Understanding Smart Beta: beyond diversification and low risk investing

Amundi Discussion Papers Series

DP-04-2014 May 2014

Understanding Smart Beta: beyond diversification and low risk investing Alessandro Russo, Quantitative Research

For professional investors only

Abstract

S

mart 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-04-2014

3

4

Amundi Discussion Papers Series - DP-04-2014

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%

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

10%

TMT bubble

RISK PARITY INDEX

MKT CAP INDEX (MSCI WORLD)

Amundi Discussion Papers Series - DP-04-2014

Source: Amundi Research

5

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.

I - Smart Beta Strategies 1. 1 The minimum variance portfolio 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 Vw) Such that e w = 1 T

T

where w is the vector of the optimal portfolio weights, V is the variance-covariance matrix, and eT is a vector of ones. 6

Ω=

wσ

ww σσρ

Amundi Discussion Papers Series - DP-04-2014

,

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 (wTVw) ratio, which is the ratio (Ω) of average diversification is the so calledMin diversification stocks’ volatility on portfolio volatility, was Such that easTwit = 1 originally introduced by Choueifaty and Coignard in 2008.

Ω=

,

wσ

ww σσρ

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-04-2014

7

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-04-2014

Ω=

Ω=

ww w σσ σ ρ w w σ, σ ρ = ww σσρ In order to come out with full risk parity, the, following relationship must hold: ,Ω

=

= =

=

=

~

~

= =

=

Where RC i is the risk contribution of = the i th asset, = and MC =i is its marginal contribution to risk, defined as follows

= be the same for any asset or asset In other words, the risk contribution should class and the weight of each asset or asset class should be proportional to the 1 to risk: 1 inverse of its marginal contribution ~

1

Actually, marginal contributions to risk are both function of volatilities and = the rest of=the portfolio, with correlations depending correlations of any asset with on portfolio composition itself. In other words, weights are the unknowns and = of marginal contributions that depend should be proportional to the inverse N n the solution is on weights themselves: the problem is clearly recursive, and N n 2ρ 2− w w σ σ wi2σ i2 endogenous. wi w jσ iσ j ρ iji − j i wji σiji

∑

∑

∑

∑

i ,Nj =1 in=1 i =1 ρ(2009) As Maillard, Roncalli, and = ρ avgTeiletche avg = have pointed N −1 N out, full risk 2parity N −1 N w w − σ σ ρ wi σ i2 cannot ∑ j i j ij hypotheses be obtained in a closed formula unless ∑ somei2unrealistic (such as wi w jσi =iσ 2∑∑ i , j =w 1 i w∑∑ 1 j jσ iσ j = ρ avg equal correlation among all the assets in the investment universe) are made, and i = 1 j > i N −1 N i =1 j >i may not be achieved through optimisation either, if the number of assets involved 2∑∑ wi w jσ iσ j i , j =1

is very high, and correlations are very heterogeneous. i =1 j >i 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-04-2014

9

=

=

=

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 1 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 N n quarter-end from according to the three methodologies discussed above, at any 2 − wi waverage σ σ ρ wi2σ of 2003 to 2012. In the chart below, we show the contribution j i j ij i any GICS i , j =1 i =1 sector, computed over these quarterly ρ =observations.

∑

avg

∑

N −1 N

2∑∑ wi w jσ iσ j Percentage Risk Contributions by Sectors i =1 j >i

TELECOM INDUSTRIALS

ENERGY

20%

10%

UTILITIES

FINANCIALS 0%

INF. TECH

CONS. DISCRET

HEALTH CARE

MATERIALS CONS. STAPLES

MSCI EMU

Eq. Weighted

Risk Weighted (1 Step)

Risk Weighted (2 Steps) Source: Amundi Research

10

Amundi Discussion Papers Series - DP-04-2014

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 ENERGY

INDUSTRIALS

UTILITIES

FINANCIALS

CONS. DISCRET

INF. TECH

HEALTH CARE

MATERIALS CONS. STAPLES

Risk Weighted (2 Steps)

Risk Weighted (2 Steps with Correlations)

10% Target Source: Amundi Research

Amundi Discussion Papers Series - DP-04-2014

11

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-04-2014

Weight Distribution: Total Risk 100% 90% 80% 70% 60%

High Risk

50%

Average Risk

40%

Low Risk

30% 20% 10% 0%

Diversification

Minvar

Risk Parity

Msci

Source: Amundi Research

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%

High Common Factor Risk

50%

Average Common Factor Risk

40%

Low Common Factor Risk

30% 20% 10% 0%

Diversification

Minvar

Risk Parity

Msci

Source: Amundi Research

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-04-2014

13

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%

High Specific Risk

50%

Average Specific Risk

40%

Low Specific Risk

30% 20% 10% 0%

Diversification

Minvar

Risk Parity

Msci

Source: Amundi Research

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-04-2014

Such that e w = 1

3

Ω=

Diversification w w σ σRatio ρ ,

2,8 2,6 2,4 2,2 2 1,8 1,6

wσ

=

=

=

1,4

Minvar Risk Parity Msci

1,2 1

Diversification

=

Diversification Ratio Total Risk

Diversification Ratio Common Factor Risk

Source: Amundi Research

Unsurprisingly, we find that the minimum variance portfolio is well diversified indeed, while the risk parity portfolio also provides some diversification improvement, 1 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

∑w w σ σ

ρ avg = i , j =1

i

j

i

n

2 2 j ρ ij − ∑ wi σ i i =1

N −1 N

2∑∑ wi w jσ iσ j i =1 j >i

Average Correlation 70% 60% 50%

Diversification

40%

Minvar

30%

Risk Parity

20%

Msci

10% 0% Average Correlation Total Risk

Average Correlation Common Factors Source: Amundi Research

Amundi Discussion Papers Series - DP-04-2014

15

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 70-80 assets have an entropy measure of roughly 40-45, meaning that they have a capital diversification equivalent to an equally weighted portfolio of 40-45 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 10000

LOG Scale

1000

100

1 276 10

1

47 Diversification

740

39 Minvar

Risk Parity

Msci Source: Amundi Research

16

Amundi Discussion Papers Series - DP-04-2014

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-04-2014

17

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 FTSE Amundi EDHECTOBAM Diversif. R.E. M.D.

