An ERI Scientific Beta Publication. Scientific Beta Diversified Multi-Strategy Index

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1 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March 2014

2 2 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March 2014 Table of Contents 1. Introduction to the Diversified Multi-Strategy Index Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index Factor-Tilted Diversified Multi-Strategy Indices Long-term Performance of Diversified Multi-Strategy Indices Summary...31 References...35 About ERI Scientific Beta...39 ERI Scientific Beta Publications...41 Printed in France, March The authors can be contacted at beta.com.

3 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Abstract The ERI 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-Weighted weighting schemes. The combination of these different strategies allows the diversification of risks that are specific to each strategy. Moreover, as the single strategy s performance will show different profiles of dependence on market conditions, a Multi-Strategy approach can help investors smooth the overall performance across market conditions. In this paper, we first provide an overview of the conceptual groundings of the Scientific Beta Diversified Multi-Strategy index, along with a detailed performance and risk analysis. Secondly, we show that the Diversified Multi-Strategy index presents a good trade-off between risk and return as it is a strategy that can achieve outperformance similar to that of its component strategies, while maintaining a low tracking error. In fact, the strategy has a return that is equivalent to the average return of its five components and a tracking error level that is lower than the average tracking error of its constituents. Therefore, for investors who are agnostic about either their capacity to identify the model with superior assumptions or their capacity to take the risk of choosing a particular model in the wrong market conditions, the Scientific Beta Diversified Multi- Strategy index presents itself as a good candidate. We also show how the Diversified Multi-Strategy weighting scheme can be used to construct smart factor indices well-diversified factor-tilted portfolios which extract the factor premia by selecting appropriate stocks for the desired beta. Smart factor indices allow high-performance allocations to be constructed either in terms of absolute return (Sharpe ratio) or in relative terms (information ratio) compared to cap-weighted indices, which remain the performance reference for long-only passive investment.

4 4 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March 2014 About the Authors Saad Badaoui is 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. 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 Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index

6 6 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index 1.1 Context Modern Portfolio Theory (MPT) states that investors should allocate their wealth between a tangency portfolio, or a Maximum Sharpe Ratio portfolio (MSR) portfolio and a riskless asset. In practice, when trying to follow this advice, one obviously has to come up with proxies because neither the true tangency portfolio nor a perfectly risk-free asset can be exactly observed. Traditionally equity investing has, however, heavily drawn on the Capital Asset Pricing Model (CAPM) and capweighted equity indices have long been perceived by many practitioners as reasonable proxies for the tangency portfolio. But a consensus is emerging that market cap-weighted indices tend to be poorly diversified portfolios that are not good proxies for the tangency portfolio. 1 Following such a criticism, more recent papers have documented that cap-weighting suffers from numerous shortcomings and various alternative weighting schemes or so called-smart beta strategies have been proposed to improve on cap-weighting (see Amenc et al. (2011a), Arnott, Hsu and Moore (2005), Choueifaty and Coignard (2008) and Maillard, Roncalli and Teiletche (2008), to name a few). Although it is now commonly accepted that moving away from cap-weighting tends to enhance diversification and increase risk-adjusted performance over long horizons, it has to be recognised that each alternative weighting scheme exposes the investor to two types of risks, namely the strategy specific risk (the risk related to the assumptions underlying the strategy and the risk related to making errors when estimating input parameters) and the systematic risk (exposure to common equity risk factors such as value or small cap exposure). ERI Scientific Beta offers five alternative weighting schemes which, for sake of clarity, are briefly defined below. 2 (1) The Scientific Beta Maximum Deconcentration strategy 3 corresponds to an adjusted equalweighting strategy which takes into account implementation constraints. More specifically, the strategy minimises the Herfindahl Index of the portfolio with an upper and a lower bound on stock weights. 4 (2) The Scientific Beta Diversified Risk Weighted strategy aims to achieve equal risk contribution from all stocks under the assumption of identical pair-wise correlation across stocks, and it is the same as inverse volatility weighting. The strategy is implemented with upper and lower bounds on individual weights to avoid a highly concentrated portfolio. (3) The Scientific Beta Maximum Decorrelation aims at minimising portfolio volatility under the assumption that stock volatilities are identical and only correlations are taken into account. The strategy is implemented with upper and lower bounds on individual weights to avoid a highly concentrated portfolio. 1 - Intuitively, the fact that cap-weighted indices are inefficient and poorly diversified is not surprising because they are heavily concentrated in the largest market-cap stocks as a result of their one-dimensional construction mechanism that only takes into account a stock s market cap and thus does not allow for any mechanism that can enforce proper diversification. 2 - For more a detailed discussion on the differences and commonality between the alternative weighting schemes available on the ERI Scientific Beta platform, we refer the reader to the paper Overview of Diversification Strategies available at In the absence of any constraints, Maximum Deconcentration coincides with the equal-weighting (also known as the 1/N weighting scheme), which owes its popularity mainly to its robustness and it has been shown to deliver attractive performance despite highly unrealistic conditions of optimality, even when compared to sophisticated portfolio optimisation strategies (De Miguel et al. (2009a)). 4 - We impose an upper bound u i and a lower bound l i on the weight of each constituent security, where i=1,,n and N is the nominal number of constituents. To avoid concentration, we set λ=3. The following steps are implemented to make sure this is the case: All negative weights will be set to zero. The remaining positive weight will be normalised so that they sum to. The lower bound will be added to all weights. The weights now sum to one. If the weights exceed the upper bound, these will be set equal to the upper bound and then reallocate the amount to all stocks that are below the upper bound but above the lower bound, pro-rated by the part of their weight that exceeds the lower bound. If this procedure leads to further stocks exceeding the upper bound, the above procedure will be repeated until the upper bound is respected by all securities.

