Understanding Smart Beta: beyond diversification and low risk investing

Transcription

1 Amundi Discussion Papers Series DP May 2014 Understanding Smart Beta: beyond diversification and low risk investing Alessandro Russo, Quantitative Research For professional investors only

2

3 Abstract Smart Beta is the answer of asset management industry to some well know drawbacks of market capitalization-based equity indices as price noise, overrepresentation of large caps, absence of auto-corrective mean reversion mechanism. Some of these features may result in high volatility and massive drawdowns, thus potentially compromising the risk return payoff of traditional equities, at least when the investment horizon is shorter than 8-10 years. In this study we provide a formal description of three popular risk-based smart beta strategies (the minimum variance portfolio, the portfolio maximizing the diversification ratio, and the risk parity portfolio), providing some insights in terms of composition. Specifically we point out that all of them provide some interesting diversification enhancement relative to standard indices, and all of them contain low systematic risk characteristics. But still they exhibit different features that can be exploited in a diversified alternative beta allocation, as well as in some timing or rotation strategy. We show that low market beta and the low risk anomaly explain a relevant portion of the variability of the active returns of the minimum variance strategies, with some variance explained by sector reversal and dividend yield. Yet the unexplained variability corresponds to some non-negligible positive contribution to performance, while filtering the universe for some quality criteria provides additional value. As for the diversification-based strategies, low market beta and low risk anomaly are still the more significant factors, with the addition of small cap and sector reversal. Small cap and sector reversal are the most relevant factors for risk parity strategies, while low beta and low risk anomaly are less explanatory. If the investor s relevant risk measure is absolute risk, smart beta may become a new equity core. In this case, however, liquidity of smart beta strategies must be consistent with the amount of assets the investor holds. We finally discuss whether these strategies should be considered as passive or rather active strategies. Key words: smart beta, portfolio diversification, minimum variance, risk parity, entropy Amundi Discussion Papers Series - DP

4 4 Amundi Discussion Papers Series - DP

5 Understanding Smart Beta: beyond diversification and low risk investing Introduction Equity markets have been very challenging during the last 25 years: international indices often shifted from extraordinary bull market conditions to prolonged drawdowns with high realized volatility. During the first decade of the new century equity investors faced a major and unfavorable change in traditional risk-return payoffs. Such a background stimulated discussions over traditional market cap weighted index and growing evidence of their inefficiency had been pointed out. Market cap weighted indexes rely on stocks prices only and, as markets are not in equilibrium all the times, market value weights may suffer price noise. In extreme circumstances where bubbles arise, since market cap weighted indices mimic a buy and hold strategy (with no auto-corrective mean reverting mechanism embedded), overvalued stocks as telecom before 2000 or financials before 2008 become over-weighted. In addition, in market cap weighted index large cap are over represented, and small cap almost neglected. Weight of Information Technology and Telecom 40% 35% 30% 25% 20% 15% 10% 5% 30/12/94 28/4/95 31/8/95 29/12/95 30/4/96 30/8/96 31/12/96 30/4/97 29/8/97 31/12/97 30/4/98 31/8/98 31/12/98 30/4/99 31/8/99 31/12/99 28/4/00 31/8/00 29/12/00 30/4/01 31/8/01 31/12/01 30/4/02 30/8/02 31/12/02 30/4/03 29/8/03 31/12/03 30/4/04 31/8/04 31/12/04 29/4/05 31/8/05 30/12/05 28/4/06 31/8/06 29/12/06 30/4/07 31/8/07 31/12/07 30/4/08 29/8/08 31/12/08 30/4/09 31/8/09 31/12/09 30/4/10 31/8/10 31/12/10 29/4/11 31/8/11 30/12/11 30/4/12 31/8/12 31/12/12 TMT bubble RISK PARITY INDEX MKT CAP INDEX (MSCI WORLD) Amundi Discussion Papers Series - DP

6 The asset management industry has been proposing several alternative ways of building equity indices and portfolios, aiming to mitigate the inefficiency embedded in price-based index construction rules. These alternative indices or portfolios are known as smart beta equities and they generally belong to absolute risk-returns strategies: away from the notion of tracking error or information ratio, they focus on Sharpe ratio or risk adjusted return, and absolute volatility metrics. They can ideally be grouped into two categories: fundamental-based and risk-based portfolios. In the first family, as in the case of the RAFI index, stocks weights are proportional to some fundamental metrics, as revenues, income, cash flows, or dividends. In the second family, stocks may be weighted according to some risk metrics such as volatility, correlation and contribution to volatility, or may maximize some risk-based utility function (minimize volatility or maximize diversification). Within this category, risk-based weighting schemes may be applied to a restricted investment universe, according to the exposure of the stocks to some fundamental, technical, and style measures (also known as risk factors like value, momentum, volatility, or size). In the last few years, Amundi has deeply investigated smart beta equities, developing its own range of solutions aiming to Sharpe ratio improvement. They are based either on the use of instruments providing favorable asymmetry (options and other derivatives), or they belong to the risk-based family of alternative beta portfolios as minimum variance, optimal diversification, and risk parity The minimum variance portfolio I - Smart Beta Strategies Amundi claims several years of experience in minimum variance equity management, with two Europe portfolios (since 2007 and 2009 respectively) and some more recent portfolios on world developed markets, Japan, emerging markets, Pacific ex Japan, and other customized universes. The efficient frontier and the minimum variance portfolio The efficient frontier represents the set of portfolios that earn the maximum rate of return for every given level of risk. The minimum variance portfolio is the one sitting on the very edge of the efficient frontier. In building such a portfolio, expected returns are not needed as the only requirement is to minimize volatility, while being fully invested. The simple objective function is thus: Min (w T Vw) Such that e T w = 1 where w is the vector of the optimal portfolio weights, V is the variance-covariance matrix, and e T is a vector of ones. 6 Amundi Discussion Papers Series - DP