MSCI World RW

Amundi Risk Parity

MSCI World MinVol

14%

29%

61%

35%

20%

14%

10%

78%

62%

61%

83%

84%

86%

66%

64%

82%

85%

84%

79%

65%

59%

54%

48%

48%

48%

91.4%

91.2%

FTSE EDHEC-R.E. Amundi Diversification

14%

FTSE TOBAM M.D.

29%

78%

MSCI World RW

61%

62%

66%

Amundi Risk Parity

35%

61%

64%

79%

MSCI World MinVol

20%

83%

82%

65%

48%

Amundi MinVar

14%

84%

85%

59%

48%

91.4%

Amundi MinVar - Piot

10%

86%

84%

54%

48%

91.2%

Amundi Amundi MinVar MinVar Piot

95.4% 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-04-2014

Explained Variance 100%

4.0%

95%

3.5%

90%

3.0%

85% 80%

2.5%

75%

2.0%

70%

1.5%

65%

1.0%

60%

0.5%

55% 50%

PC 1

PC 2

PC 3

PC 4

Cumulative Percentage Variance (LS)

PC 5

PC 6

Variance of Each Component

PC 7

PC 8

0.0%

Source: Amundi Research

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

Cumulative Variance By Strategy

Cumulative Variance By PC

PC 3 Source: Amundi Research

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-04-2014

19

Variables Equity Market Sector Reversal Momentum Small Cap Value

Description

Note

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

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 Beta-neutral long-short of low Low (Systematic) Risk systematic risk stocks (L) versus high regression over all the other Anomaly systematic risk stocks (S) explanatory variables

Dividend

Msci World High Dividend

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

2,5

1,8

2,2

1,6

1,9

1,4

1,6

1,2

1,3

1

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 Low Syst. Risk

Sector Reversal

Moment.

Small Cap

Value

Dividend

0,7

Msci World

Source: Amundi Research

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-04-2014

CORRELATIONS

Mkt Beta

Low Syst. Sector Moment. Small Cap Risk Reversal

Mkt Beta

0.0%

Value

Dividend

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

39.5%

-1.4%

-18.0%

32.9%

-5.1%

-36.8%

8.8%

9.1%

-19.0%

Low Syst. Risk

0.0%

Sector Reversal

0.0%

0.0%

Moment.

0.0%

0.0%

39.5%

Small Cap

0.0%

0.0%

-1.4%

-5.1%

Value

0.0%

0.0%

-18.0%

-36.8%

9.1%

Dividend

0.0%

0.0%

32.9%

8.8%

-19.0%

0.0% 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)

MKT (negative) 2,0 1,5

Dividend

MKT (negative)

LMHbeta

50,0% 12,5% 3,1% 0,8% 0,2% 0,0% 0,0% 0,0%

Dividend

1,0 0,5 Value

Sector Reversal

Small Cap

PC 1

PC 2

Momentum

LMHbeta

Value

Sector Reversal

Small Cap

PC 1

PC 2

Momentum

Source: Amundi Research

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-04-2014

21

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: 2003 - 2013 250% 200% 150% 100% 50% 0% -50% -100% -150% FTSE EDHEC-R.E.

Unexpl. + Interact.

Amundi Diversif.

MKT

FTSE TOBAM MD

Low Syst. Risk

MSCI World RW

Amundi Risk Parity MSCI World MinVol

Sector Reversal

Momentum

Small Cap

Amundi MinVar

value

Amundi MinVar Piot

Dividend

Total

Source: Amundi Research

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 Unexpl. + Interact.

MKT

Low Syst. Risk

Sector Reversal

Momentum

Small Cap

value

Amundi MinVar Piot

Dividend Source: Amundi Research

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-04-2014

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-04-2014

23

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 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

10 Bln Usd Prog. Trade

24

Program Trade - MSCI Risk Weighted

25 Bln Usd Prog. Trade

0%

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20

50 Bln Usd Prog. Trade

Amundi Discussion Papers Series - DP-04-2014

Source: Amundi Research

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

10 Bln Usd Prog. Trade

25 Bln Usd Prog. Trade

0%

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d20

50 Bln Usd Prog. Trade

Source: Amundi Research

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.

10 BLN USD

Minimum Volatility

Risk Weighted

43%R.W. 57%M.V.

Minimum Volatility

Risk Weighted

25 BLN USD

43%R.W. 57%M.V.

Minimum Volatility

50 BLN USD Source: Amundi Research

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-04-2014

25

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

10 BLN USD

Risk Weighted

43%R.W. 57%M.V.

Minimum Volatility

Risk Weighted

25 BLN USD

Smart Beta weight

43%R.W. 57%M.V.

Minimum Volatility

50 BLN USD Source: Amundi Research

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.

10 BLN USD

Minimum Volatility

Risk Weighted

43%R.W. 57%M.V.

Minimum Volatility

Risk Weighted

25 BLN USD tracking error vs CW Equity

tracking error vs 60-40

43%R.W. 57%M.V.

Minimum Volatility

50 BLN USD Source: Amundi Research

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-04-2014

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%

MSCI Min Vol: historical data

10%

-------

12%

14%

16%

18%

MSCI World: historical data

Source: Amundi Research

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-04-2014

27

smart beta. In the same way, introducing smart beta while keeping the weight of equity unchanged, we improve the expected return of the portfolio, while reducing its risk. These statements are formally correct, have proven to hold up over the last decade, and may be confirmed in the future. However they imply a precise hypothesis: the performance drivers discussed above will deliver performance in line with those we have seen in the recent past. On the contrary, if we apply an alternative and less favorable scenario where sector reversal, low risk anomaly, small caps, and all other residual factors are not going to deliver any additional return, investing in smart beta would be simply equivalent to investing in low beta equity. This is the reason why we believe that clearly identifying performance drivers (even demystifying some beliefs about these strategies) and being confident with them is a required condition for investors to buy smart beta. To formalize this unfavorable scenario into our simplified efficient frontier, we may set the expected return of the MSCI Minimum Volatility Index to a level that equalizes the risk-adjusted return of the MSCI World Index. Historical Returns