7 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index (4) The Scientific Beta Efficient Minimum Volatility attempts to minimise the portfolio volatility by using an endogenous concentration adjustment 5 within the optimisation procedure. (5) The Scientific Beta Efficient Maximum Sharpe Ratio aims to maximise the Sharpe ratio (the riskadjusted performance) while imposing concentration constraints in the form of lower and upper bounds on stock weights. These short descriptions 6 put forward the idea that, although every strategy aims directly or indirectly to increase diversification, every weighting scheme has its own set of strategy specific risks. The dissimilarity represents an opportunity to diversify away the strategy specific risk by combining the strategies together. In the following section, we discuss the concept of systematic and specific risks of smart beta strategies in more detail. 1.2 Strategy Specific and Systematic Risks Systematic risks come from the fact that new indices or benchmarks can be more or less exposed to particular risk factors depending on the methodological choices guiding their construction, but also on the universe of stocks supporting this construction scheme. For example, compared to the cap-weighted reference index, a minimum volatility scheme will lead to overweighting low volatility stocks. More generally, given that a cap-weighted index is typically concentrated in the largest capitalisation stocks, any deconcentration of the benchmark will inevitably lead to an increase in the exposure to smaller stocks, such as mid-cap stocks. The category of specific risks corresponds to all the risks that are unrewarded in the long run, and therefore not ultimately desired by the investor, but that can have a strong influence on either the volatility and the max absolute drawdown of the index, or the tracking error or max relative drawdown of the index. Specific risks can correspond to important financial risk factors that do not explain, over the long term, the value of the risk premium associated with the index. There are many of these unrewarded financial risk factors. The academic literature considers, for example, commodity, currency or sector risks not to have a positive long-term premium. These risks can have a strong influence on the volatility, tracking error, max drawdown or max relative drawdown over a particular period, which might sometimes be greater than that of systematically-rewarded risk factors (e.g. exposure to the financial sector during the 2008 crisis or to sovereign risk in 2011). In line with portfolio theory, among the unrewarded financial risks, we also find specific financial risks (also called idiosyncratic stock risks) which correspond to the risks that are specific to the company itself (its management, the risk of the poor quality of its products, the failure of its sales team, the relevance of its R&D and innovation, etc.). It is this type of risk that asset managers are supposed to be the best at knowing, evaluating and choosing in order to create alpha, but portfolio theory 5 - The constraint can be defined as putting a lower bound on the effective number of stocks of the portfolio. We set the effective number to be at least one-third of the nominal number of stocks in the universe (N/3), so the constraint translates into: 6 - All described strategies are subject to liquidity and turnover constraints for improved implementability (as described in Sub-section 1.5).

