Behind the performance of Equally Weighted Indices · EW portfolio and the performance of the...

OSSIAM RESEARCH TEAM

Behind the performance of Equally Weighted Indices

May, 04, 2011

WHITE PAPER

1

Behind the performance of EquallyWeighted Indices

Bruno Monnier and Ksenya Rulik

May, 04, 2011

Abstract

Bruno MonnierQuantitative [email protected]

Ksenya Rulik, PhD, CFAHead of Quantitative [email protected]

Equally weighted portfolios that allocate the same weight toevery portfolio constituent emerged recently as an attractivealternative to the traditional market-capitalization weightedscheme. The equally-weighted versions of traditional equityindices tend to outperform their market-cap counterpartsover the long run. The article examines the sources of thisoutperformance. We show that Equally Weighted portfo-lio on European stocks outperforms the traditional indexbecause the portfolio is more exposed to mid and small cap-italizations, and also due to homogeneous repartition of theweights inside the large cap sector. The rebalancing effect,however did not contribute positively to the portfolio per-formance.


2


3

A Spreading Concept

Equal Weight approach in broad equity invest-ing is one of the most successful recent nov-elties in the alternative equity indexing space.Giving the same weight to all stocks in the uni-verse is seemingly the most obvious strategyand as such a most straight-forward bench-mark. Boosted by the expansion of ETFs, aperfect wrap that helps to spread and democ-ratize the Equal Weight concept, the productfamily already counted more than USD 3.5bln AUM as of Apr-2011 under this wrapper1.All major index providers have launched EqualWeight versions of their flagship indices withinthe last 8 years. Two examples covering thelargest US and European stocks are equallyweighted versions of S&P 500 and STOXXEurope 600 indices, launched, respectively, inJanuary 2003 and October 2010. A growingamount of publications on equal weight in-vesting is coming from industry professionalsas well as from the academia2. The majorquestion being investigated is excess perfor-mance of equally weighted portfolios againstthe dominant benchmarks: market capital-ization weighted portfolios. The debate isstill open since performance comparison re-sults exhibit high dependency on period andequity basket selected. Frequent argumentsthat are often invoked in relation to the equallyweighted strategies are size-insensitive alloca-tion, resulting in overweighting small stockscompared to a market-capitalization weightedportfolio, contrarian-like rebalancing enforcedat each reset of the portfolio to equal weights(buy low, sell high), and potentially highturnover associated with the rebalancing activ-ity. Here we intend to shed some light on theimpact of these features on the equal weightstrategy.

What to expect from an equallyweighted allocation?

Quantitative investment generally involvescomplex modeling in order to extract mean-ingful and valuable insights from data re-lated to past observations. What can be saidabout a strategy as straightforward as theequal weighting (further referred as EW) whichmostly disregards available information?

Actually, the EW is not totally informationfree, as it involves the choice of an investmentbasket. The choice of portfolio constituents isitself a major information. Taking the compo-sition of a broad market index as the invest-ment universe for an EW portfolio allows tobuild a basket that is representative of the cho-sen equity market or sector. Such a basket isgenerally closely monitored by the market andsatisfies reasonable liquidity criteria.

Once the basket is chosen, an EW index canbe set up as a pure rule based strategy, andthe EW methodology is very stable from oneindex provider to another. An EW index:

1. has the same constituents as its marketcapitalization weighted counterpart (MWindex),

2. allocates the same investment amount toall its constituents,

3. is rebalanced periodically (usually quar-terly) to restore the equally weighted allo-cation.

The process is estimation free, which meansthat unlike most quantitative based indices, itrequires no estimation of either risk profile orexpected returns. EW index performance iseasy to interpret: it is the average performanceof all assets in the universe over the period.

Notwithstanding different allocation schemeand periodic rebalancing feature, the perfor-mance of EW portfolio is closely related to that


4

Index 2003-2006 2007 2008 2009 2010 Total Std %

SPXEWTR 107.37 1.93 -41.16 50.93 20.58 126.35 23.46

SPTR 73.44 6.22 -38.3 29.56 13.91 67.75 21.11

Excess Return 33.93 -4.29 -2.85 21.37 6.67 58.61 4.54

SXXEWR 152.38 -3.28 -48.85 49.32 19.63 123.03 20.73

SXXR 100.6 2.29 -44.14 32.99 11.94 70.62 20.42

Excess Return 51.78 -5.57 -4.71 16.33 7.7 52.41 4.96

Table 1: Indices’ performance comparison

of the market-capitalization weighted bench-mark. Indeed, correlation between market-capitalization weighted and equally weightedindices on the same basket are often of the or-der of 95-99%, and their risk levels are verysimilar. This high level of correlation is notsurprising, since an EW strategy is designed toprovide access to the chosen market segment,where the corresponding market factor is thedominant one.