7 We will show in the next section that the minimization of variance is achieved though both the selection of low risk stocks (low systematic and low specific risk stocks), and the selection of those stocks that are exposed to uncorrelated even negatively correlated factors. In other words, we will prove that the minimum variance portfolio contains both a low risk story, and a diversification story. An enhanced process Although we recognize the advantage of such a process being transparent and intuitive, we are conscious of some typical drawbacks that may arise from minimum variance portfolios: as shown in Clarke, de Silva and Thorley (2011), minimum variance portfolios may be quite concentrated on a few low volatility stocks, may exhibit rather high turnover, may be exposed to value related factors such as dividend yield, may be invested in small capitalization stocks (with some relevant implications on liquidity), and may have some volatile exposure to momentum. Similarly, Thomas and Shapiro (2007) highlight the risk of the minimum variance portfolio being excessively concentrated on a few low risk sectors, and the lack of control for involuntary factor exposures. They also express their preference for tilting portfolios toward some successful stock ranking criteria. These are all relevant issues in portfolio construction. In order to take them into account, the best practice of the industry is to implement an enhanced portfolio construction process, employing filters to the investment universe, applying optimisation constraints, and allowing discretionary interventions by the fund managers. We will briefly describe Amundi s investment process in the annex. However, in the next section of this study, except where it is explicitly mentioned, we will ignore any aspect that is beyond the pure smart beta portfolio construction, as we want to focus on the impact that the unconstrained minimum variance process has on portfolio composition. 1.2 The portfolio maximizing the diversification ratio Several reasonable diversification measures exist, and maximizing each of them would lead each time to a different portfolio. One of the most popular measures of diversification is the so called diversification ratio, which is the ratio (Ω) of average stocks volatility on portfolio volatility, as it was originally introduced by Choueifaty and Coignard in Ω = w σ, w w σ σ ρ Since correlations among any pairs of assets are lower than one, the denominator is lower than the numerator and the ratio is always higher than one. Maximizing this Amundi Discussion Papers Series - DP

8 ratio is thus equivalent to minimizing the average correlation across all the stocks in the portfolio. Better diversification and lower correlations explain why the risk of the portfolio maximizing the diversification ratio is always lower than the risk of a standard market index. In addition to that, the optimisation contains a pseudo-minimization of the denominator that is satisfied via the selection of low systematic risk stocks. On the other hand, at the numerator, the optimisation results in the selection of high specific risk stocks since they increase average volatility, while having little impact on the denominator: specific risk doesn t matter at the denominator as it is easily diversified away. As a result, the portfolio maximizing the diversification ratio may show an average total volatility that is not statistically different from that of a standard market index, but will necessarily result in below average systematic risk stocks (the denominator effect), and above average specific risk stocks (the numerator effect). Very often the portfolio maximizing the diversification ratio is presented as a portfolio belonging to the efficient frontier, or even being the tangency portfolio (the portfolio maximizing the Sharpe ratio). Actually, this portfolio corresponds to the maximum Sharpe ratio portfolio only in the hypothesis that expected returns are strictly proportional to their total volatility. If this hypothesis does not hold, still being the portfolio that maximizes our specific definition of diversification (Ω), such a portfolio is below the efficient frontier and does not correspond to the tangency portfolio. Neither can we state that the portfolio maximizing the diversification ratio corresponds to the market portfolio, as we would assume that such a market portfolio is completely insensitive to expected returns. Maximizing diversification is an intuitive and transparent process, but as for the minimum variance process it may contain the typical drawbacks of optimisationbased portfolios, such as overconcentration, lack of liquidity, (involuntary) style exposures, turnover, low fundamental quality. For these reasons, when dealing with diversification-based strategies, we believe that an enhanced process similar to the minimum variance one may be sound. However from now on, we will ignore any aspect that is beyond the pure smart beta portfolio construction, as we want to focus on the impact that the risk-based process alone has on portfolio composition. 1.3 The risk parity portfolio Risk parity means that each asset (asset class, equity sector, single stock) has an equal contribution to the total risk of the portfolio. 8 Amundi Discussion Papers Series - DP