Historical Volatility

Risk Adjusted returns

MSCI World

9.48%

15.72%

0.60

MSCI World MinVol

6.88%

11.41%

0.60

JPM GBI

4.75%

6.86%

0.69

This is equivalent to the hypothesis that the MSCI Minimum Volatility Index is simply a low beta index, as it was a combination of cash and a traditional index. Thus, investing in low beta equity with the same risk adjusted return of traditional equity would be equivalent to imposing the constraint of a minimum holding in cash, thus making the frontier less attractive than using unconstrained equity. Efficient Frontiers - Historical Data and Risk Adjusted Returns 12% 11% 10% 9% 8% 7% 6% 5% 4%

4%

6%

8%

10%

12%

------- MSCI Min Vol: historical data ------- MSCI World: historical data - - - - MSCI Min Vol: same risk adjusted return and correlation of MSCI World

28

14%

Amundi Discussion Papers Series - DP-04-2014

16%

18%

Source: Amundi Research

Actually, in a balanced asset allocation with smart beta, we still have to investigate if some additional benefit could come from lower correlation with bonds: if so, smart beta equities would be more diversifying. Unfortunately this is not the case as bonds’ correlation with the MSCI Minimum Volatility Index is 32%, while its only 20% with the MSCI Index (cf. previous table). Taking true correlation into account we have an even less interesting profile: Efficient Frontiers - Historical Data and Risk Adjusted Returns 12% 11% 10% 9% 8% 7% 6% 5% 4%

4%

6%

8%

10%

12%

14%

------- MSCI Min Vol: historical data ------- MSCI World: historical data - - - - MSCI Min Vol: same risk adjusted return and correlation of MSCI World - - - - MSCI Min Vol: same risk adjusted return of MSCI World; historical correlation

16%

18%

Source: Amundi Research

We may wonder if this evidence is limited to the MSCI World Minimum Volatility Index, or correlation with bonds is higher for any smart beta. Actually this is rather generalized evidence, with the exception of the FTSE EDHC Risk Efficient Index that is close to traditional equity, even from a correlation standpoint. Correlations with Bonds 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

FTSE EDHEC -Risk Efficient Smart Beta

Amundi Diversif.

FTSE TOBAM MD

MSCI World RW

Amundi Risk Parity

MSCI World MinVol

MSCI World

Amundi MinVar

Amundi MinVar - Piot

Source: Amundi Research

3.4 Diversifying and timing smart beta strategies As we have seen in previous sections, there are several factors behind the performance of smart beta equities. Though we may identify some significant common behavior across them, the relevant factors explaining such performance deviations from a standard index are not the same for every smart beta strategy. Amundi Discussion Papers Series - DP-04-2014

29

Furthermore we observe that smart beta strategies perform differently according to the conditions of the equity market as a whole (bear or bull market, trading range, high or low volatility, high or low average correlation). These are all strong arguments for diversifying across smart beta strategies, and not holding just one of them. 3.4.1 Diversifying across smart beta strategies There are several ways to diversify across smart beta strategies, and diversification is possible even if the number of strategies involved is very limited. Diversifying across smart beta may also be useful in addressing the issue of building a reasonable multi-strategy smart beta benchmark. We provide several cases of multi smart beta allocation and for illustrative purposes we stay within the MSCI family (MSCI World Minimum Volatility, and MSCI Risk Weighted). We first consider the case of an investor within an absolute risk-return framework. If the investor wants to achieve diversification by equalizing the two indices’ contribution to absolute risk, according to a long term (10 years) covariance matrix, he would allocate 57% of his assets to the minimum variance and 43% to the risk weighted indices respectively. Equal Active Risk Contribution by Strategy 100% 80%

57%

50,0%

43%

50,0%

60%

77%

40% 20%

23%

0% Weights MSCI World RW

Total Risk Contribution MSCI World MinVol

Active Risk Contribution Source: Amundi Research

As requested, each strategy has an equal contribution to absolute risk but it is interesting to notice that risk relative to a standard index is concentrated on the minimum variance strategy. We can translate the analysis on performance drivers, using the estimated parameters of linear regressions and their covariance matrix, from section 3.1. From an absolute risk perspective, the market factor explains roughly 90% of the absolute variance, with no surprise as we are dealing with equity portfolios. From an active risk perspective, risk is rather concentrated over low beta (obvious as minimum variance has very low beta), low risk anomaly, and dividend yield; 10% of active variance is unexplained. 30

Amundi Discussion Papers Series - DP-04-2014

Contributions to Absolute Risk 100%

Unexplained Momentum

80%

Sector Reversal

60%

Value

92,08%

40%

Dividend Low Syst. Risk

20% 0%

Contributions to Active Risk

Small Cap MKT Beta

Factor Contributions

100%

10,06%

80%

12,96%

60%

15,43%

40%

48,67%

20% 0%

Factor Contributions Source: Amundi Research

In a second example, we assume that another investor prefers to diversify from an active risk perspective. He still diversifies on the two indices, and does not yet control for factor exposures directly. In this case he would rather invest 73% in the risk-weighted index and 27% in the minimum variance index respectively.

Equal Active Risk Contribution by Strategy 100% 80% 60%

100%

33% 67%

26.7%

50%

73.3%

40%

80% 60%

50%

20% 0%

Contributions to Active Risk

40%

8.13% 5.61% 12.37%

Unexplained Momentum Sector Reversal

16.69%

Value

17.19%

Dividend Low Syst. Risk

20% Weights MSCI World RW

Total Risk Contribution

Active Risk Contribution

MSCI World MinVol

0%

37.47%

Small Cap MKT Beta

Factor Contributions Source: Amundi Research

By doing so, active risk would be balanced across the two strategies and, as a side effect, diversification across the performance drivers would improve as well, while the percentage of active risk with an unknown source would be reduced. However, the investor might be much more sensitive to diversification across the factors than across the two indices themselves. In this third example, we assume that the investor is willing to maximize the diversification of the sources of active risk. We thus maximize the measure of entropy as defined in section 2.2, computed over the active risk contributions by factors, or performance drivers.