8 8 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index considers it to be neither predictable nor rewarded, so it is better to avoid it by investing in a welldiversified portfolio. A globally effective diversification weighting scheme reduces the quantity of unrewarded risk, whether it involves unrewarded risk factors or unrewarded specific financial risks. However, like any model, it is imperfect and can itself lead to non-negligible residual exposures to certain unrewarded risks. For example, minimum volatility portfolios, which are robust proxies for efficient portfolios, and therefore well diversified, are often exposed to significant sector biases. Naturally, ERI Scientific Beta always tries to implement diversification models that are the least exposed possible to these unrewarded risks. For example, the use of norm constraints is a good compromise between the desire to fully utilise the potential to reduce the volatility in an efficient way procured by a min-vol-type weighting scheme, while avoiding over-concentration in a small number of low vol stocks. Specific or unrewarded risks can also correspond to operational or non-financial risks that are specific to the implementation of the diversification model. As such, for example, a Maximum Decorrelation scheme depends on a good estimation of the correlation matrix for the robustness of the diversification proposed. As part of the quality assurance for these indices, ERI Scientific Beta attaches a high price to the technical quality of the models used and their implementation to reduce this type of specific risk (for example, our research on the estimation of correlation matrices is part of this approach). In spite of all the attention paid to the quality of model selection and the implementation methods for these models, this specific operational risk, like the unrewarded financial risks described above, remains present nonetheless and it therefore seems interesting to be able to reduce even further the exposures that each weighting scheme, even if it is smart, is not able to diversify. This is the objective of Diversified Multi-strategy approach. 1.3 Objectives of the Scientific Beta Diversified Multi-Strategy Index: The ERI Scientific Beta Diversified Multi-Strategy weighting scheme combines in equal proportions the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk-Weighted weighting schemes. The combination of these different strategies is used to reduce the unrewarded or specific risks of each strategy. The Diversified Multi-Strategy approach enables all of the unrewarded risks associated with each of the weighting schemes to be well diversified. Positioning with Other Scientific Beta Diversification Strategy Indices: The methodology utilised for the Scientific Beta Diversified Multi-Strategy index is based on the idea of combining portfolio strategies a topic that has been discussed extensively in the academic literature. In fact, Jorion (1986), Kan and Zhou (2007), De Miguel, Garlappi and Uppal (2009a) and Brandt, Santa-Clara and Valkanov (2009) have studied similar ideas in various portfolio problems. Moreover, many papers have highlighted the practical benefits of such a combination. Martellini, Milhau and Tarelli (2013) find that combining equal-weighted portfolios and Minimum Volatility

9 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index portfolios leads to a higher Sharpe ratio than holding any of the component strategies in isolation. Tu and Zhou (2010) combine the equal-weighted portfolio (also known as the 1/N rule) with Markowitz type portfolio optimisation strategies and show that it is valuable to combine portfolio strategies in the presence of estimation errors. 7 Kan and Zhou (2007) show that when there is parameter uncertainty, following the standard prescription of portfolio theory to hold only the MSR (or tangency) portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the parameter estimation risk of the MSR portfolio. In particular, the authors show that a portfolio that optimally combines the riskless asset, the MSR portfolio and the global minimum variance portfolio dominates a portfolio with just the riskless asset and the MSR portfolio, suggesting that it is possible to benefit from the combination of different weighting schemes if their estimation errors are not perfectly correlated. Similarly, Amenc et al. (2012b) show that the minimum volatility portfolios provide defensive exposure to equity that does well in adverse market conditions whereas Maximum Sharpe Ratio portfolios provide a higher access to the upside of the equity market. Thus, combining both approaches naturally leads to a smoother conditional performance and would be a reasonable approach for all investors except those explicitly endowed with trustworthy forward-looking views about equity market performance. In the same spirit, the Scientific Beta Diversified Multi-Strategy index equally weights the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Weighted weighting schemes with the aim to diminish the strategy specific risks and ultimately smooth the outperformance of a smart beta portfolio. The equal-weighting across all strategies adopted by the Scientific Beta Diversified Multi- Strategy index is an intentionally simple and robust approach. Investors may be able to benefit from deriving optimal combinations of different weighting schemes that may involve more detailed selection of strategies to be combined as well as more sophisticated approaches of determining the weighting of the different strategies. After having discussed the objective behind the Scientific Beta Diversified Multi-Strategy index, in the following section, we explain the various implementation choices that have been made on the Scientific Beta platform. Implementation Choices Implementation choices have to be made on parameter estimation procedures, as well as on weight constraints that the strategy is subjected to. For a complete description of how the strategy is implemented we refer the reader to the Strategy Construction Rules of the Scientific Beta Diversified Multi-Strategy Indices available at Below, we provide a summary of the key implementation choices. Inputs As a first step, the ERI Scientific Beta Diversified Multi-Strategy index separately applies the strategy 7 - The intuition presented by the authors is the following: the 1/N rule (i.e. equal-weighting) is biased but has zero variance. However, a sophisticated rule (i.e. alternative weighting) is asymptotically unbiased but can have large variance (especially in small samples). When we combine the 1/N rule with a sophisticated rule, an increase of the weight on the 1/N rule increases the bias but decreases the variance. Thus the performance of the combination rule depends on the trade-off between the bias and the variance. Finally, the authors add that the performance of the combination rule can be improved and maximised by choosing an optimal weight.