9 In order to come out with full risk parity, the following relationship must hold: = = = Where RC i is the risk contribution of the i th asset, and MC i is its marginal contribution to risk, defined as follows = In other words, the risk contribution should be the same for any asset or asset class and the weight of each asset or asset class should be proportional to the inverse of its marginal contribution to risk: ~ 1 Actually, marginal contributions to risk are both function of volatilities and correlations of any asset with the rest of the portfolio, with correlations depending on portfolio composition itself. In other words, weights are the unknowns and should be proportional to the inverse of marginal contributions that depend on weights themselves: the problem is clearly recursive, and the solution is endogenous. As Maillard, Roncalli, and Teiletche (2009) have pointed out, full risk parity cannot be obtained in a closed formula unless some unrealistic hypotheses (such as equal correlation among all the assets in the investment universe) are made, and may not be achieved through optimisation either, if the number of assets involved is very high, and correlations are very heterogeneous. For this reason the asset management industry proposes several proxies. By far, the easiest but probably the most naïve proxy for risk parity is the equally weighted portfolio: no estimation is made on volatility and correlation and assets are equally weighted. It would correspond to the true risk parity portfolio assuming that all stocks have the same volatility, and all the pairs of stocks have identical correlation. With no risk estimation, the equally weighted scheme only removes the risk concentration driven by market capitalization: since sectors, countries, or whatever groups of stocks (based on some style criteria, for instance) are not equally populated, equally weighting stocks would result in higher concentration of risk over those sectors, countries, or styles that are over-represented. Another proxy for risk parity would be the risk weighted scheme where stocks are weighted proportionally to the inverse of their volatility. This weighting scheme removes the risk concentration driven by market cap and adjusts for volatility, but the resulting portfolio is a true risk parity solution only in the hypothesis of Amundi Discussion Papers Series - DP

10 equal correlation across all pairs of assets. However, when correlations are quite homogenous, although every stock has a similar risk contribution, we would still have concentration over those families of stocks that are overrepresented. In order to smooth the risk concentration over such an overrepresented group of stocks, a two-step risk weighting scheme may be used: risk-weighted sector baskets should be created first, and the overall portfolio should be created afterwards by weighting those baskets for the inverse of their volatility. We can check for the accuracy of each of these solutions computing the percentage contribution (PC i ), for any basket of stocks: = In a test over the constituents of the MSCI Emu, we have built risk parity portfolios according to the three methodologies discussed above, at any quarter-end from 2003 to In the chart below, we show the average contribution of any GICS sector, computed over these quarterly observations. Percentage Risk Contributions by Sectors TELECOM INDUSTRIALS 20% ENERGY UTILITIES 10% FINANCIALS 0% CONS. DISCRET INF. TECH HEALTH CARE MATERIALS CONS. STAPLES MSCI EMU Eq. Weighted Risk Weighted (1 Step) Risk Weighted (2 Steps) 10 Amundi Discussion Papers Series - DP

11 The MSCI index is extremely concentrated on Financial stocks (black line). Removing the market cap bias we reduce risk concentration on Financials, but we introduce the same problem on some other over-represented sectors such as Consumer Discretionary and Industrials (dotted black line). After correcting for volatility at stock level only, risk distribution only marginally improves (red line). For a better solution two steps are needed: risk parity should first be achieved within each sector, and then at a portfolio level (light brown line). In any case, this two-step risk weighting scheme still generates some deviations from a 10% target contribution to total risk. In order to further improve the precision of our risk parity, we have tested an additional method where correlations are taken into account at least across the sectors, in the second step. We account for correlations using the marginal contribution to total risk of any risk parity sector. We observe marginal contributions of any sector, in the most neutral portfolio composition: the equally weighted composition. Equal weights as a starting point have the advantage of not being too far from the (still unknown) optimal solution. In this way the marginal contributions that we use for target weight calculation are a very good proxy for the marginal contribution that we will observe after weight calculation, thus ensuring a well-balanced risk contribution. We then weight sector baskets proportionally to the inverse of these measures. Percentage Risk Contributions by Sectors TELECOM INDUSTRIALS ENERGY UTILITIES FINANCIALS CONS. DISCRET INF. TECH HEALTH CARE MATERIALS CONS. STAPLES Risk Weighted (2 Steps) Risk Weighted (2 Steps with Correlations) 10% Target Amundi Discussion Papers Series - DP

12 Taking into account correlations at least across sectors reduces the dispersion of risk contributions, and the deviations from a 10% target become negligible. In any case, whatever the precision of our risk parity (with the exception of the equally weighted approximation), in order to contribute the same to portfolio risk, high risk stocks must have lower weight relative to stocks with lower risk. This is the main reason why risk parity portfolios are generally exposed to the low risk anomaly, as we will show hereafter. In addition, risk parity strategies have an embedded mean reverting mechanism, as stocks and sectors with positive performance and increasing weights will be reduced in order to be aligned back to a risk parity weight. Reversal at a sector level is a successful risk control strategy, and a two-step approach accounts for it more effectively. II - Low Risk Anomaly and Diversification 2.1 The Low Risk Anomaly Financial theory assumes that higher risk is remunerated on average by higher returns. However, the outperformance of low volatility stocks during the last 50 years has been among the most puzzling anomalies in equity markets. At the same time, low risk investing has recently gained a remarkable interest, due to its documented performance coupled with the unprecedented volatility experienced during the last two global financial crises. In our previous work, we showed how researchers have been documenting such anomaly since the early nineties: Fama and French (1992) show a rather negative relationship between risk and returns, and Baker and Haugen (1991) find significant reduction in volatility with no reduction in returns, for US minimum variance portfolios. We find that most of the relevant empirical studies focus on systematic risk; some of them state that the low risk anomaly holds regardless of which dimension of risk systematic or total is used for stock selection. Only few exceptions instead (Ang et al, 2006) rather refer to idiosyncratic volatility. In this section we show with a practical example that all of the three smart beta strategies discussed so far are exposed to the low risk anomaly. We build three portfolios (in Barra One, at the model date of 12/31/2012), restricting the investment universe to the constituents of the MSCI World Index. We impose that no stock can exceed a 5% weight. We then group stocks into three equally populated families, according to their risk: low risk, average risk and high risk stocks. Finally we observe the percentage allocated to each family of stocks, for each of the three portfolios as well as for the MSCI World. 12 Amundi Discussion Papers Series - DP