To appreciate the value added by the EWinvesting, one has to focus on excess return -the difference of the returns of equally weightedand market-cap weighted portfolios (Table 1).Here we consider two distinctive features ofEW portfolios: periodic rebalancing and size-neutral allocation, and show how each of thesefeatures translates into properties of excess re-turn. In the remaining sections, we probe theexistence of a rebalancing bonus for the EWstrategy, then we estimate the magnitude ofthe costs associated with portfolio turnover, fi-nally we assess the impact of size neutrality onthe excess return.

For this study we use a broad European uni-verse, represented by the components of theSTOXX Europe 600 index, along with the per-formance of auxiliary subportfolios represent-ing performance of non-overlapping subgroupsof the main index, containing stocks of dif-ferent size buckets3. To simulate the perfor-mance of EW portfolios we use the proceduredescribed above, with quarterly rebalancing

made each quarter-end. We also reconstructthe corresponding market-capitalization port-folios by weighting the stocks by their free-floatmarket capitalization.

Effect of rebalancing: is it allabout being contrarian?

Market capitalization weighting approach rep-resents the only truly passive investment strat-egy. Equal weighting cannot remain pas-sive, since price movements imply an alloca-tion drift. At the end of a given period thestocks that performed better than the averageend up having higher weights and the stocksthat underperformed the average turn under-weight with respect to the initial equal alloca-tion. Consequently, one has to reduce periodi-cally the investment in relative over-performersand to increase positions in relative under-performers to restore the equally weighted al-location. Though it may seem a pure mainte-nance operation, there are claims that this isone of the performance drivers of the strategy.This can be viewed as:

• A profit taking scheme: realise the relativeprofits at the end of the period. The EWindex doesn’t let itself be carried away ina momentum pattern.

• A contrarian strategy: it buys (sells)stocks that have been going out of favour


5

(gained momentum) so it may profit fromfuture price corrections when informationis fully incorporated in market prices.

These arguments in favor of the equal weightinvesting seem intuitive and self-evident, andas such they remain under-investigated. Doesthe equally weighted strategy really benefitfrom rebalancing? What is the magnitude ofits contribution to the excess performance?

We propose to assess the payoff related torebalancing by using the following decompo-sition. We compare period-by-period perfor-mance of two portfolios (Figure 1):

1. an equally weighted portfolio that at thebeginning of each period is rebalanced toexact equally weighted allocation, and

2. a ”non-rebalanced” equally weighted port-folio that was exactly equally weighted oneperiod before but hasn’t been rebalancedrecently.

Figure 1: Rebalancing Test Construction

Another way to visualize this test is to imag-ine a swap entered in by two parties with pay-ments made at each rebalancing date. Partiesexchange the performance of the ”rebalanced”EW portfolio and the performance of the ”non-rebalanced”’ EW portfolio (here a new ”non-rebalanced” portfolio is fixed at the preceding

rebalancing date). By cumulating the swappayments one has an idea of the magnitudeand persistence of the rebalancing effect.

The two portfolios follow the same EqualWeight concept, and thus have essentially thesame fundamental exposures. The differencesin performance of these strategies are thusclosely related to the stock allocation adjust-ment performed at the last rebalancing.

Figure 2 depicts the cumulated gains andlosses associated with rebalancing activity overa 8 year period for the broad European EWportfolio. This is compared to the cumulatedexcess return of the EW portfolio with respectto the market capitalization weighted one (acumulative sum of one-quarter excess returnsis used here). Indeed, the rebalancing pay-off can be seen as a part of the excess returncoming from the rebalancing activity, the restbeing explained by factors other than rebal-ancing. The magnitude of this effect is small

Figure 2: Excess Performance : Contributionof periodic rebalancing 4

compared to that of the total excess return,as one could expects given the similarity be-tween the two test portfolios. Important infor-mation is in the shape and in the trend of thiscontribution. There was no systematic rebal-ancing benefit over time for the EW strategy,


6

with no definite trend. Volatility of the con-tribution changes with the changes in marketconditions, being more important in the timesof market stress. On average, the rebalancingeffect was -2.4 basis points per quarter, withstandard deviation of 0.5%. This appears tobe marginal with respect to the excess perfor-mance of equally weighted index over marketcapitalization weighted index, that was on av-erage 1.2% per quarter, with standard devia-tion of 3.05%. The rebalancing contribution isnot stable, or even positive, over time and thuscannot be deemed a reliable source of perfor-mance. The rebalancing adjustment though isessential to the design of the Equally Weightedportfolio, as its keeps the portfolio close to thetarget weights.