Amundi Discussion Papers Series - DP-04-2014

31

Maximum Entropy Over Factor Contributions to Active Risk 100% 80%

100%

16.1%

21%

Contributions to Active Risk

32%

80%

7,36% 6% 11%

60% 40%

68%

20% 0%

Momentum Sector Reversal

17%

60%

83.9%

79%

Unexplained

Value

27%

40%

Dividend Low Syst. Risk

20% Weights

Total Risk Contribution

MSCI World RW

Active Risk Contribution

0%

MSCI World MinVol

Small Cap

29%

MKT Beta Factor Contributions Source: Amundi Research

In this case, in order to reduce the still dominant contribution of low market beta, the allocation in the risk-weighted index would increase. Contrarily, small cap, dividend yield, and low risk anomaly contributions are increased. The change in the latter, however, is mainly due to a base effect: portfolio exposure to the low risk factor decreases, but as the active risk decreases as well (risk weighted index has a much lower tracking error than minimum volatility, relative to the standard index), its risk contribution as a percentage marginally increases. As a side effect, unexplained active variance is further reduced. As a fourth and last case, we now consider an investor that is comfortable with an objective of diversification across factors in an active management framework, but that is willing to introduce into his allocation some exposure to the sector reversal factor, because of its regular and low-volatility historical contribution to performance. The exposure to this factor is negligible in the three previous allocations. The smart beta portfolio that is most exposed to sector reversal is the Amundi Risk Parity, because of the two-step stock-sector construction process. We thus repeat the last case study, adding Amundi Risk Parity to the set of available strategies. Maximum Entropy Over Factor Contributions to Active Risk 100% 80% 60%

21% 41%

40% 20% 0%

37%

42,9%

32%

80%

34% 40,9%

5% 7% 4% 7% 16%

100%

34%

60%

Weights

Total Risk Contribution MSCI World RW

Active Risk Contribution MSCI World MinVol

Unexplained Momentum Sector Reversal Value

28%

40%

Dividend Low Syst. Risk

20%

Amundi Risk Parity

32

16,3%

Contributions to Active Risk

0%

32%

Small Cap MKT Beta

Factor Contributions

Amundi Discussion Papers Series - DP-04-2014

Source: Amundi Research

The overall allocation to the risk parity strategies is basically unchanged, but split into the MSCI Index and the Amundi process. This latter now accounts for 37% of the assets, 41% of absolute risk, and 34% of active risk. Sector reversal would be introduced as a source of active risk with a 7% contribution, while the entropy measure on the risk factor would increase to 5.02 from 4.89. Unexplained risk would be further reduced to 5%. 3.4.2 Timing smart beta strategies As several factors drive smart beta performance, the most straightforward way to implement some timing over the different indices or strategies, should be to time the underlying factors and consistently allocate strategies. Investors may develop a reliable style rotation model, and may apply some allocation where risk contributions match return expectations, rather than maximizing some diversification measure as we have done in previous case studies. Another way to time smart beta strategies might be to investigate their behavior according to different market conditions. The following chart exhibits the 12-month cumulative outperformance of each of the three Amundi strategies relative to the standard index, with a quarterly frequency, from June 2003 to December 2013. Results are interesting and often intuitive as well. Rolling 12-Month Outperformance (LS) Relative to MSCI World (RS) 3.5 2

3.0

3

1

2.5 4

2.0

5

Amundi Minvar

Amundi Diversification

Amundi Risk Parity

MSCI World

2013 12

2013 09

2013 06

2013 03

2012 12

2012 09

2012 06

2011 12

2011 09

2012 03

2011 06

2011 03

2010 12

2010 09

2010 06

2010 03

2009 12

2009 09

2009 06

2009 03

2008 12

2008 09

2008 06

2008 03

2007 12

2007 09

2007 06

2007 03

2006 12

2006 09

2006 06

2006 03

2005 12

2005 09

2005 06

2005 03

2004 12

2004 09

2004 06

2004 03

2003 12

2003 09

1.5

2003 06

0.25 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25

1.0

Source: Amundi Research

In long and steady bull markets as was the case from 2003 to mid-2007, the risk parity portfolio often exhibits the best returns, while during market crashes minimum variance is by far the winning strategy. When the impressive rebound of March 2009 starts, minimum variance starts lagging the two other strategies, while diversification and especially risk parity react well since they keep on delivering some positive outperformance. When the market is suffering some higher volatility without exhibiting a clear trend as in the period between mid-2011 and mid-2012, minimum variance is the winning strategy with some nice resistance by the diversification strategy as well. Amundi Discussion Papers Series - DP-04-2014

33

During the recent low volatility bull market period, smart beta strategies are slightly lagging overall (with better risk adjusted returns than the market index, however), but the risk parity strategy still captures the trend fairly well. We are conscious that forecasting the market conditions of the future is not an easy task, and actually this is not our goal. On the other hand, we recognize that volatility, correlation and turbulence, may be behind each of the five “states of the world” described above. In this section, we describe the dynamic allocation model that Amundi implements on a real money multi-smart beta fund on Eurozone equities. The model is based on three stand-alone dynamic strategies: each of them is based on a market signal, has an equally weighted target allocation on the three smart beta, and assigns an overweight and an underweight of 5% to the most and least profitable strategy, according to the market signal. The first model is based on market implied volatility, and works as a typical risk off – risk on model. When the average level of the VIX Index, computed over the last 10 days, is higher than the average computed over the last 25 days (increasing VIX), we overweight the minimum variance portfolio and we underweight risk parity, according to the conditional next-month average returns that we have computed historically. When the 10-day average is lower than the 25-day average (decreasing VIX) we overweight risk parity and we underweight minimum variance. According to the VIX model, the weight of the diversification-based smart beta is always neutral. When the relative difference between the two averages is less than 5% we do not apply any under/over weights as we allow the model to be in a neutral position, in order to reduce turnover and avoid false signals. The chart below exhibits the next-month average annualized returns, conditional to the VIX configuration, as estimated from beginning 2003 to mid-2012 (our sample period). Average Returns Increasing Vix 0.0%

Average Returns Decreasing Vix 25.0% 20.0%

-5.0%

15.0%

-10.0%

10.0% -15.0% 5.0% -20.0% Risk Parity

Diversif.