13 Weight Distribution: Total Risk 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Diversification Minvar Risk Parity Msci High Risk Average Risk Low Risk In the chart above we see that while the minimum variance portfolio is exclusively invested in stocks with below average risk, the risk parity portfolio has only a slight tilt toward low risk stocks, compared to the standard index. The portfolio maximizing the diversification ratio is apparently well balanced in absolute terms toward low or high risk stocks, while it clearly underweights average risk stocks. As a conclusion, using total risk as a grouping criterion, we see a clear and intuitive exposure to low risk anomaly for the minimum variance, a slight but intuitive exposure for the risk parity portfolio, and no exposure at all but rather a barbell allocation for the portfolio maximizing the diversification ratio. However we traditionally distinguish two components of risk: the systematic component (or common factor component according to Barra One terminology) and the specific component. This distinction is needed because, as we have documented, the systematic risk is the most relevant measure when addressing the low risk anomaly and, if we restrict our analysis to this component only, the picture changes. Weight Distribution: Common Factor (Systematic) Risk 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Diversification Minvar Risk Parity Msci High Common Factor Risk Average Common Factor Risk Low Common Factor Risk The portfolio maximizing the diversification ratio now exhibits a much more significant percentage invested in low risk stocks. The low risk feature of the risk Amundi Discussion Papers Series - DP

14 parity portfolio is somehow more significant as well, while unsurprisingly, the minimum variance portfolio is still exclusively invested in low risk stocks. Interestingly we observe some different effects while investigating specific risk. Weight Distribution: Specific Risk 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Diversification Minvar Risk Parity Msci High Specific Risk Average Specific Risk Low Specific Risk This time, the portfolio maximizing the diversification ratio exhibits almost 50% of the weight invested in high specific risk stocks, and only marginal weight in low specific risk stocks. We have explained in section 1 that the maximization of the diversification ratio contains a pseudo-minimization of the denominator that is satisfied via the selection of low systematic risk stocks. On the other hand, at the numerator, the optimisation results in the selection of high specific risk stocks since the latter increase the numerator, while having little impact on the denominator: specific risk doesn t matter at the denominator as it is easily diversified away. As a result, the portfolio maximizing the diversification ratio may show an average total volatility that is not statistically different from that of a standard market index, but will necessarily result in below average systematic risk stocks (the denominator effect), and above average specific risk stocks (the numerator effect). 2.2 Diversification Diversification according to the risk model We now move to investigate how the three investment processes behave in terms of diversification. In addition to the portfolio maximizing the diversification ratio, we expect the minimum variance optimisation to exploit uncorrelated stocks as well as low risk stocks; in the same way, we have seen that the two-step risk parity process also somewhat relies on low correlations (at least across sectors) and volatilities. In other words we are supposed to find some diversification evidence in the minimum variance and in the risk parity portfolios as well. In order to check for diversification we compute the diversification ratio first. 14 Amundi Discussion Papers Series - DP

15 Diversification Ratio 3 2,8 2,6 2,4 2,2 Diversification 2 1,8 1,6 Minvar Risk Parity 1,4 1,2 Msci 1 Diversification Ratio Total Risk Diversification Ratio Common Factor Risk Unsurprisingly, we find that the minimum variance portfolio is well diversified indeed, while the risk parity portfolio also provides some diversification improvement, relative to the standard market index. We compute the same measure excluding the specific risk component both at the numerator and at the denominator and, while finding the same hierarchy, we confirm that the specific risk inflates diversification measures, and better explains why a process maximizing diversification is tilted toward high specific risk stocks. We than compute the average correlation of stocks, according to the CBOE methodology: N n 2 2 wi w jσ iσ jρij wi σ i i, j= 1 i= 1 ρavg = N 1 N 2 i= 1 j> i w w σ σ i j i j Average Correlation 70% 60% 50% Diversification 40% 30% 20% 10% Minvar Risk Parity Msci 0% Average Correlation Total Risk Average Correlation Common Factors Amundi Discussion Papers Series - DP