10 10 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index rules relevant to the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Weighted indices. As a second step the index combines in equal proportions the weights resulting from these five weighting schemes. At each quarterly rebalancing date, the weights for each diversification strategy within the Multi Strategy index is thus set to 1/5th. For a complete description of how each input for each strategy is computed, we refer the reader to Sections 3 to 12 of the Strategy Construction Rules of the ERI Scientific Beta Diversified Multi-Strategy index, available at Optimisation The weights of all five strategies (i.e. the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Weighted weighting schemes) are obtained using optimisation techniques which make use of the principal component analysis (PCA) for robust risk parameter estimation and for Efficient Maximum Sharpe Ratio, proxy stock expected returns by stock semi-deviation. The Efficient Maximum Sharpe Ratio, the Diversified Risk Weighted and the Maximum Decorrelation weighting schemes impose ex-post deconcentration adjustments on the portfolio weights. The Efficient Minimum Volatility weighting scheme optimises its objective under norm-constraints. By contrast, and given its objective, the Maximum Deconcentration weighting scheme is not subject to further concentration adjustments. Lastly, the turnover control and liquidity adjustments (see below) are imposed on each of these weighting schemes using the cap-weighted reference weights. In the combination step, the Multi-Strategy portfolio is obtained by an equal-weighted combination of these five indices. Liquidity Adjustment It should be noted that Scientific Beta indices are based on a universe of stocks belonging to the largest capitalisation range and that have been subjected to liquidity screens. Thus, our universe for the US contains 500 stocks and for other developed markets it contains 1,500 stocks. In such a universe, liquidity issues are limited and smart beta strategies can be implemented with ease. Additional details are provided in the white paper on the ERI Scientific Beta Equity Universe. In order to further foster liquidity in the resulting index, additional adjustments of weights are implemented to achieve two objectives: one is to limit liquidity issues that may arise upon investing and another is to limit the liquidity issues that may occur upon rebalancing a smart beta strategy. The principle used to make such adjustments is to impose a threshold for the weight of a stock and for the weight change at rebalancing, relative to the market-cap-weight of the stock in its universe. 8 The liquidity adjustments are applied to the five constituent strategies before combination. Turnover Control ERI Scientific Beta indices are governed by an optimal turnover control technique which is based on rebalancing thresholds (see Leland (1999); Martellini and Priaulet (2002)). At each quarterly rebalancing date, we look at the newly optimised weights of the strategy portfolio. These weights will not be implemented if the resulting overall weight change remains below the threshold. The 8 - Specifically, liquidity adjustments consist of two rules: Rule 1 - We cap the stock s weight to a maximum of 10 times the free-float adjusted market cap-weight. Rule 2 - In order to limit the impact on liquidity of the rebalancing of weights, we cap the change in weight for each stock to its free-float adjusted market cap-weight. This means that we avoid making large rebalancings in the smallest stocks. Note that after renormalising weights, the effective multiple will change again so that effectively the index could weight some stocks at a higher multiple of their cap-weight. In case of the occurrence of an effective optimal rebalancing, the fact that we apply liquidity adjustments will also shift the resulting weights from the in-sample optimal weights, in favour of ensuring out-of-sample ease of implementation.

11 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index threshold is calibrated using the past data, and it is fixed at the level that would have resulted in not more than a 30% annual one-way turnover historically. The idea behind this rule is to avoid rebalancing when deviations of new optimal weights from the current weights are relatively small. This technique significantly reduces transaction costs without having a big impact on the strategy's performance. The turnover control is applied to the five constituent strategies before combination. In the following section, we discuss in detail the risk and return characteristics, the sector exposure, the conditional performance and the conditions of optimality of the Scientific Beta Diversified Multi-Strategy index.

12 12 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Introduction to the Diversified Multi-Strategy Index