Minvar

MSCI

0.0%

Risk Parity

Diversif.

Minvar

MSCI

Source: Amundi Research

The second model is based on average market correlation. We have computed average correlation according to the CBOE methodology, on single country indices, as well as on the GICS industry group indices of the MSCI World.

34

Amundi Discussion Papers Series - DP-04-2014

As for the case of the VIX, in the charts below we report the average annualized returns computed over months following an average two-week correlation higher than the 104-week average (low correlation), and months following an average twoweek correlation higher than the 104-week average (high correlation). Again, the 5% threshold for neutral signals applies, and the sample period ends in mid-2012. Average Returns High Correlation

Average Returns Low Correlation

15.0%

10.0%

5.0%

10.0%

0.0% 5.0% -5.0%

0.0%

Risk Parity

Diversif.

Minvar

-10.0%

MSCI

Risk Parity

Diversif.

Minvar

MSCI

Source: Amundi Research

The intuition behind this is that when correlation is very high (left chart), there is less benefit in searching for diversification over risk factors, while searching for diversification across assets directly is probably more effective. When average correlation is lower (right chart), strategies based on diversification across risk factors benefit more than those diversified on stocks directly, since the former favor those stocks exposed to uncorrelated factors. Overall, returns on the righthand chart are lower, as the low correlation across sectors and countries includes English Version a typical pre-crisis situation (October 2008 and July 2011). Average Correlation and Returns in the Eurozone Estimation Period: 01/2003 - 06/2012 0,2 0,15 0,1 0,05 0 -0,05 -0,1

High Corr

Low Corr

Neutral

05/01/12

08/01/12

11/01/11

02/01/12

05/01/11

08/01/11

11/01/10

Delta 2W - 2Y Av Corr

02/01/11

05/01/10

08/01/10

11/01/09

02/01/10

05/01/09

08/01/09

02/01/09

11/01/08

08/01/08

02/01/08

05/01/08

11/01/07

08/01/07

05/01/07

02/01/07

11/01/06

08/01/06

05/01/06

02/01/06

11/01/05

05/01/05

08/01/05

02/01/05

11/01/04

08/01/04

02/01/04

05/01/04

11/01/03

08/01/03

05/01/03

-0,2

02/01/03

-0,15

Source: Amundi Research

1.04

2.50 2.00 1.50

1.03 Amundi Discussion Papers Series - DP-04-2014

1.02

e Returns

Returns

Our third indicator is a turbulence index. We define market turbulence as the crosssection dispersion of returns, computed over the GICS industry group indices. As this Performance indicator is closely correlated with the VIX index, we normalize by the VIX itself, as we want 3.50 1.05 to capture the turbulence that is not already explained by the market implied volatility. 3.00 35

As for the correlation indicator, we compute rolling averages on two weeks and 104 weeks, we apply the neutrality threshold at 5%, and we finally compute next-month annualized average returns. Average Returns High Turbulence

Average Returns Low Turbulence

15.0%

8.0%

6.0%

10.0%

4.0% 5.0% 2.0%

0.0%

Risk Parity

Diversif.

Minvar

MSCI

0.0%

Risk Parity

Diversif.

Minvar

MSCI

Source: Amundi Research

Results are less intuitive than in the two previous cases, but the turbulence indicator is uncorrelated with the implied volatility and average correlation signals. As mentioned, our final dynamic strategy consists in the portfolio that averages the three model portfolios based on the three market signals above. Each model portfolio overweights the best performing strategy according to the observed signal at the end of the previous month. The chart below shows the gross total return performance of the market-weighted index, an equally weighted basket of the three smart beta strategies, and the dynamic strategy described so far. Starting mid-September 2012 data are out-of sample, while starting from June 2013 the strategy feeds a real money portfolio. Turnover Sharpe Ratio

72.06%

IR

1.27

Mkt Wght

Constant Mix

Dynamic Strategy

0.29

0.64

0.67

Return / Conditional Var (5%)

0.53

1.01

1.08

Return

6.1%

9.4%

9.9%

Conditional Var (5%)

-12.6%

-9.3%

-9.1%

Drawdowns

-56.2%

-50.1%

-49.3%

Volatility

17.5%

13.2%

13.2%

Compared to an equally weighted composite of smart beta strategies, the dynamic model outperforms by more than 40 basis points per year. There is no significant impact on the absolute volatility, even though the drawdown of 2008 is reduced. The Sharpe ratio rises to 0.67 from 0.64 , and the ratio of returns to Conditional Var improves too (1.08 versus 1.01). 36

Amundi Discussion Papers Series - DP-04-2014

Low Corr

Neutral

05/

08/

11/

02/

05/

08/

11/

Delta 2W - 2Y Av Corr

02/

05/

08/

11/

02/

05/

08/

02/

11/

08/

02/

05/

11/

08/

05/

02/

11/

08/

05/

02/

11/

05/

08/

02/

11/

08/

02/

05/

11/

08/

05/

02/

High Corr

Source: Amundi Research

Performance 3.50

1.03

2.00

1.02

Strategy with Timing (LS)

Const. Mix (LS)

Mkt W Index (LS)

Cum. Active (RS)

2014

2013

2012

2011

2010

2009

2008

2007

0.99

2006

1.00

0.50

2005

1.01

1.00 2004

1.50

2003

Returns

1.04

2.50

Active Returns

1.05

3.00

Source: Amundi Research

IV - Are smart beta passive or active strategies?

