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 October 2013

2 2 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October 2013 Table of Contents 1. Introduction to the Diversified Multi-Strategy Index Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index Flagship Index: Details on the Scientific Beta USA High Liquidity Diversified Multi-Strategy Index Summary...33 References...37 About ERI Scientific Beta...41 ERI Scientific Beta Publications...45 Printed in France, October The authors can be contacted at beta.com.

3 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October 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 Parity weighting schemes. The combination of these different strategies allows the diversification of risks that are specific to each strategy by exploiting the imperfect correlation between the different strategies parameter estimation errors and the differences in their underlying optimality assumptions. 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 similar outperformance as 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. However, a strategy such as the ERI Scientific Beta Multi-Strategy index may not be an appropriate choice of strategy for investors with strong views on future market conditions as it can prevent them from achieving high outperformance levels in case they have some ability to time the market accurately.

4 4 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October 2013 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 October Introduction to the Diversified Multi-Strategy Index

6 6 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October 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 Parity 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 1 - Intuitively, the fact that cap-weighted indices are inefficient and poorly diversified is not surprising because they 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 in 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 October Introduction to the Diversified Multi-Strategy Index strategy is implemented with upper and lower bounds on individual weights to avoid a highly concentrated portfolio. (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 assumptions and set of parameters it draws on. 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 All smart beta strategies are exposed to strategy specific and to systematic risks. Systematic risks refer to the exposures to common equity risk factors such as the value factor or the small cap factor. Like active managers who will not only expose investors to systematic risk factor tilts but also to a manager-specific risk related to how they process information and how they conduct their investment processes, smart beta strategies are also exposed to strategy specific risk. This specific risk can be further divided into two components. In fact, any strategy is faced with optimality risk (i.e. the risk that the assumptions under which the strategy would be theoretically optimal do not hold) and parameter estimation risk (i.e. the risk of making errors on the risk and return properties of stocks). The costs of parameter estimation error may in some cases entirely offset the benefits of optimal portfolio diversification (see e.g. De Miguel et al., 2009b). Thus, the choice in risk and return parameter estimation for efficient diversification is between "trying", which has a cost related to parameter estimation risk, i.e. the risk of a substantial difference between the estimated parameter value and the true parameter value, or "not trying", which also has an optimality risk, related to the risk that a strategy can be very far from the mean-variance optimal portfolio in terms of risk return profile. It is clear that choosing a weighting scheme corresponds to choosing a model of optimal portfolio construction. In fact, any weighting scheme can be understood as reflecting a set of assumptions under which the resulting portfolio would lead to an optimal portfolio in the sense of MPT (see Martellini, 2013 or Melas and Kang, 2010). Evaluating the optimality risk requires understanding how a particular portfolio weighting scheme is situated in comparison with the optimal portfolio 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 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 October Introduction to the Diversified Multi-Strategy Index constituted by the Maximum Sharpe Ratio (MSR) portfolio. The comparative table shown below (Table 1) recalls the conditions of optimality for each alternative weighting scheme proposed on the ERI Scientific Beta platform. Table 1: Specific risks and conditions of optimality of the Scientific Beta Strategies The table below lists the optimality and parameter estimation risks of the Scientific Beta Efficient Maximum Sharpe Ratio, the Scientific Beta Efficient Minimum Volatility, the Scientific Beta Maximum Deconcentration, the Scientific Beta Maximum Decorrelation and the Scientific Beta Diversified Risk Parity indices, together with the conditions on the parameters for the relevant strategy to be identical to the Maximum Sharpe ratio or optimality conditions. It also exhibits the analytical form of optimal weights that solve the relevant strategy in the absence of weight constraints. Here, w* is a vector of optimal weights, μ i is the expected return of the i-th stock in excess of risk-free rate, λ i is the Sharpe ratio of the i-th stock, σ i is the volatility of the i-th stock, ρ i,j is the correlation between stock i and stock j for i j, Σ is the NxN covariance matrix of N stocks, Ω is the NxN correlation matrix of N stocks and is a Nx1 vector of ones. Scientific Beta Strategy Maximum Deconcentration Efficient Maximum Sharpe ratio Efficient Minimum Volatility Maximum Decorrelation Diversified Risk Parity Unconstrained Closed-Form Solution Optimality Cost Ignorance of individual volatilities, expected excess returns and pair-wise correlations None Ignorance of expected returns Ignorance of individual volatilities and expected excess returns Ignorance of diversity of correlation levels and Sharpe ratios Parameter Estimation Risk Required Parameter - No risk or return parameter required Accuracy and robustness of correlation matrix, volatilities and expected return Accuracy and robustness of correlation matrix and volatilities Accuracy and robustness of the correlation matrix Accuracy and robustness of the estimated individual volatilities Correlation matrix, stock volatilities and expected returns Correlation matrix, stock volatilities Correlation matrix, Individual volatilities (and average pairwise correlation) Optimality Conditions μ i = μ i σ i = σ i ρ i,j = ρ i Optimal by construction μ i = μ i μ i = μ i σ i = σ i λ i = λ i ρ i,j = ρ i Table 1 clearly shows that behind any alternative weighting scheme there is an important assumption that makes it optimal in the MPT framework. Therefore, from a pragmatic perspective, it seems reasonable to assume that different market conditions may favour different assumptions, and thus alternative weighting schemes may display dissimilar performance depending on market conditions. Amenc et al. (2012b) show that even in a relatively short span of nine years, no single strategy consistently outperforms all other strategies, even though all strategies show outperformance with respect to cap-weighted indices more often than they show underperformance. This kind of behaviour points to the fact that each strategy is favoured by certain kinds of market conditions, which means that no strategy can be assumed to be uniquely superior to the others and there is always a risk that the chosen model may not yield attractive performance in a given period.