13 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index

14 14 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index In this section, we present a comparative analysis of the performance and risks of the Scientific Beta Diversified Multi-Strategy index with its five components. This comparison is crucial not only to put forward the benefits and the drawbacks that accompany the Scientific Beta Diversified Multi-Strategy index, but also to give investors a clearer picture as to why (and when) it may be important to choose a multi-strategy index instead of a single strategy. Risk and Return Properties ERI Scientific Beta provides common performance and risk measures across all indices that are available on the platform. In addition to volatility, ERI Scientific Beta reports loss measures such as maximum drawdown and Value-at-Risk (VaR). 9 All risk and performance measures are reported both in absolute terms and relative to the cap-weighted reference index. In fact, similar to reporting the volatility of a risk measure for investors who are interested in returns per se, the volatility of the return difference with reference to the cap-weighted index (the so-called tracking error) becomes a relevant risk measure for investors who are concerned about performance relative to the cap-weighted reference index. One way annual turnover is computed as the annualised sum of realised absolute deviation of individual stock weights across quarters. Capacity is the weighted average market capitalisation of the index (in $m). It is a systematic metric that can be compared with that of the cap-weighted index to assess the liquidity of the strategy. Table 1 shows absolute performance summary statistics for the Scientific Beta USA Diversified Multi- Strategy index as well as its component strategies (the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Weighted strategies) from inception (21/06/2002) to 31/12/2012. Table 1. Absolute Performance and Risk Characteristics and Implementation This table reproduces absolute performance and risk characteristics for the Scientific Beta USA Efficient Maximum Sharpe Ratio, the Scientific Beta USA Efficient Minimum Volatility, the Scientific Beta USA Maximum Deconcentration, the Scientific Beta USA Maximum Decorrelation, the Scientific Beta USA Diversified Risk Weighted and the Scientific Beta USA Diversified Multi-Strategy indices, as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. Absolute Performance and Risk Maximum Deconcentration Diversified Risk Weighted Scientific Beta USA Indices Maximum Decorrelation Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Diversified Multi-Strategy Annualised Returns 7.79% 7.99% 7.67% 8.58% 7.86% 8.00% Annualised Volatility 22.46% 21.27% 21.09% 18.23% 20.12% 20.58% Sharpe Ratio Sortino Ratio One Way Turnover 27.2% 28.6% 31.8% 29.5% 31.5% 25.2% Capacity ($m) 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. The risk-free rate used is the Secondary Market US Treasury Bill (3M) in US Dollars. All results are in USD. 9 - Any analysis of the reward a portfolio provided in the form of returns needs to be adjusted for the amount of risk it procures. Volatility is often used as a convenient risk measure and this leads to an assessment of returns, volatility and the Sharpe ratio. Asymmetric risk measures go beyond volatility and provide a measure of loss risk or downside risk which may be perceived as a more relevant risk measure for investors in practice.

15 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index The table shows that the Scientific Beta Diversified Multi-Strategy index, which equally weights its constituents, has an annualised return of 8.00% and an annualised volatility of 20.58% which leads to a Sharpe ratio of Although the Sharpe ratio of 0.31 is not as high as that of the Scientific Beta USA Efficient Minimum Volatility index, it still matches or outperforms the rest of the Scientific Beta strategies. As far as the volatility is concerned, the Scientific Beta Diversified Multi-Strategy index has a value of 20.58% which is comparable to the Scientific Beta USA Efficient Maximum Sharpe Ratio index which has the second lowest volatility among all strategies. It is interesting to see that the Diversified Multi-Strategy index not only has a manageable turnover of 25.2%, but it also has the lowest turnover among all strategies. This means that it can be implemented without incurring excessive transaction costs. The capacity measure of the Diversified Multi-Strategy index is $24.2bn while that of the cap-weighted index (not shown here) is $84.5bn. It means that the strategy is about one-fourth as liquid as the cap-weighting strategy, which is known to have very large investment capacity. In what follows, we show the extreme risk measures available on the Scientific Beta platform which are the historical VaR which corresponds to the 5th percentile of the distribution of returns, the Cornish- Fisher VaR which consists of adjusting the VaR for the skewness and kurtosis of the distribution of returns (which are admittedly not normally distributed), and finally 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. The latter measure, which is quite sensitive to the data frequency, is computed based on a daily price index. Table 2 below shows the summary of the extreme risk statistics of the Diversified Multi-Strategy index as well as the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Weighted indices from inception (21/06/2002) to 31/12/2012. Table 2. Absolute Extreme Risk Characteristics This table reproduces absolute extreme risk characteristics for the Scientific Beta USA Efficient Maximum Sharpe Ratio, the Scientific Beta USA Efficient Minimum Volatility, the Scientific Beta USA Maximum Deconcentration, the Scientific Beta USA Maximum Decorrelation, the Scientific Beta USA Diversified Risk Weighted and the Scientific Beta USA Diversified Multi-Strategy Indices, as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. Extreme Risk Maximum Deconcentration Diversified Risk Weighted Scientific Beta USA Indices Maximum Decorrelation Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Diversified Multi-Strategy Cornish Fisher 5% VaR 2.05% 1.92% 1.93% 1.60% 1.82% 1.86% Historical 5% VaR 2.16% 2.00% 2.01% 1.71% 1.90% 1.95% Maximum Drawdown 56.43% 54.39% 53.09% 47.33% 52.35% 52.73% All statistics are annualised averages. The risk-free rate used is the Secondary Market US Treasury Bill (3M) in US Dollars. All results are in USD.