Title Arial 9 Bold (1 or 2 lines maxi) Defining an investment strategy as “active” or “passive” is usually not an easy task. Of course there are some extreme circumstances where such a definition is obvious: let’s consider an ETF benchmarked to the S&P 500 and the investment fund Berkshire Hathaway run by Warren Buffett: it would be hard not to classify them as “passive” and “active” respectively. However, there are some frequent intermediate situations where we can distinguish different levels or intensities in being active or passive. A classic condition for a “passive” strategy is that we clearly identify the systematic replication of a widely recognized, transparent and investable benchmark. According to our definition, we must recognize both the elements in order to match the “passive” condition: Title Arial 9 Bold (1 or 2 lines maxi) 1.  B enchmark characteristics: widely recognized (generally accepted), transparent and investable; 2. Systematic replication. On the other hand, we define as “active” whatever strategy exhibits pronounced deviations (both in terms of holdings and in terms of returns) from a benchmark index. Widely recognized and transparent Benchmark Prior to this point, we need to clarify whether the market cap index should be considered as the benchmark of a smart beta strategy. We believe this should not be the case, as the main argument for smart beta investing is the well-documented inefficiency of market capitalization benchmarks. As a consequence, smart beta Title Arial 9 Bold (1 2 linesweighted maxi) strategies should not be benchmarked to or market indices, nor is their impressive tracking error a valuable argument for defining them as “active”. Amundi Discussion Papers Series - DP-04-2014

37

However, market weighted indices offer an interesting reference point for comparison to our discussion. Together with their composition, index providers disclose the rules applied for companies’ inclusion or exclusion from the index (typically: geographical belonging, sector classification, free float, and size), as well as the rules for index weighting. All of them rely on continuously and publicly available information as market capitalization. To some extent, market cap weighted benchmarks may be replicated even without knowing their composition directly: in order to derive it, investors could combine construction rules with publicly available information, at the cost of a negligible margin of error. The case for smart beta benchmark is different. Let’s have an example focusing on some minimum variance benchmarks (such as the MSCI Minimum Volatility index), or on some diversification benchmarks (such as the FTSE EDHEC Risk Efficient Index, or the FTSE TOBAM Maximum Diversification). These indices do not rely on some objective and easily measurable metrics, as in the case for market capitalization: rather, all of them depend on: 1. Some risk measure estimation (the variance covariance matrix of stocks) 2. An optimizer, and its numerical algorithms 3. T  he objective function that is maximized: portfolio variance is minimized (or some diversification measure maximized), subject to some constraints (minimum stocks threshold, stocks’ upper bounds, sector concentration constraints, etc.) All the points mentioned above contain provider-specific features (risk model, optimizer), while some of them (the set of constraints) are also very discretionary and better shaped to design an investment strategy than to build a traditional investment benchmark. Smart beta benchmarks require the estimation of a variance covariance matrix. A simple historical data approach is almost impossible: a statistical and parsimonious method (such as principal component analysis, or fundamental factor models) is usually needed, as a covariance matrix may ideally contain millions of parameters. Such benchmarks are thus dependent on some necessarily complex risk model. Furthermore, smart beta composition is definitely influenced by the numerical algorithm (often very complex too) of the optimizer. This point is rather critical as we often observe some better consistency among risk forecasts provided by different risk models, than among portfolios optimized by different optimizers: little differences in risk and correlation estimates may determine huge differences in optimal stock weights, and differences in numerical algorithms across optimizers magnify those discrepancies in portfolio composition. Furthermore, in order to prevent some typical drawbacks of some optimisationbased smart benchmarks (as excessive concentration on a few sectors or a few

38

Amundi Discussion Papers Series - DP-04-2014

and sometimes illiquid- stocks, involuntary exposure toward styles such as small caps or momentum) some prudent constraints may be needed: –– minimum holding thresholds; –– g eneral upper bound on each stock (in absolute terms or as a function of the daily liquidity); ––  sector and country holdings may be constrained in a range around their weights in a traditional index; –– the index may be prevented to have major exposure to some style factors. Although reasonable, realistic, and prudent, these rules are discretionary and lead to a benchmark that is provider-specific, rather than universally recognized, as it would be required instead. As a consequence, for instance, the minimum variance indices so far available in the market exhibit reciprocal (historical) tracking errors ranging from 4% to 6%. Definitely more than the tracking errors among market weighted indices, which are usually lower than 1%. In conclusion, while the disclosure of parameters and models may satisfy the transparency condition, the dependency on different risk models and optimizers, and the common practice of applying various and sometimes heterogeneous constraints prevent the benchmark to be easily recognized and universally representative. We might argue that, as far as there is no universally representative smart beta benchmark for any of the three categories, passive management is basically precluded for smart beta: many alternative benchmarks exist and all are very different from each other. We think this conclusion is too radical, it is highly influenced by a traditional definition of benchmark, and it does not recognize some significant trends in the passive asset management industry. Nowadays passive management is experiencing spectacular growth thanks to a highly comprehensive product offer. These products are not limited to those asset classes with a universally recognized benchmark available. In contrast, every asset class or strategy, even the more exotic or customized, may be packaged in an ETF. The only requirements are the mere existence of a benchmark (and very often we would better say the existence of an underlying asset), and the concrete possibility for the fund manager to replicate its payoff. We believe that the universal recognition of the benchmark should rather be replaced by some less stringent requirement such as the mere existence of the benchmark itself, its transparency and its investability. If several and different minimum variance, or risk parity, or diversification benchmarks exist, we may potentially have several passive mandates replicating them, each with a very different payoff, but all mimicking the payoff of their own benchmark.

Amundi Discussion Papers Series - DP-04-2014

39

Of course, a smart beta fund manager that is formally benchmarked to a traditional market cap index, would concretely be a passive manager if he actually tracks an existing smart beta benchmark, regardless of the decision of declaring the true benchmark. On the other hand, a highly innovative or customized smart beta solution could be packaged in a passive product by asking an index provider to produce a tailormade benchmark. We think that disclosing a benchmark is a not a pure formality, neither is it a trivial decision by the fund manager. A formal benchmark implies the involvement of an index provider that provides objective calculation and transparency, and also implies a formal commitment by the fund manager of never deviating from the benchmark itself. Furthermore having an official benchmark would be a costly decision as smart beta benchmarks are far more expensive than traditional ones. As a conclusion, once we have verified that a pertinent benchmark exists, is transparent, investable and computed by a third party (the index provider), the only criterion that we need to apply in order to categorize a smart beta product as active or passive, is whether or not the fund manager implements a systematic replication of it. Systematic replication Once the benchmark is built and made available, the goal of a passive fund manager is to systematically apply and comply with it, rebalancing at a prespecified frequency with no room left for incorporating (time varying) views on market and stocks. In other words, stock picking is not contemplated, and tracking error relative to the benchmark or relative to the reference strategy must be ideally equal to zero. On the other hand, for a strategy to be defined as “active”, deviation from the benchmark must be relevant, and the main drivers of such deviations are investment decisions. The latter depend on time-varying forecasts of the future profitability of stocks. According to this criterion, smart beta investments may fall in both the active and the passive category. The easiest example of an active strategy is some optimisation-based smart beta strategy (minimum variance or diversification), where the process is applied to a restricted list of stocks, based on some qualitative and judgmental criteria (the best investment ideas of the buy-side analysts, for instance). Similarly, a smart beta portfolio is actively managed where the investment universe is filtered by some quantitative or systematic criteria, if this filtering is specific to the fund manager, and generates some non-negligible tracking error relative to any of the existing benchmarks available. In the same way, portfolios where risk factors’ exposures are managed according to market views are active portfolios. Finally, any risk parity portfolio that systematically 40