What is the impact of the port-folio turnover?

Implementing an equal weight strategypresents some concerns. The most apparentdrawback is a rebalancing cost that is higherthan for a passive investment. There are twomain sources of turnover. The first one isspecific to the EW strategy, it arises whenthe stocks already present in the portfolio arerebalanced to the target weights. This kind ofturnover is directly linked to cross-sectionaldispersion of returns in the universe, andis absent in an investment that follows amarket-capitalisation weighted index. Indeed,one can show that this price-driven part of re-balancing is proportional to the cross-sectionalmean absolute deviation (MAD) of returns(quarterly returns if the strategy is rebalancedquarterly, monthly returns is the strategy isrebalanced monthly, etc..)

turnover ∼∑M

i=1 |rit −Rt|M(1 +Rt)

=MAD

1 +Rt(1)

where R is the average one-period return ofthe stocks in the portfolio, ri are the returnsof single stocks, and M is the number of stocksin the portfolio. In the case of normally dis-tributed returns across the universe with zeromean (R = 0), the MAD is just proportionalto the cross-sectional dispersion of the stocks’

returns: MAD =√

2π std, or MAD ∼ 0.8 std.

That is, this part of turnover is proportionalto the cross-sectional dispersion of stock re-turns and does not depend explicitly on thenumber of stocks M. For example, if EW strat-egy is rebalanced quarterly, the relevant mea-sure is the cross-sectional dispersion of quar-terly returns, that for a broad European basketsince 2003 was situated between [8.8%, 39.1%],with the average of 13.6%. This gives an esti-mation that the order of magnitude for this”structural” turnover is around 10.9% quar-terly. This is only slightly higher than the his-torical estimate of the structural turnover onour European broad EW portfolio, that is 9.2%per quarter on average.Another source of turnover is linked to changesin the investment universe. These changes canbe quite frequent in a large basket: stockspreviously meeting the inclusion criteria failto do so upon the current review and are re-placed accordingly by the runners-up. Somecorporate actions, like spin-offs and mergers,also affect the composition of the portfolio.Such a turnover is inherent to both market-capitalization weighted and equally weightedindices, although not with the same orderof magnitude. The main criteria for inclu-sion being size, universe revisions affect mostlysmaller capitalization stocks. Given that amarket-capitalization weighted index has tinyweights allocated to the smallest stocks, theturnover generated will be smaller than foran EW portfolio that allocates systematicallymore weight to the small stocks. Swappingone small stock for another would generate a


7

turnover of roughly 0.05% for a capitalization-weighted portfolio compared to 0.3% for anEW portfolio. Changes in the universe rep-resent a non negligible portion of the overalltransaction cost. The split of the total (an-nual) turnover into the two factors is in Table:

Turnover Dispersion Universe Total(%) Contribution Change

EW 36.8% 17.4% 54.2%

MW 0 5% 5%

Table 2: Breakdown of annual turnover

The turnover of the equal-weighted strategyis clearly dominated by the dispersion factor,accounting for 68% of the total turnover. in-vestment universe changes result in a turnoverof 5% per year for the passive MW portfolio,and a three times larger turnover for the EWportfolio. Still, in absolute terms the total im-pact of rebalancing cost on the performanceis negligible. Assuming a transaction fee of 5basis points, the transaction cost drag for theEW index is less than 3 basis points per year.

Effect of Size Neutrality: Oneweight fits all?

Size exposure is by far the greatest differencebetween the market-capitalization weightedand equally weighted portfolios. In the EWversion of the Stoxx Europe 600 index weightsof the largest companies are divided roughlyby 10 while weights of the smallest companiesare multiplied by 10 relative to the MW index.Further, if we rank the STOXX 600 universe bymarket capitalization and divide it into threeterciles (Large 200, Mid 200 and Small 200)the weight of the Large tercile will be morethan halved, the weight of the Mid tercile willbe doubled and finally the weight of the Small

tercile will be multiplied by 6 in the EW port-folio relative to its MW counterpart.

It is convenient to split our broad Eu-ropean portfolio into separate sub-portfoliosrepresenting the three size terciles. Eachsuch sub-portfolio can be constructed usingmarket-capitalization weighting (MW Large,MW Mid, MW Small), or equal weighting (EWLarge, EW Mid, EW Small). For example, abroad EW portfolio can be seen as an equalweight combination of EW Large, EW Mid andEW Small, while a broad MW portfolio is com-posed of a weighted sum of the MW Large,MW Mid and MW Small sub-portfolios.