9 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Introduction to the Diversified Multi-Strategy Index Parameter estimation risk is a subject that is well-known to all portfolio construction specialists. One of the principal concerns of researchers in finance has been to reduce this risk. This reduction is based on two principles. The first is to have a parsimonious portfolio construction model to reduce the number of parameters to be estimated. The second element is the technique for estimating the parameters. 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, it may be reasonable to assess whether anything can be gained from combining models and thus diversifying strategy specific risk (i.e. optimality risk and parameter estimation risk). To this end, the ERI Scientific Beta Multi-Strategy index draws on the idea of diversification by combining, in equal proportions, the five alternative weighting schemes introduced in section 1.1. While the parameter estimation and optimality risks are specific to the strategy itself, we also have the systematic risk that affects all strategies. It is a risk that comes from the fact that new indices or smart beta strategies can be more or less exposed to particular risk factors depending on the methodological choices guiding their construction; this exposure can be expressed either in absolute terms or more often in relative terms with respect to the cap-weighted index which is representative of the same universe of securities. For example, an index construction scheme that uses indicators of the firm s economic size leads more often than not to the index being exposed to style biases such as value or small cap biases compared to its cap-weighted reference index (e.g. fundamentally weighted indices have a value bias due to their use of accounting measures 7 ). In the same way, compared to the cap-weighted reference index, a scheme that favours lowvolatility stocks will lead to overexposure to some sectors and of course to a very different exposure to the volatility factor. These systematic risk exposures or the factor tilts can be controlled at the strategy level by applying the weighting scheme to a characteristic based stock selection rather than to the broad stock universe. In Section 2.6, we discuss the performance and risk analysis of Diversified Multi-Strategy on high liquidity and large cap stock selections. It must be noted that the diversification across different weighting schemes only reduces the strategy specific (optimality + parameter estimation) risks and it is not designed to control systematic risks. In the following section, we discuss the construction principles of the ERI Scientific Beta Multi- Strategy index in details and provide more foundation on the notion of diversifying across strategies. 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 Parity weighting schemes. The combination of these different strategies is used to reduce the strategy specific risks. In particular, since different weighting schemes are optimal for different sets of underlying assumptions, their combination may 7 - Perold (2007) argues that Fundamental indexing is a strategy of active security selection through investing in value stocks. Jun and Malkiel (2008) assess the performance of the FTSE RAFI index and find that the alpha of this index is zero after adjusting for market, value and small cap exposure.