Amundi Discussion Papers Series - DP-04-2014

applies some unique weighting schemes (as the two-step approach discussed in previous sections) is actively managed, if those weighting rules differ from those applied by the available benchmarks. As an opposite example, any replication of an index is passive, even if the index is built by maximizing a highly innovative utility function, through a sophisticated numerical algorithm, employing highly specific sector and country constraints, and investment universe restrictions. The requirements are that the index is produced by an independent index provider that discloses calculation methodology, and that the fund manager assures very low tracking error.

Conclusion Smart Beta equities are the asset management industry’s answer to some wellknown drawbacks of market capitalization-based equity indices such as price noise, overrepresentation of large caps, absence of an auto-corrective meanreversion 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 – minimum variance, diversification, and risk parity. 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 (thus further investigation is needed), while filtering the universe for some quality criteria proves to provide additional value. As for the diversification-based strategies (portfolio maximizing the diversification ratio, risk efficient portfolio, etc.), “low market beta” and “low risk anomaly” are still the most significant factors, with the addition of “small cap” and “sector reversal”. Performance drivers behind the risk parity strategies are basically the same, but we notice that the “low beta” and “low risk anomaly” are less explanatory than “small cap” and “sector reversal”. ”Sector reversal” as a source of outperformance is more relevant for risk parity than for any other smart beta, especially where (as is the case in Amundi’s process) risk parity is achieved through a two-step stocksector construction process. Smart beta may become a “new equity core” if the investor’s relevant risk measure is absolute risk. In this case, however, the liquidity of those strategies must be consistent with the amount of assets the investor holds. If the investor’s relevant risk measure is relative risk, smart beta might still become a new equity core,

Amundi Discussion Papers Series - DP-04-2014

41

but some more pertinent benchmarks should be designed, because smart beta investing generates high tracking error relative to standard indices. A clever benchmark, as well as a clever multi-smart allocation should exploit the circumstance that the exposures to performance drivers are not identical for all smart beta equities, and thus there is room for diversification. Another argument for diversifying across smart beta is the different behavior they exhibit in some typical market conditions. In addition to diversification, investors can translate these different behaviors into some profitable timing strategies. Finally, we discuss whether smart beta should be considered as passive or rather active strategies. According to the pure replication criterion, most smart beta strategies should fall into the passive category, with the exception of those (such as for the Amundi minimum variance) where the portfolio construction processes are combined with discretionary and judgmental investment decisions by the fund manager. The second traditional criterion of transparency and wide recognition of the benchmark should be replaced by the less stringent requirement of the mere existence of a benchmark. If the fund manager replicates an existing smart beta benchmark, the answer is obvious – if he designs his own smart beta process, then the asset manager himself determines the active or the passive nature of his product by requiring or not that a tailor-made benchmark is created and maintained by an index provider.

42

Amundi Discussion Papers Series - DP-04-2014

Appendix Optimisation-based smart beta portfolios at Amundi Quality Stocks We believe that fundamental equity selection can provide some valuable enhancement in the risk return profile of equity portfolios, at least in the long run. At the same time we do not want to renounce an optimisation process which is completely independent from expected returns. Expected returns are very noisy in forecast and thus responsible for well known “error maximization” problems. For this reason, we apply a qualitative filter to our investment universe, excluding the lowest quality stocks from the optimisation. Basically, each quarter we rank the constituents of the MSCI World Developed Markets according to a Piotroski (2000) score and we exclude the two bottom quintiles. Keeping 60% of constituents available for investments, the optimizer is left with a high degree of freedom and it tilts the optimal portfolio toward good quality stocks, without using explicit expected returns. Turnover and liquidity High turnover is a critical issue in many systematic investment strategies like Minimum Variance and other optimisation-based strategies. In our case, turnover in the investment universe is limited as the Piotroski score is based on balance sheet data that varies very little during one quarter. Furthermore we also rebalance our portfolio quarterly, as suggested by Baker and Haugen (1991). Nevertheless, more than turnover itself, our concern is indeed liquidity: we aim to avoid small illiquid companies as we want to be able to liquidate our portfolio in a reasonable time lag, without incurring significant market impact costs. To address this requirement, we limited the amount held in any stock to the following percentage:

where UB i is the upper bound on the ith stock, D is the number of days that we accept to liquidate the fund, ADV i is the average daily volume over the last quarter, and NOT is a notional amount of assets under management of USD 1 billion: quite conservative as it is still far above the current size of our fund. Sector, country, and stock concentration As mentioned above, Minimum Variance and Diversification portfolios provide excellent diversification across risk factors, but may tend to be poorly diversified across sectors, countries or single stocks. We have thus applied some constraints at these levels, without preventing the optimizer from choosing solutions that are far enough from a market index. Amundi Discussion Papers Series - DP-04-2014

43

On countries and sectors we accept deviations from the market index of 5% to 10%, while for single stocks we apply a general upper bound (GUB), thus modifying the actual upper bound as follows:

Management of asymmetries in factor returns Furthermore, we are conscious that optimisation-based smart beta portfolios may be systematically or incidentally exposed to fundamental factors such as size, value or momentum. We observe that much of our size exposure is corrected away by the liquidity constraints. As for other factor exposures, we have decided not to manage them systematically as –again– we do not want to excessively restrict the optimisation process. On the other hand, we regularly monitor the behavior of all the risk factors of the BARRA model (size, value, growth, momentum, leverage…). The goal of this monitoring is to detect bubbles or suspicious asymmetries like excessive positive skewness in recent performance: in the case of significant alerts, from time to time the fund manager hedges the risk of an exploding bubble, imposing a neutral exposure to the suspected factor.