16 Average correlations do not change the picture: the portfolio maximizing the diversification ratio is the best diversified across risk factors, but once again we find some evidence of diversification in the minimum variance and in the risk parity portfolios. Again, the specific risk component reduces measured correlation. Capital diversification Risk-based measures of diversification like diversification ratio and average correlation show that smart beta are better diversified than a standard index, while within smart beta, optimized portfolios are better diversified than risk parity portfolios. This is because while the optimisation mainly selects a limited number of highly uncorrelated stocks, a risk weighting scheme still invests in all the stocks in the investment universe, regardless of their true diversifying properties. Optimisationbased portfolios are thus quite concentrated on a few low-risk, low-correlation stocks and investors are comfortable with such a portfolio when the confidence in the risk model is very high. In contrast, investors may be concerned by the effect of using a risk model that is not properly specified, where a relevant risk factor is neglected, or where the optimisation relies on incorrectly estimated correlations. In these cases, investors may correctly believe that the ultimate insurance against unexpected risks is capital diversification. In order to address the capital diversification of the three portfolios, we employ the entropy measure on the weights of their constituents. The entropy of a portfolio may be read as the equivalent number of assets held, if those assets were equally weighted. As shown in the chart below, optimisation-based portfolios that typically invest in assets have an entropy measure of roughly 40-45, meaning that they have a capital diversification equivalent to an equally weighted portfolio of assets. The risk parity portfolio is obviously much better diversified in terms of capital allocation, with an entropy measure of roughly 1300, out of a maximum possible of 1600 (the number of investment universe constituents, if equally weighted). Also the risk parity portfolio has almost double the entropy of the standard market index, even investing in the same number of stocks. Entropy LOG Scale Diversification Minvar Risk Parity Msci 16 Amundi Discussion Papers Series - DP

17 We believe that risk parity is more suitable for investors that are not completely confident about the estimation of the full variance covariance matrix, thus favoring capital diversification over risk-model diversification. However, in order to improve capital diversification of the optimisation-based portfolios, some more prudent constraints may be used on the maximum weight of any holdings (compared to the 5% that we use in this example). III - Smart Beta in asset allocation Since their introduction into the industries, many questions have been raised about the use of smart beta in asset allocation: investors wonder about the implication of introducing smart beta equities in traditional equity-bond allocation. Another point of growing interest is whether smart beta should replace traditional equity as an alternative equity core, or whether they should constitute a new satellite. A similar issue is whether smart beta equities should be used to improve active returns relative to a traditional benchmark, or whether they should rather be used by investors seeking absolute returns, and thus replace the traditional benchmark. Crucial to all these questions is the detection of the drivers behind the risk-return profiles of smart beta equities, as investors must be comfortable with them before introducing them into a strategic asset allocation (will these drivers keep on delivering low risk outperformance in the long run?). Also, we need to investigate if smart beta equities exhibit some evidence of different and hopefully more favorable correlations with bonds. Finally, investors should monitor liquidity as any equity strategy deviating from free float adjusted market cap is by definition less liquid than the latter. Is liquidity enough to allow for such a radical switch from traditional equities to smart beta? 3.1 Performance drivers Smart beta strategies have proven to be more efficient than market cap indices from a risk-return standpoint. Their returns over the last decade are at least equal to and very often higher than those of standard indices, while volatility and drawdowns are systematically lower. We try to explain the sources of these favorable deviations from market cap indices, for some well-known global equity smart beta benchmarks, as well as for some Amundi smart investment processes. As for the diversification family, we have analyzed two well-known indices the FTSE Tobam Maximum Diversification, and the FTSE Edhec Risk Efficient Amundi Discussion Papers Series - DP

18 together with an Amundi process aiming to enhance diversification by minimizing average correlations (it should be noted that the Amundi process is applied to a restricted list of high dividend stocks in the global developed markets). As for the risk parity family, we investigate the MSCI World Risk Weighted together with an Amundi risk parity process, as explained in section 1 (the biggest difference with MSCI being the two-step sector-company approach for the Amundi process). In the minimum variance family we study the MSCI Minimum Volatility, and two Amundi processes: the first is a minimum variance with some liquidity constraints, while the second is a very similar process applied to a restricted list of high quality stocks according to the Piotroski score. In the Table below we show the correlation matrix of active returns relative to the corresponding benchmark for each strategy. CORRELATION FTSE EDHEC- R.E. Amundi Diversif. FTSE TOBAM M.D. MSCI World RW Amundi Risk Parity MSCI World MinVol Amundi MinVar Amundi MinVar - Piot FTSE EDHEC-R.E. 14% 29% 61% 35% 20% 14% 10% Amundi Diversification 14% 78% 62% 61% 83% 84% 86% FTSE TOBAM M.D. 29% 78% 66% 64% 82% 85% 84% MSCI World RW 61% 62% 66% 79% 65% 59% 54% Amundi Risk Parity 35% 61% 64% 79% 48% 48% 48% MSCI World MinVol 20% 83% 82% 65% 48% 91.4% 91.2% Amundi MinVar 14% 84% 85% 59% 48% 91.4% 95.4% Amundi MinVar - Piot 10% 86% 84% 54% 48% 91.2% 95.4% We can easily recognize the three family blocs with the FTSE Edhec Risk Efficient somehow being an outlier among its family as well as among the full sample of strategies. This is due to the specific constraints that affect holdings on each stock: any constituent cannot be weighted less than one-third of an equal weighting schemes, neither more than 3 times such a quantity. Though these constraints are sound, they make this index half way between a market weighted and an equally weighted portfolio, and not that close to an unconstrained portfolio maximizing diversification. Not surprisingly, this index is well correlated to the MSCI World Risk Weighted index that applies similar constraints. Interestingly we notice that the diversification bloc is highly correlated with the minimum variance block, while the risk parity block stays somewhere in the middle. In any case, the correlation matrix suggests that there is some common behavior behind the active returns of each strategy and this intuition is confirmed by the principal component analysis (always on active returns), summarized in the chart below. 18 Amundi Discussion Papers Series - DP