10 10 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Introduction to the Diversified Multi-Strategy Index result in more robust outperformance. Moreover, the parameter estimation risks across strategies are imperfectly correlated and thus can be diversified away. 1.4 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 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. 8 Kan and Zhou (2007) show that when there is parameter uncertainty, following the standard prescription of portfolio theory to hold only the Maximum Sharpe Ratio (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 maximum Sharpe ratio portfolio. In particular, the authors show that a portfolio that optimally combines the riskless asset, the Maximum Sharpe Ratio portfolio and the Global Minimum Variance portfolio dominates a portfolio with just the riskless asset and the Maximum Sharpe Ratio 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 Parity 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 selections of strategies to be combined as well as more sophisticated approaches of determining the weighting of the different strategies 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. 9 - It is important to note that the optimal combinations of several diversification strategies require an estimation procedure that carries additional parameter estimation risk.

11 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Introduction to the Diversified Multi-Strategy Index 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. 1.5 Implementation Choices As mentioned above (Table 1), implementation choices have to be made on parameter estimation, 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 rules relevant to the Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Parity 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 Parity 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 Parity 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

12 12 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Introduction to the Diversified Multi-Strategy Index 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. 10 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 threshold is calibrated using the past data, and it is fixed at the level that would have resulted in no 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 brings down 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 Specifically, liquidity adjustments consist 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.

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

14 14 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October 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 a clearer picture to investors as to why (and when) it may be important to choose a multi-strategy index instead of a single strategy. In what follows, we start with an analysis of the risk factor exposures of the Scientific Beta Diversified Multi-Strategy index and its components. 2.1 Risk Factor Exposures Like any weighting scheme, the Diversified Multi-Strategy index can lead to exposures to well-known equity risk factors. Investors must be aware of all the factors they are being exposed to if they wish to clearly understand which part of the strategy performance is related to the exposure to systematic risk factors. As the consensus in academic finance and also among practitioners suggests that the simple single market factor used in the CAPM model does not do a good job in capturing the cross section of expected stock returns, there has been development of multi-factor models that account for a range of priced risk factors. Here, we employ the Fama-French three-factor model to assess exposures to three well-known systematic factors: the market factor as represented by the market cap-weighted reference index; the small cap factor (Small-Minus-Big or SMB); and the value factor (High-Minus-Low or HML) (see Fama and French, 1992). Table 2 below shows the coefficient estimates and R² of the regression of the Diversified Multi-Strategy index s excess returns (over the risk-free rate) as well as Efficient Maximum Sharpe Ratio, the Efficient Minimum Volatility, the Maximum Deconcentration, the Maximum Decorrelation and the Diversified Risk Parity indices excess returns on the three Fama-French factors from index inception (21/06/2002) to the end of 2012 (31/12/2012). The table shows that the Scientific Beta Diversified Multi-Strategy index has a market beta that is less than one (i.e. 0.93), which implies that the index is less sensitive to market fluctuations than its cap-weighted reference. The coefficient value of 0.93 represents the average market exposure of the Diversified Multi-Strategy index s constituents. Secondly, the Scientific Beta Diversified Multi-Strategy index shows a clear bias towards the small-cap factor as it is a common feature among all the constituting strategies. In terms of value or growth exposure, the index shows a much less pronounced bias with a coefficient close to zero though the slight growth exposure is statistically significant. Compared to its component strategies, we can clearly see that the Diversified Multi-Strategy index does not have any extreme exposure to systematic risk factors. Rather the index shows moderate coefficient values compared to some of the single strategies. For instance, the Diversified Multi-Strategy index exhibits an exposure of 0.34 to the small-cap (SMB) factor which lies between the Scientific Beta USA Max Deconcentration and Scientific Beta USA Efficient Minimum Volatility indices which respectively have the