44

Amundi Discussion Papers Series - DP-04-2014

Acknowledgements I would like to thank Sylvie de Laguiche for discussions, suggestions, and comments that improved the quality of the manuscript.

Bibliography Ang A., Hodrick R.J., Xing, Y., Zhang, X. 2006. The Cross Section of Volatility and Expected Returns. The Journal of Finance. Vol. LXI, No. 1 (February) Baker M., Bradley B., Wurgler J. 2009. A Behavioral Finance Explanation for the Success of Low Volatility Portfolio. New York University, Working Paper Baker M., Bradley B., Wurgler J. 2011. Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly. Financial Analysts Journal, Vol. 67, No. 1, CFA Institute Baker N. L., Haugen R. A. 1991. The Efficient Market Inefficiency of Capitalization-Weighted Stock Portfolios. The Journal of Portfolio Management, Vol. 17, No. 3 (March) Clarke R., De Silva H., CFA, Thorely S., CFA. 2011. Minimum Variance Portfolio Composition. The Journal of Portfolio Management, Vol. 37, No. 2 (Winter) Clarke R., De Silva H., CFA, Thorely S., CFA. 1991. Minimum Variance Portfolios in the US Equity Market. The Journal of Portfolio Management, Vol. 33, no. 1 (Fall) Clarke, R., De Silva, H., Thorley, S. 2012. Risk Parity, Maximum Diversification, and Minimum Variance: An Analytic Perspective. Journal of Portfolio Management, Vol. 39, No. 3,(Spring 2013) Carvalho R.L., Lu X., Moulin P. 2011. Demystifying Equity Risk-Based Strategies: A Simple Alpha Plus Beta Description. The Journal of Portfolio Management, Vol. 38, no. 3 (Spring) Choueifaty, Y., Coignard, Y. 2008. Towards Maximum Diversification. The Journal of Portfolio Management, Vol.35, No. 1 (Fall) Markowitz H. 1952. Portfolio Selection. The Journal of Finance, Vol. VII, No.1 (March) Maillard S., Roncalli T., Teiletche J. 2009. On the Properties of Equally-Weighted Risk Contributions Portfolios. Social Science Research Network, Working Papers Series (September) Piotroski J. D. 2000. Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers. Journal of Accounting Research, Vol. 38, Supplement 2000 Russo A. 2013. Low Risk Equity Investments: Empirical Evidence, Theories, and the Amundi Experience. Amundi Working Papers, WP-033-2013 (March) Sharpe W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, Vol. XIX, No. 3 (September) Shefrin H., Statman M. 2000. Behavioral Portfolio Theory. Journal of Financial and Quantitative Finance, Vol. 35, No. 2 (June) Thomas R., CFA, Shapiro R., CFA. 2007. Managed Volatility: A New Approach to Equity Investing. State Street Global Advisors

Amundi Discussion Papers Series - DP-04-2014

45

Chief Editors:

Pascal BLANQUÉ Deputy Chief Executive Officer Head of Institutional Investors and Third Party Distributors Group Chief Investment Office

Philippe ITHURBIDE Global Head of Research, Strategy and Analysis

Pia BERGER, Assistant Editor Research, Strategy and Analysis Benoit PONCET, Graphic Designer - Research, Strategy and Analysis

Amundi Discussion Papers Series - DP-04-2014

47

Amundi Discussion Papers Series May 2014

In the European Union, this document is only for the attention of “Professional” investors as defined in Directive 2004/39/EC dated 21 April 2004 on markets in financial instruments (“MIFID”), to investment services providers and any other professional of the financial industry, and as the case may be in each local regulations and, as far as the offering in Switzerland is concerned, a “Qualified Investor” within the meaning of the provisions of the Swiss Collective Investment Schemes Act of 23 June 2006 (CISA), the Swiss Collective Investment Schemes Ordinance of 22 November 2006 (CISO) and the FINMA’s Circular 08/8 on Public Advertising under the Collective Investment Schemes legislation of 20 November 2008. Under no circumstances may this material be distributed in the European Union to non “Professional” investors as defined in the MIFID or in each local regulation, or in Switzerland to investors who do not comply with the definition of “qualified investors” as defined in the applicable legislation and regulation. This document neither constitutes an offer to buy nor a solicitation to sell a product, and shall not be considered as an unlawful solicitation or an investment advice. The portfolios mentioned in this document, Amundi Diversification, Amundi Risk Parity and Amundi Minimum Variance, are back test portfolios given for illustrative purposes only. Past performance and simulations shown in this document do not guarantee future results, nor are they reliable indicators of future performance. Amundi accepts no liability whatsoever, whether direct or indirect, that may arise from the use of information contained in this material. Amundi can in no way be held responsible for any decision or investment made on the basis of information contained in this material. The information contained in this document is disclosed to you on a confidential basis and shall not be copied, reproduced, modified, translated or distributed without the prior written approval of Amundi, to any third person or entity in any country or jurisdiction which would subject Amundi or any of “the Funds”, to any registration requirements within these jurisdictions or where it might be considered as unlawful. Accordingly, this material is for distribution solely in jurisdictions where permitted and to persons who may receive it without breaching applicable legal or regulatory requirements. The information contained in this document is deemed accurate as at the date of publication set out on the first page of this document. Data, opinions and estimates may be changed without notice. Document issued by Amundi, a société anonyme with a share capital of €596,262,615 - Portfolio manager regulated by the AMF under number GP04000036 – Head office: 90 boulevard Pasteur – 75015 Paris – France – 437 574 452 RCS Paris www.amundi.com Photo credit: Thinkstock by Getty Images

research-center.amundi.com