16 16 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index The table reveals that the indicators of the risk of loss (e.g. VaR, Cornish VaR and Max Drawdown) are the highest for the Scientific Beta USA Max Deconcentration index and the lowest for the Scientific Beta USA Efficient Minimum Volatility index. The Scientific Beta USA Diversified Multi-Strategy index, however, has a risk of loss that is situated between these two indices. The findings on extreme risk are consistent with those of the normal risk measures such as the volatility presented in Table 1. Finally, it is also important to analyse the relative risk of the alternative weighting schemes that cover the same universe as cap-weighting indices, which remain the major reference indices in the investment industry. A quite robust method to measure the consistency of outperformance is to compute outperformance probabilities for investment horizons of 1 (or 3) years. This measure is the historical empirical probability of outperforming the benchmark over a typical investment horizon irrespective of the entry point in time. It is computed using a rolling window analysis with 1- or 3-year window length and one week step size. Table 3(a) below shows the Diversified Multi- Strategy index as well as the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Weighted indices relative performance and risk characteristics, with respect to the cap-weighted reference index, from inception (21/06/2002) to 31/12/2012. Table 3(a). Relative Performance and Risk Characteristics This table reproduces relative performance and risk characteristics over a cap-weighted benchmark for the Scientific Beta USA Efficient Maximum Sharpe Ratio, the Scientific Beta USA Efficient Minimum Volatility, the Scientific Beta USA Maximum Deconcentration, the Scientific Beta USA Maximum Decorrelation, the Scientific Beta USA Diversified Risk Weighted and the Scientific Beta USA Diversified Multi-Strategy indices as of 31/12/2012, based on the whole history of index returns beginning on 21/06/2002. The Scientific Beta United States cap-weighted benchmark comprises 500 securities weighted in proportion to their free-float market-capitalisation weights Relative Performance and Risk Annualised Excess Returns Maximum Deconcentration Diversified Risk Weighted Scientific Beta USA Indices Maximum Decorrelation Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Diversified Multi-Strategy 1.80% 2.00% 1.69% 2.59% 1.88% 2.01% Tracking Error 3.28% 2.79% 3.33% 4.42% 3.18% 2.84% Information Ratio Treynor Ratio Outperformance Probability (1 year) 66.7% 74.7% 66.5% 76.7% 78.5% 77.7% Outperformance Probability (3 year) 89.3% 90.1% 92.6% 100% 99.2% 99.0% 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. The risk-free rate used is the Secondary Market US Treasury Bill (3M) in US Dollars. All results are in USD. Interestingly, the relative analysis of the performance and risk characteristics of all strategies with respect to the Scientific Beta cap-weighted index shows a different picture when compared to the absolute analysis. The Scientific Beta USA Efficient Minimum Volatility index has the highest excess return combined with the highest tracking error. This is to be expected as this behaviour of Minimum Volatility strategies is well documented in the literature and it has been attributed to the fact that

17 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index Minimum Volatility indices have much lower market exposure than cap-weighted indices (see e.g. Chan et al. (1999); or Baker et al. (2011) for related evidence on tracking error of low volatility portfolios). On the other hand, the lowest tracking error is attributed to the Scientific Beta USA Diversified Risk Weighted index. Table 3(a) clearly shows the potential of the Diversified Multi-Strategy weighting scheme to diversify away the risk by combining different strategies. The excess return of the Diversified Multi-Strategy weighting scheme corresponds to the mean excess return of the five constituent strategies while its tracking error (2.84%) is lower than the mean tracking errors of its components (3.40%). This leads to a high Information Ratio (of 0.71). Also, the outperformance probability of the Diversified Multi- Strategy weighting scheme is well above the average outperformance probability of the constituent strategies. Clearly, the Scientific Beta USA Diversified Multi-Strategy index presents some interesting characteristics as it stabilises the risk of deviating from the cap-weighted index (i.e. the relative risk) while achieving reasonable excess returns. In other words, the Scientific Beta USA Diversified Multi- Strategy index presents a good trade-off between relative risk and relative return. In order to support the results presented in Table 3(a), we show in Table 3(b) below the excess returns, tracking errors, and information ratios of the previous alternative weighting schemes at different periods. Table 3(b). Relative Performance and Risk Characteristics This table reproduces the excess returns, tracking errors, and information ratios for the Scientific Beta USA Efficient Maximum Sharpe Ratio, the Scientific Beta USA Efficient Minimum Volatility, the Scientific Beta USA Maximum Deconcentration, the Scientific Beta USA Maximum Decorrelation, the Scientific Beta USA Diversified Risk Weighted and the Scientific Beta USA Diversified Multi-Strategy indices as of 31/12/2012, based on the last year, the last three years, the last five years and the whole history of index returns beginning on 21/06/2002. All results are in USD. Scientific Beta USA Indices Relative Performance and Risk Excess Returns (Full History) Tracking Error (Full History) Information Ratio (Full History) Excess Returns (5 years) Tracking Error (5 years) Information Ratio (5 years) Excess Returns (3 years) Tracking Error (3 years) Information Ratio (3 years) Maximum Deconcentration Diversified Risk Weighted Maximum Decorrelation Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Diversified Multi-Strategy 1.80% 2.00% 1.69% 2.59% 1.88% 2.01% 3.28% 2.79% 3.33% 4.42% 3.18% 2.84% % 2.02% 1.51% 3.44% 2.01% 2.09% 3.70% 2.94% 3.38% 5.26% 3.39% 2.97% % 1.74% 0.96% 2.34% 1.35% 1.53% 2.71% 2.15% 2.56% 3.77% 2.52% 2.20%