19 Explained Variance 100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 8 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0% Cumulative Percentage Variance (LS) Variance of Each Component The common behavior is confirmed by the 85% variance explained by the first factor, and by the 91% variance explained by the first two factors alone. One can argue that we have such a high percentage explained as we use redundant information, since many strategies in our analysis (almost all the strategies within each family bloc) are very similar to each other, thus resulting in overlapping behaviors. For this reason we run a simplified PCA on a restricted sample of one strategy per family (FTSE Tobam Maximum Diversification, Amundi Risk Parity, Amundi Minimum Variance). Explained Variance 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% PC 1 PC 2 PC 3 Cumulative Variance By Strategy Cumulative Variance By PC With no common factor in place (that is, with perfectly uncorrelated strategies) any principal component would coincide with a stand-alone strategy, while we can see that the first component of our simplified sample explains as much variance as the two most volatile strategies. There is definitely some common behavior underlying the active returns of smart beta strategies and the true challenge is to identify such a common performance drivers. In order to detect those drivers, we regress the first two principal components of the complete sample of eight strategies, over the explanatory variables listed below. Amundi Discussion Papers Series - DP

20 Variables Description Note Equity Market Sector Reversal Momentum Small Cap Value Dividend Low (Systematic) Risk Anomaly The standard market index Long-short of equally weighted basket of GICS sectors versus the MSCI World MSCI World Momentum MSCI World Equally Weighted MSCI World Value Msci World High Dividend Beta-neutral long-short of low systematic risk stocks (L) versus high systematic risk stocks (S) Residual returns of linear regression on MSCI World Residual returns of multiple linear regression on MSCI World and the Value factor Residual returns of multiple linear regression over all the other explanatory variables All variables are adjusted for market beta in order to avoid double counting for the market beta effect and to limit multicollinearity. The dividend yield factor has been simultaneously regressed over the market index and the value factor, to delete positive correlation between value and dividend. As for the low risk anomaly, we have built a long basket of stocks belonging to the lowest quintile according to systematic risk (cf. common factor risk, estimated by Barra One), and a short basket with stocks belonging to the highest quintile; baskets are then weighted inversely proportional to their ex ante Beta in order make the long-short beta-neutral, and residual (ex-post) market exposures as well as any involuntary exposure to other factors are canceled out via a multiple regression over all explanatory variables. Cumulative Factors Performance 2 1,8 1,6 1,4 1,2 1 0,8 01/06/03 01/04/04 01/02/05 01/12/05 01/10/06 01/08/07 01/06/08 01/04/09 01/02/10 01/12/10 01/10/11 01/08/12 01/06/13 2,5 2,2 1,9 1,6 1,3 1 0,7 Low Syst. Risk Sector Reversal Moment. Small Cap Value Dividend Msci World The sample period has been characterized by strong equity markets despite the massive drawdown of 2008, a strong low risk anomaly effect (except during the rebound of 2009), positive momentum, positive sector reversal (the latter is interesting as it exhibits very low volatility), and small caps. Value and dividend yield have been flat. 20 Amundi Discussion Papers Series - DP

21 CORRELATIONS Mkt Beta Low Syst. Risk Sector Reversal Moment. Small Cap Value Dividend Mkt Beta 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Low Syst. Risk 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Sector Reversal 0.0% 0.0% 39.5% -1.4% -18.0% 32.9% Moment. 0.0% 0.0% 39.5% -5.1% -36.8% 8.8% Small Cap 0.0% 0.0% -1.4% -5.1% 9.1% -19.0% Value 0.0% 0.0% -18.0% -36.8% 9.1% 0.0% Dividend 0.0% 0.0% 32.9% 8.8% -19.0% 0.0% Correlation of all the explanatory variables with the market factor and the low volatility factor (as well as between value and dividend yield) are equal to zero by construction, while other correlations are sufficiently low to exclude muticollinearity problems. As mentioned, we regress the first two principal components of smart beta strategies, over the full set of explanatory variables, and we analyze their exposures and their explained variance. Exposures Variance Explained (Log Scale) Dividend MKT (negative) 2,0 1,5 1,0 0,5 - LMHbeta Dividend MKT (negative) 50,0% 12,5% 3,1% 0,8% 0,2% 0,0% 0,0% 0,0% LMHbeta Value Sector Reversal Value Sector Reversal Small Cap Momentum Small Cap Momentum PC 1 PC 2 PC 1 PC 2 The first principal component has a very significant negative market beta, and significant exposures to all the other explanatory variables with the exception of momentum (positive but not significant). The variance explained is 60% for market beta, 15% for the low risk anomaly, 5% for the dividend factor, and about 1% for value, small caps and sector reversal. The second component has small cap and sector reversal exposure, both of them significant, but with small caps only explaining a non-negligible portion of variance (5%). Overall we would argue that the active performance of smart beta strategies is finally due to low market beta, low risk anomaly, small caps, and sector reversal. However we recognize that each strategy may have different exposure to these Amundi Discussion Papers Series - DP