15 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index highest (0.43) and the lowest (0.19) exposure to small-cap factor among the five constituting weighting schemes. Table 2. Analysis of Risk Factor Exposures with the Fama-French Factor Model. The table shows the coefficient estimates and R-squared of the regression of index's excess returns (over the risk-free rate) 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 Parity and the Scientific Beta USA Diversified Multi-Strategy indices as of 31/12/2012 using the Fama-French 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. Fama-French Factor Maximum Deconcentration Diversified Risk Parity Scientific Beta USA Indices Maximum Decorrelation Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Diversified Multi-Strategy Alpha (Annualised) 0.13% 0.69% 0.41% 2.31% 0.90% 0.89% Market Small-Minus-Big High-Minus-Low R² 100% 100% 99% 98% 99% 99% We use simple OLS regression and the t-statistic is computed using paired difference testing on the OLS estimates of betas. The 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. Beyond exposure to style and size factors shown here, for equity investors, quantifying the sector exposure is also an important factor in the decision making process as investors may have a preference for certain sectors and/or want to avoid large investments in specific sectors. In what follows, we discuss the sector exposure of the Scientific Beta Multi-Strategy index and its constituent strategies. 2.2 Sector Exposures Since the smart beta strategies can tilt a portfolio to certain sectors and in extreme cases lead to totally omitting others in the resulting investment, it is important to analyse the sector weights of such strategies. This is particularly relevant for investors who are interested in a specific weighting strategy, but are concerned that some sectors may be under represented. Therefore, this comparative analysis of the sector exposure enables investors to have insight into the effect of the strategy's methodology on sector weights. In Table 3 below, we show sector weights and deviations relative to the cap-weighted reference index 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 Parity strategies based on the portfolio's stock weight profile as of the last rebalancing date in 2012 (21/12/2012)

16 16 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index Table 3. Sector Allocation. The table shows (1) absolute industry exposures (in weight percentage) (2) relative industry exposures (in weight percentage) with regard to the cap-weighted reference index 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 Parity and the Scientific Beta USA Diversified Multi-Strategy indices, based on each index's weight profile at the last rebalancing date (21/12/2012). 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. Sector Exposure Maximum Deconcentration Diversified Risk Parity Scientific Beta USA Indices Maximum Decorrelation Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Diversified Multi-Strategy Absolute Relative Absolute Relative Absolute Relative Absolute Relative Absolute Relative Absolute Relative Energy 10.30% -1.40% 9.60% -2.10% 11.90% 0.10% 6.50% -5.30% 10.90% -0.90% 9.80% -1.90% Basic Materials 6.30% 2.90% 5.60% 2.10% 5.80% 2.30% 4.40% 1.00% 5.30% 1.80% 5.50% 2.00% Industrials 13.10% 2.20% 12.30% 1.30% 6.90% -4.10% 7.90% -3.10% 7.40% -3.60% 9.50% -1.50% Cyclical Cons % 3.10% 14.40% 1.80% 14.80% 2.20% 13.10% 0.60% 14.30% 1.80% 14.50% 1.90% Goods & Services Non Cyclical Cons. 7.80% -2.00% 9.70% -0.10% 12.50% 2.60% 17.20% 7.30% 14.00% 4.20% 12.20% 2.40% Goods & Services Financials 18.20% 1.40% 17.20% 0.40% 16.30% -0.50% 11.80% -5.00% 14.70% -2.10% 15.60% -1.10% Healthcare 9.60% -1.50% 10.10% -1.00% 11.30% 0.20% 15.50% 4.30% 11.90% 0.80% 11.70% 0.60% Technology 10.90% -5.20% 10.20% -5.90% 12.30% -3.80% 8.30% -7.90% 10.80% -5.40% 10.50% -5.60% Telecommunication 1.60% -2.20% 1.70% -2.10% 1.60% -2.20% 2.50% -1.40% 1.20% -2.60% 1.70% -2.10% services Utilities 6.30% 2.80% 9.00% 5.50% 6.70% 3.20% 12.90% 9.40% 9.40% 5.90% 8.90% 5.40% Table 3 shows a similarity between sector deviations of the Maximum Deconcentration and Diversified Risk Parity strategies. This is to relate to the fact that the Diversified Risk Parity index departs from equal-weighting by granting more weight to the stocks that have the lowest volatilities. Hence, low volatility sectors like Utilities show a weight increase from the Maximum Deconcentration index to the Diversified Risk Parity index (from 2.80% to 5.50%), and the more volatile Technology sector a decrease (from -5.20% to -5.90%). On the other hand, the two efficient diversification approaches also display similarities, with significant positive relative exposures to defensive sectors like Non-cyclical consumer goods and services and Utilities as well as an important underweighting of the Technology and Industrials sectors. The overweighting of the Cyclical consumer and utilities sectors and underweighting of the Technology and Telecoms sectors is uniform across these five strategies. Therefore, the Diversified Multi-Strategy weighting scheme, being an equal-weighted combination of these strategies, also shows an overweighting in Cyclical consumer (+1.90%) and Utilities (+5.40%) and an underweighting in Technology (-5.60%) and Telecommunications (-2.10%). Due to this averaging effect, the Diversified Multi-Strategy index does not exhibit extreme relative weights as seen in the case of Efficient Minimum Volatility Index. As a matter of fact, for the case of the Efficient Minimum Volatility index, an extreme overweighting of 9.40% (underweighting of 7.90%) of the Utilities (Technology) sector is observed. In the case of the Scientific Beta Diversified Multi-Strategy index, the highest overweighting and underweighting of any sector is less extreme