Figure 3: Performance Large/Mid/Small

MW Small and MW Mid size sub-portfoliosshowed much stronger performance during bullmarkets than the MW Large sub-portfolio, fol-lowed by stronger corrections (Figure 3). Onecan see that the broad MW portfolio perfor-mance was very close to that of the MW Largesub-portfolio, following from the dominanceof large stocks in the market-capitalizationweighting. Indeed, the 200 Largest stocks rep-resent 80% of the total market-capitalizationin the broad MW portfolio.

Proceeding along this line, one can decom-pose the excess performance of the EW port-folio in a way that reflects:


8

Portfolio 2003-2006 2007 2008 2009 2010 Total std

EW All 128.07 -4.75 -49.61 45.7 17.39 87.21 19.86

EW Large 91.8 1.78 -48.82 34.39 12.7 51.33 20.95

EW Mid 141.75 -7.94 -48.56 45.8 18.26 97.42 19.65

EW Small 154.72 -7.98 -51.43 56.1 21.18 115.33 19.76

MW All 79.2 -0.17 -45.56 28.04 8.64 35.47 19.92

MW Large 68.14 1.51 -45.01 25.28 6.12 24.79 20.25

MW Mid 138.01 -7.55 -47.11 41.17 19.6 96.49 19.22

MW Small 156.55 -5.93 -51.16 49.5 22.49 115.84 19.57

Table 3: Performance Large/Mid/Small

1. Size allocation: the effects of differentexposure to the market-cap weighted sizesub-portfolios in EW and MW cases,

2. Size selection: the effects coming fromaltering the weighting inside each size sub-portfolio, i.e. switching from market-capitalisation weighting to equal weight-ing inside each size tercile.

We can summarize this decomposition as fol-lows:

∆REW−MW =M∑i=1

(1

M− wi) ri =

=1

3

∑K=L,M,S

∑i

(1

M ′− 3wi) ri =

=1

3

∑K=L,M,S

∑i

(1

M ′− wKi ) ri+

+∑

K=L,M,S

(1

3− 1

βK)wKi ri =

=1

3

∑K=L,M,S

∆RKEW−MW+

+∑

K=L,M,S

αKRKMW

Here the M ′ = M/3 is representing the num-ber of stocks in the broad and size portfolios(M = 600 in our example). wi are the stock

weights in the MW portfolio, wKi = βKwi areweights in MW Large, Mid and Small portfo-lios (rescaled to 100% leverage).

As results from the historical study, the ma-jor part of the excess performance of EW port-folio over MW portfolio is related to the sizeallocation effect (Figure 4), driven by the ex-cess performance of mid and small stocks overthat of the large stocks (Table 3). The selectioneffect, while significantly positive, accounts forless than 1/4 of the total excess performance.On average the selection effect amounts to 27basis points per quarter while the allocation ef-fect amounts to 99 basis points. Interestingly,

Figure 4: Excess Return : Size Selection andSize Allocation Effects 4


9

the size-neutral allocation gives very differentresults across the three size terciles (Figure 5).Only the Large size portfolio really benefitsfrom the EW allocation. On the contrary, theMid and Small size portfolios have essentiallyflat contribution, apart the effect of the sharprebound of the smallest stocks in 2009.

This confirms that Equal Weight allocationis a remedy in the case when there are signif-icant asymmetries present in the market capi-talization, as is the case of the strong mega-capbias of the Large MW portfolio (Figure 6).

Figure 5: Size Allocation Effect : Small, Mid,Large terciles 4

Conclusion

Though extremely simple in its concept, theEqual Weight alternative raises many non-trivial questions when one attempts to in-terpret its performance relative to a tradi-tional market-capitalization weighted bench-mark. This strategy has an objective of pro-viding access to a chosen equity market seg-ment while systematically avoiding stock con-centration problems. As such, this investingtechnique requires periodic portfolio adjust-ments, that come at a cost of higher portfo-lio turnover, but generate no significant per-

formance drag. Being clearly related to theobserved return dispersion, these costs stayedon average under 3 basis points during the past10 years for the broad European portfolio thatwe used here as an example. Contrary to thecommonly used argument, we found no definitebenefit from the rebalancing contrarian fea-ture on the excess performance of the equallyweighted portfolio with respect to its market-capitalization weighted counterpart. The totaleffect of the ”rebalancing payoff” for the broadEuropean portfolio under study was slightlynegative over the past 8 years, having no def-inite trend in between. Instead of being anadditional performance driver, the rebalancingplayed a role of technical adjustment needed tokeep the allocation close to the objective.