18 18 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index Excess Returns (1 year) Tracking Error (1 year) Information Ratio (1 year) 0.25% -0.28% -0.03% -1.33% -1.65% -0.58% 2.27% 1.90% 2.18% 3.36% 2.34% 2.00% Table 3(b) confirms the results of Table 3(a) as the tracking errors based on shorter sample periods are also low, indeed they are the minimum or very close to the minimum tracking error across all strategies analysed. The information ratio of Diversified Multi-Strategy is well above the average information ratio and more often than not it is the highest across the constituent strategies. In the following sub-section, we present the calendar-year performances, tracking errors, and information ratios of the Scientific Beta Multi Strategy index and its components. Calendar-Year Performance and Tracking Errors In this sub-section, we aim to compare the annual excess returns, tracking errors, and information ratios for the Scientific Beta Diversified Multi-Strategy index and its five constituent strategies. It is important to see if the diversification benefits (i.e. reducing risk and smoothing the overall return) of the Diversified Multi-Strategy index hold not just over the full period since inception of these indices, but also consistently for shorter sub-periods. Table 4 presents the calendar-year performances and tracking errors of the Scientific Beta USA Diversified Multi-Strategy index and its five constituent strategies since the year Table 4. Calendar-Year Performance, Tracking Errors, and Information Ratios of the Scientific Beta USA Diversified Multi-Strategy Index and its Five Constituents This table shows the calendar-year relative returns (over cap-weighted reference index) in Panel A, the calendar-year tracking errors in Panel B, and calendar-year information ratios in Panel C for the Scientific Beta USA Efficient Maximum Sharpe Ratio, the Scientific Beta USA Efficient Minimum Volatility, the Scientific Beta USA Maximum Deconcentration, the Scientific Beta USA Maximum Decorrelation, the Scientific Beta USA Diversified Risk Weighted and the Scientific Beta USA Diversified Multi-Strategy indices since year The average relative return and tracking error, in each period, across the five constituent strategies are also shown. The lowest tracking errors in Panel B are highlighted in bold. In Panel A, the worst and best performances for each year are indicated in green and red colours respectively. Max Deconcentration Diversified Risk Weighted Max Decorrelation Scientific Beta USA Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Average across 5 strategies Diversified Multi-Strategy Panel A: Calendar Year Annualised Relative Returns Year % -0.28% -0.03% -1.34% -1.65% -0.61% -0.58% Year % 0.45% -2.51% 4.72% 0.48% 0.21% 0.19% Year % 5.29% 6.04% 3.40% 5.44% 5.23% 5.23% Year % 6.73% 5.73% -0.06% 5.43% 5.48% 5.48% Year % 0.02% 0.25% 6.93% 1.26% 1.22% 1.20% Year % -2.04% -0.60% -2.37% -0.44% -1.13% -1.13% Year % 0.08% -2.40% 2.55% -0.42% -0.26% -0.26% Year % 3.86% 5.00% 3.73% 4.45% 4.33% 4.34% Year % 6.34% 6.18% 7.21% 5.76% 6.22% 6.23% Panel B: Calendar Year Annualised Tracking Error Year % 1.90% 2.18% 3.36% 2.34% 2.41% 2.00% Year % 2.37% 2.77% 4.54% 2.81% 3.11% 2.43%

