytics. Scientific Beta Standard analytics correspond to what we consider as the basic reporting requirements for Smart Beta indices: a set of tools that allows to better understand the risk/return characteristics of the indices. Those statistics are calculated and updated on and are available free of charge. The Scientific Beta Standard analytics are: Index Overview; Latest Performances; Annual Performances; Performance and Risk Statistics; Holding Based Characteristics and Weight Profile Analysis. Sections 2 and 3 of this paper draw on Standard Analytics. Scientific Beta Advanced analytics require a subscription. Advanced analytics provide additional tools that not only help explain the performance of Scientific Beta smart indices but also provide insights into their performance attribution. Subscribers of our advanced analytics have access to the following tools: Relative Risk Analysis, CAPM Analysis, Fama-French Analysis, Carhart Analysis, Sector and Country Allocation, Sector Attribution, Analysis of Conditional Performance (Bull/Bear, High/Low Vol market) and Turnover and Capacity Analysis. Sections 4 to 8 of this paper draw on Advanced Analytics. These analytics are available to users of the Scientific Beta website in different areas. For any strategy index, has a specific index page, which recalls the key construction principles of the strategy index (weighting scheme, stock selection, and risk control mechanisms) and shows a performance graph. On the same page, users can access both Standard and Advanced analytics for this index on the left hand side which gives them the flexibility to choose which analytics they are interested in depending on how far they would like to pursue the analysis of the performance and risk. Furthermore, the analysis of the performance and risk is made easy due to the availability of two useful modes of display: (1) the choice of the analysis period wherein the user can select either the past 1 year, 3 years, 5 years or the full historical period since inception; and (2) the choice of viewing the analysis of the performance in absolute or relative terms (i.e. with respect to the cap-weighted reference index). Moreover, ERI Scientific Beta provides an option to create a Watchlist which will contain a preferred set of Smart Beta indices chosen by the users themselves. Through this Watchlist, the users can access both Standard and Advanced analytics as described above in order to view a comparative analysis among the Smart Beta indices they have chosen to monitor on their Watchlist. For the sake of illustration, the following figure shows the sector outperformance attribution for the six available weighting schemes applied to a US universe, which are the Scientific Beta USA Efficient

43 An ERI Scientific Beta Publication Scientific Beta Analytics: Examining the Performance and Risks of Smart Beta Strategies October Conclusions: How to use Scientific Beta Analytics Minimum Volatility Index, the Scientific Beta USA Maximum Deconcentration Index, the Scientific Beta USA Efficient Maximum Sharpe Ratio Index, the Scientific Beta USA Diversified Risk Parity Index, the Scientific Beta USA Diversified Multi Strategy Index 22 and the Scientific Beta USA Maximum Decorrelation Index. Figure 1. Sector attribution results on The table shows the results of Menchero Multi-period attribution, in which the index's outperformance with regard to its cap-weighted reference index is broken down into the stock effect, the sector effect, and the interaction effect. The reported numbers are averaged over all quarters from 21/06/2002 to 31/12/2012. The analysis is displayed for the Scientific Beta USA Efficient Minimum Volatility Index, the Scientific Beta USA Maximum Deconcentration Index, the Scientific Beta USA Efficient Maximum Sharpe Ratio Index, the Scientific Beta USA Diversified Risk Parity Index, the Scientific Beta USA Diversified Multi Strategy Index and the Scientific Beta USA Maximum Decorrelation Index. The Scientific Beta USA cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation. In this example, the sector attribution analysis across the six Smart Beta strategies reveals that stock selection contributes positively to the outperformance of all strategies with respect to their reference cap-weighted index while sector allocation decisions for some strategies are actually unfavourable to performance. More generally, displaying performance and risk analytics for all indices in the user s Watchlist allows for straightforward comparison of the indices that most interest a specific investor. In our discussion above (Section 2 to Section 8), we only presented two illustrations of using the analytics on the Scientific Beta USA Efficient Minimum Volatility Index and the Scientific Beta USA Maximum Deconcentration Index. However, Scientific Beta allows investors to customise their index using a variety of key construction choices such as geographic universe, stock selection, weighting scheme and risk control features. The Benchmark Builder function available in com allows subscribing users to choose flexibly among a wide range of options for each of the key steps in the benchmark construction process, rather than relying on a pre-packaged bundle of choices proposed by commercial index providers, by selecting the different characteristics (regional universe, stock selection, weighting, and risk control schemes) among 2,442 Smart Beta indices available on the platform. In this context, Scientific Beta s analytics are crucial tools to assess the performance and risk features of the multitude of possible customised Smart Beta strategies The Scientific Beta Diversified Multi-Strategy index combines in equal proportions the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Parity weighting schemes. For more information on this strategy, we refer the reader to the Scientific Beta Diversified Multi-Strategy index available in