Figure 6: Market capitalization Asymmetries :Blue - MW sorted weights, Green - EWweights


10

The size allocation of the equally weightedportfolio could be better understood in the al-location/selection framework, similar to thatof the sector decomposition commonly usedin the industry. Splitting the size exposureof the equally weighed portfolio into the sizeallocation (over/under-weighting of differentsize factors) and size selection (implementingequal weighting inside each size tercile), al-lows to appreciate the benefits of size-neutralweighting across different size segments. Asa result, the main driver of the excess perfor-mance came from altering the global size expo-sure (overweighting mid and small stocks andunderweighting the large stocks), while somesmaller but significant part came also fromimposing Equal Weight allocation inside eachsize segment. In particular, the Equal Weightscheme worked well only in the Large size sub-portfolio, manifesting the benefit of correctingthe mega-cap bias.

Notes

1ETF Landscape Global Handbook, BlackRock, Q12011

2See for example ”Equal Weight Indexing: SevenYears Later” by Liyu Zeng, Shrikant Dash (S&P Re-search), July 2010; ”Equal Weight ETFs” by AnthonyDavidow (RydexShares), January 2011; and ”OptimalVersus Naive Diversification: How Inefficient is the 1/NPortfolio” by Victor DeMiguel, Lorenzo Garlappi andRaman Uppal, Review of Financial Studies, vol. 22,2009.

3Underlying data is courtesy of Stoxx. The Stoxxindices are the intellectual property (including registeredtrademarks) of STOXX Limited, Zurich, Switzerlandand/or its licensors (”Licensors”), which is used underlicense. None of the products based on those Indices aresponsored, endorsed, sold or promoted by STOXX andits Licensors and neither of the Licensors shall haveany liability with respect thereto.

4Cumulative excess return by quarter, this gener-ates discrepancies with compounded performance fig-ures such as those of Table 3


80, avenue de la Grande Armée

75017 Paris – France

[email protected]

+ 33 1 78 40 56 90

About Ossiam

Ossiam is a research-driven French asset management firm (authorized by the Autorité des Marchés Financiers) and specializes in delivering smart beta* solutions. Efficient indexing is at the core of Ossiam’s business model. The firm was founded in response to a post-subprime crisis demand from investors for simplicity, liquidity and transparency. Given the environment, there was a growing need among investors for enhanced beta exposure and risk hedging. Ossiam is focused on the development of innovative investment solutions for investors via a new generation of indices.

*'Smart beta' refers to systematically managed, non-market-cap-weighted strategies covering any asset class.

Ossiam, a subsidiary of Natixis Global Asset Management, is a French asset manager authorized by the Autorité des Marchés Financiers (Agreement No. GP-10000016). Although information contained herein is from sources believed to be reliable, Ossiam makes no representation or warranty regarding the accuracy of any information of which it is not the source. The information presented in this document is based on market data at a given moment and may change from time to time.

This material has been prepared solely for informational purposes only and it is not intended to be and should not be considered as an offer, or a solicitation of an offer, or an invitation or a personal recommendation to buy or sell participating shares in any Ossiam Fund, or any security or financial instrument, or to participate in any investment strategy, directly or indirectly.

It is intended for use only by those recipients to whom it is made directly available by Ossiam. Ossiam will not treat recipients of this material as its clients by virtue of their receiving this material.

This material reflects the views and opinions of the individual authors at this date and in no way the official position or advices of any kind of these authors or of Ossiam and thus does not engage the responsibility of Ossiam nor of any of its officers or employees. All performance information set forth herein is based on historical data and, in some cases, hypothetical data, and may reflect certain assumptions with respect to fees, expenses, taxes, capital charges, allocations and other factors that affect the computation of the returns.

Past performance is not necessarily a guide to future performance. Any opinions expressed herein are statements of our judgment on this date and are subject to change without notice. Ossiam assume no fiduciary responsibility or liability for any consequences, financial or otherwise, arising from, an investment in any security or financial instrument described herein or in any other security, or from the implementation of any investment strategy.

This information contained herein is not intended for distribution to, or use by, any person or entity in any country or jurisdiction where to do so would be contrary to law or regulation or which would subject Ossiam to any registration requirements in these jurisdictions.

Behind the performance of Equally Weighted Indices · EW portfolio and the performance of the...

Documents

Transcript of Behind the performance of Equally Weighted Indices · EW portfolio and the performance of the...