22 explanatory variables, and we need to estimate them separately. We thus run seven multiple linear regressions, and once regression parameters are estimated, we run performance attribution in order to quantify the impact that any of these drivers have on the cumulative active return of the eight strategies. We show cumulative effect over the period from the end of June 2003 to the end of December 2013 in the following Chart. Cumulative Active Returns vs. Standard Index: % 200% 150% 100% 50% 0% -50% -100% -150% FTSE EDHEC-R.E. Amundi Diversif. FTSE TOBAM MD MSCI World RW Amundi Risk Parity MSCI World MinVol Amundi MinVar Amundi MinVar - Piot Unexpl. + Interact. MKT Low Syst. Risk Sector Reversal Momentum Small Cap value Dividend Total The following chart instead shows the contribution to ex-post tracking error (computed as the percentage explained variance times the realized tracking error) for each of them. Explained Variability of Active Returns by Components 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% FTSE EDHEC-R.E. Amundi Diversif. FTSE TOBAM MD MSCI World RW Amundi Risk Parity MSCI World MinVol Amundi MinVar Amundi MinVar - Piot Unexpl. + Interact. MKT Low Syst. Risk Sector Reversal Momentum Small Cap value Dividend With the exception of the FTSE Edhec Risk Efficient, the regression model explains 80% to 90% of the variance of active returns and its F-test is significant for all the strategies investigated. The model is thus overall well specified. Intuitively the low market beta has a negative effect during upward markets, and it explains a big percentage of the variance of active returns. Interestingly, those strategies exhibiting the lowest market beta offset much of this negative effect with a positive contribution by the low risk anomaly. 22 Amundi Discussion Papers Series - DP

23 All strategies benefit from sector reversal, with the Amundi Risk Parity benefiting the most. In this case, the variance explained is particularly high as the construction process of this portfolio is based on a systematic sector rebalancing (cf. section 1 about the two-step company-sector methodology). Small cap effect explains both performance and variance for diversification-based portfolios and risk parity portfolios, while it is basically absent on minimum variance portfolios, because small caps bring some additional volatility, and because Amundi portfolios apply some liquidity filters as well. The dividend factor explains some variance, but has little impact on returns, as it is quite flat over the period. In the same way, the value factor is basically absent in the performance chart and is also negligible in terms of explained variability. Unexplained component of returns is positive in the case of Amundi minimum variance, and it is even higher in the portfolio with a quality (Piotroski) filter: we can argue that there is some more room for investigation about minimum variance drivers, especially when the construction process is less constrained than the MSCI World Minimum Volatility. The quality filter delivers additional value. Finally, we confirm the outlier behavior for the FTSE Edhec Risk Efficient Index. We have said about the constraints applied in its construction process and, unsurprisingly, its deviations from a market weighted index are quite low in terms of cumulative active returns, and realized tracking error. The only visible source of active return is the small cap exposure. 3.2 Smart Beta for active or absolute returns, a new equity core? The choice whether smart beta should be used in an absolute or in an active riskreturn framework, depends on the utility function of the investor (or the mandate of the fund manager in the case of delegated asset management), and the governance of the investment process. While a fund manager with the objective of maximizing information ratio -under a limited tracking error constraint- may find it difficult to massively move toward smart beta equities, an institutional investor aiming to maximize wealth under some absolute risk constraint, could use smart beta equity to make up the bulk (or the new equity core ) of its equity investments. In an investment process that is based on top-down strategic asset allocation by the investment board, and equity allocation by the equity department thereafter, if the board allocates wealth based on traditional benchmarks allowing limited tracking error deviations, the equity department is likely to exploit the enhanced risk-return profile of smart beta equities only in some satellites of the global equity allocation, since smart beta equities bring high tracking error relative to a standard market index. On the other Amundi Discussion Papers Series - DP

24 hand, if the investment board accepts to change its strategic benchmark into a smart beta benchmark, smart beta equities can effectively become the new equity core. However such a radical choice implies that several conditions are met. First, the investor must be confident that the performance drivers identified above are going to deliver positive performance, just as we have seen in the recent past. The lower this confidence, the lower the likelihood that the investor will be willing to allocate a relevant portion of its equity to low beta stocks. As we have seen in performance attribution, low beta itself penalizes profitability as long as it is not offset by some other positive effects. With no positive contribution from low risk anomaly, size, sector reversal and so on, investing in low beta stocks is not efficient in a classical Markowitz framework either (cf. next section). Second, the investor should be sure that smart beta strategies provide sufficient liquidity. If the market can absorb the volumes needed for monthly or quarterly rebalancing, but cannot quickly absorb the program trades resulting from strategic asset allocation or tactical asset allocation decisions, the investor should rather prefer to allocate smart beta equities to the satellite bucket of the portfolio. On the other hand, if liquidity is not an issue, investors may switch their core equity allocation to smart beta, but should be ready to change the equity benchmark, since smart beta equities bring high tracking error relative to a standard market index. Let s consider the case of a big sovereign investor that is going to implement a big change in its strategic asset allocation, buying (selling) a relevant amount of global equity. Let s assume the investor wants to complete the program trade in 10 days, using up to 20% of the daily average volumes, each day (the daily average volumes are estimated over the last three months as of end of December 2013). We test three program trades of USD 10, 25 and 50 billion respectively, times four equity index hypotheses: the MSCI World, the MSCI World Minimum Volatility, the MSCI World Risk Weighted, and a risk weighted allocation of the latter two indices (43% MSCI World Risk Weighted and 57% MSCI World Minimum Volatility, according to a long-term estimation of volatility). Program Trade - MSCI World Program Trade - MSCI Risk Weighted 100% 100% 80% 80% 60% 60% 40% 40% 20% 20% 0% d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20 0% d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20 10 Bln Usd Prog. Trade 25 Bln Usd Prog. Trade 50 Bln Usd Prog. Trade 24 Amundi Discussion Papers Series - DP