19 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index Year % 2.14% 2.67% 3.29% 2.38% 2.64% 2.14% Year % 3.43% 3.62% 6.19% 3.45% 4.25% 3.20% Year % 4.20% 4.93% 7.57% 5.15% 5.38% 4.39% Year % 1.97% 2.55% 2.93% 2.51% 2.42% 2.11% Year % 1.93% 2.56% 2.05% 2.07% 2.22% 1.91% Year % 2.08% 2.46% 2.30% 2.12% 2.25% 2.07% Year % 2.48% 3.09% 3.06% 2.55% 2.76% 2.49% Panel C: Calendar Year Information Ratio Year Year Year Year Year Year Year Year Year The returns and tracking error are calculated based on daily total returns (with dividend reinvested). The Scientific Beta USA cap-weighted benchmark comprises Scientific Beta USA securities weighted in proportion to their free-float adjusted market-capitalisation. The Scientific Beta USA universe is composed of 500 stocks. The table shows that by combining the strategies, in some years, we achieve a tracking error that is lower than any constituent strategy. For instance, during the years 2005, 2006, 2008, 2009 and 2010 the Scientific Beta Diversified Multi-Strategy index achieves a lower tracking error than even the lowest tracking error among constituent strategies. 10 This clearly shows the diversification benefit of combining strategies. Moreover, the tracking error of the Scientific Beta Diversified Multi-Strategy index for any year is lower than the average tracking error of the other weighting schemes. 11 The results clearly demonstrate the index s ability to control the average tracking error with respect to the cap-weighted reference index. It should be noted however that diversification across strategies is not likely to be able to control the extreme relative risk, i.e. the risk of obtaining significant underperformance with respect to cap-weighted indices in situations where all strategies simultaneously face drawdowns with respect to the cap-weighted index. Indeed, such extreme relative risk events can only be avoided through hedging or through insurance as opposed to diversification (see Amenc, Goltz, Lodh and Martellini (2012b)). Concerning the relative returns, we see in the table that the Scientific Beta Diversified Multi-Strategy index averages the relative returns of all indices which lead to a smoothing of the overall performance. 12 In the table above, it is clearly shown in Panel A that some smart beta strategies can have severe underperformances (highlighted in red) in certain periods while others are successful in achieving overperformance (highlighted in green). 13 The Diversified Multi-Strategy index is never the worst nor is it the best strategy, which implies that by combining different alternative weighting schemes there 10 - The lowest tracking errors are highlighted in bold. 11- The column Average Tracking Error presents the average tracking errors of all strategies namely the Scientific Beta Efficient Minimum Volatility index, the Scientific Beta Max Deconcentration index, the Scientific Beta Max Decorrelation index, the Scientific Beta Diversified Risk-Weighted index and the Scientific Beta Efficient Max Sharpe ratio The column Average Relative Returns presents the average relative returns of all strategies namely the Scientific Beta Efficient Minimum Volatility index, the Scientific Beta Max Deconcentration index, the Scientific Beta Max Decorrelation index, the Scientific Beta Diversified Risk-Weighted index and the Scientific Beta Efficient Max Sharpe ratio index As shown in Panel A of Table 4, there are marginal differences between the relative returns of the Scientific Beta Diversified Multi-Strategy index and the average relative returns across its five constituents for the years 2008, 2011 and It is important to note that, although the Scientific Beta Diversified Multi-Strategy index equally weights its components, the equal-weighting applies every quarter only. However, between quarters the index weights are not necessarily equally weighted as index values change. Such a change can contribute to the marginal differences between the relative returns documented for the years 2008, 2011 and 2012.

20 20 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index March Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index is no risk of picking the worst performing index. For instance, during 2007, the Scientific Beta Efficient Minimum Volatility index showed an underperformance of 2.37% which was due to the strong bull market (i.e. the performance of the cap-weighted index was 7.89%). However, the averaging effect across the five weighting schemes resulted in a return of -1.13% for the Diversified Multi Strategy Index which is a much less drastic loss than that of the Scientific Beta Efficient Minimum Volatility index. 14 Therefore, if one wishes to avoid such strategy selection risk, the Scientific Beta Multi-Strategy index allows one to do so. While the year 2007 illustrated bull market conditions, the year 2011 presents an example of a bear market where the cap-weighted reference index had modest performance of 1.60%. The Scientific Beta Max Decorrelation index underperformed in these conditions with a negative relative return of -2.51%. However, diversifying across five strategies led to a relative return close to zero (0.19%). Overall, the Scientific Beta Diversified Multi-Strategy index, by averaging the returns across strategies, avoids severe underperformances and results in a smoother excess return profile. In the coming section, we will provide more discussion on the conditional performance of the Scientific Beta Multi-Strategy index under different market conditions. Conditional Performance (bull/bear and high/low volatility regimes) 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 et al. (2012a) 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 Quian (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. In this section, we display a strategy s relative returns distinctly for bull and bear markets, and for high volatility and low volatility markets. Half the calendar quarters with the highest cap-weighted reference index returns are categorised as bull markets and the rest of quarters as bear markets. The high volatility market regime consists of the top half of quarters sorted on the cap-weighted benchmark s volatility and the low volatility market regime comprises the remaining quarters Although, the Scientific Beta Efficient Minimum Volatility index is the worst performing strategy in 2007, it is the best performing one in ERI Scientific Beta computes bull and bear returns for Smart Beta indices dividing the whole time period into quarters and computing the corresponding returns for the cap-weighted reference index. Quarters are then classified as bull or bear quarters, depending on whether the return of the reference index is higher or lower than the median reference index return across all quarters. 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.