17 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index with values at +5.40% and -5.60%, respectively. Clearly, the Scientific Beta Diversified Multi-Strategy index helps to achieve a reasonable diversity across sectors compared to the extremes observed with its component strategies. It should be noted that many of the strategies implemented on the Scientific Beta platform are provided with sector constraints so that investors could also draw on such constraints to manage sector exposures. 11 After having provided an overview of risk factor and sector exposures, we now turn to discuss the relative and absolute risk and return performance the Scientific Beta Diversified Multi-Strategy index. 2.3 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). 12 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 the reference to 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 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 4 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 Parity strategies) from inception (21/06/2002) to 31/12/2012. 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 can be implemented without incurring excessive transaction costs. The capacity measure of the Diversified Multi-Strategy index is $24.2bn while that of cap-weighted index (not shown here) is $84.5bn. It means that the strategy is about one-fourth as liquid as the cap-weighted strategy, which is known to have very large investment capacity See the Scientific Beta White Paper on Risk Management of Smart Beta Strategies 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.

18 18 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October Risk-adjusted Performance of the Scientific Beta Diversified Multi-Strategy Index Table 4. 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 Parity 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 Parity 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) 22,295 23,636 23,042 27,587 24,304 24,173 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. 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 daily price index. Table 5 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 Parity indices from inception (21/06/2002) to 31/12/2012 Table 5. 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 Parity 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 Parity Maximum Decorrelation Scientific Beta USA Indices Efficient Minimum Volatility Efficient Maximum Sharpe Ratio Diversified Multi-Strategy Cornish Fisher 2.05% 1.92% 1.93% 1.60% 1.82% 1.86% 5% VaR 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 average. The risk-free rate used is the Secondary Market US Treasury Bill (3M) in US Dollars. All results are in USD.

19 An ERI Scientific Beta Publication Scientific Beta Diversified Multi-Strategy Index October 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 4. Finally, it is also important to analyse the relative risk of the alternative weighting schemes with respect to the cap-weighted index covering the same universe as cap-weighting indices remain the major references in the investment industry. Probability of outperformance is the historical empirical probability of outperforming the benchmark over a typical investment horizon of 1 or 3 years, irrespective of the entry point in time. It is computed using a rolling window analysis with 1- or 3-year window length and a 1-week step size. Table 6(a) 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 Parity indices relative performance and risk characteristics, with respect to the cap-weighted reference index, from inception (21/06/2002) to 31/12/2012. Table 6(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 Parity 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 Parity 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 66.7% 74.7% 66.5% 76.7% 78.5% 77.7% Probability (1 year) 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 as 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 Minimum Volatility indices have much lower market exposure than cap-weighted indices (see e.g. Chan