25 Program Trade - MSCI Minimum Vol Program Trade - RW(43)MV(57) 100% 100% 80% 80% 60% 60% 40% 40% 20% 20% 0% d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20 0% d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20 10 Bln Usd Prog. Trade 25 Bln Usd Prog. Trade 50 Bln Usd Prog. Trade The most liquid index is unsurprisingly the maker weighted index: a huge program trade of 50 billion may be completed in five days. The Minimum Volatility index is the least liquid, not really because it is more exposed to small caps, but rather because it is concentrated over a lower number of stocks (248), than the Risk Weighted Index (1600). As for smart beta in general, only a USD 10 billion program trade allows a relevant, though not exhaustive, completion after 10 days. In detail, this is the percentage completion after 10 days. Percentage Completion of Program Trade after 10 days 100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% Risk Weighted 43%R.W. 57%M.V. Minimum Volatility Risk Weighted 43%R.W. 57%M.V. Minimum Volatility Risk Weighted 43%R.W. 57%M.V. 10 BLN USD 25 BLN USD 50 BLN USD Minimum Volatility In order to effectively complete the program trades in 10 days, the investor cannot hold 100% of equity in smart beta and should dilute his holding with traditional and more liquid equity investments. In the table below, we show the maximum allocation in smart beta that the investor can afford, in order to complete each program trade in 10 days. Amundi Discussion Papers Series - DP

26 Maximum Allocation in Smart Beta 100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% Risk Weighted 43%R.W. 57%M.V. Minimum Volatility Risk Weighted 43%R.W. 57%M.V. Minimum Volatility Risk Weighted 43%R.W. 57%M.V. 10 BLN USD 25 BLN USD 50 BLN USD Minimum Volatility Smart Beta weight MSCI World weight If the investor is not likely to incur program trades bigger than USD 10 billion, risk weighted, minimum volatility (to a lesser extent), and a mix of the two indices may all become a new equity core, as the investor can hold up to 100% of total equity in smart beta. For higher sizes of program trades, smart beta allocation should be kept residual with respect to market weighted equity, thus smart beta would be more suited to being a satellite bucket of the portfolio. However, if comfortable with the USD 10 billion hypothesis, the investor that goes for smart beta as a new equity core, should seriously consider changing its strategic benchmark. In the next chart, we show the tracking error relative to the MSCI World Index of all equity allocations from the example above, and the tracking error of an allocation with 40% in the smart beta above and 60% in global bonds, relative to a classic balanced benchmark (40% MSCI World Index, and 60% JPM Global Bond Index). Tracking Error Relative to Standard Benchmarks 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0% Risk Weighted 43%R.W. 57%M.V. Minimum Volatility Risk Weighted 43%R.W. 57%M.V. Minimum Volatility Risk Weighted 43%R.W. 57%M.V. 10 BLN USD 25 BLN USD 50 BLN USD Minimum Volatility tracking error vs CW Equity tracking error vs The lower the impact of liquidity issues, the easier the move toward smart beta equities as a new equity core. But massive investments in smart beta equities 26 Amundi Discussion Papers Series - DP

27 bring high relative risk and it is very unlikely that the investment committee and fund managers are comfortable with tracking error as high as 2% relative to a traditional bond-equity composite benchmark, and 5% relative to a traditional equity benchmark. As a consequence, such a big move toward smart beta equities increases the likelihood that these traditional benchmarks are replaced by opportune and maybe customized smart beta indices. 3.3 Bond-Equity Allocation As historical returns may suggest, as far as the risk is lower while returns are higher, the risk-return profile of some traditional bond-equity allocation is improved by simply switching from market weighted equities to smart beta. In the chart below, we trace two simplified efficient frontiers using the JP Morgan Global Bond index for fixed income, and the MSCI World Index or the MSCI World Minimum Volatility for equities. The chart is based on historical data only (returns, variance and covariance). Historical Returns Historical Volatility Correlations with bonds MSCI World 9.48% 15.72% 20.09% MSCI World MinVol 9.58% 11.41% 31.90% JPM GBI 4.75% 6.86% Despite a slightly higher correlation with bonds, and thanks to the far better risk return profile of the MSCI Minimum Volatility Index, the improvement in the efficient frontier is straightforward: Efficient Frontiers - Historical Data 12% 11% 10% 9% 8% 7% 6% 5% 4% 4% 6% 8% 10% 12% 14% 16% 18% MSCI Min Vol: historical data MSCI World: historical data We can state that, for the same level of risk of a traditional bond-equity allocation, we can increase the relative weight of smart beta equities in the allocation (as smart beta equities are more conservative than traditional equities), thus improving performance, via both the higher percentage of equity and the higher return of Amundi Discussion Papers Series - DP