Research Insight

Demystifying Equal Weighting
Jennifer Bender, PhD

June 2012

msci.comResearch Insight
Demystifying an Equally Weighted Equity Portfolio
June 2012

Introduction
The idea of accessing risk premia through the use of index-based funds and ETFs has been gaining
momentum in recent years. MSCI Risk Premia Indices aim to reflect well-known equity premia to stock
characteristics such as value, size, or momentum. Among the risk premia indices, equally-weighted
indices are some of the oldest and most well-known. In this paper, we revisit the rationale behind equal
weighting and profile their recent performance.

Investing in Risk Premia
Portfolio returns have traditionally been attributed to a combination of passive market exposure andactive portfolio management. Any return in excess of the market return was considered added value
from active management. More recently, many return components that were considered added value(alpha) are increasingly being recognized as risk premia (beta). Systematic risk premia such as value, size
or momentum can account for a substantial part of long-term institutional portfolio performance. Overthe last few years, we have seen the development of many new indices that reflect systematic risk
premia, opening up the possibility to capture risk premia through indexation.
Risk premia strategies can be classified into two broad categories reflecting two primary ways forachieving superior risk-adjusted performance: (1) risk-based strategies aim to lower risk or improvediversification; and (2) return-based strategies aim to tilt towards a specific factor.
MSCI Risk Premia Indices for each category are shown in Exhibit 1. For additional detail on MSCI Risk
Premia Indices, we refer to Melas, Briand, and Urwin (2011).
Exhibit 1: MSCI Risk Premia Indices

Risk-Based Indices

Return-Based Indices

MSCI Equal Weighted Indices
MSCI GDP Weighted Indices•Equal allocation across parent index•Index country weights based on nominal
constituentsGDP
MSCI Risk Weighted Indices
MSCI Value Weighted Indices•Weights based on the inverse of historical •Weighted according to sales, earnings, cash
variance
flow, and book value
MSCI Minimum Volatility Indices
MSCI Factor Indices•Constructed using minimum variance•Constructed using long/short portfolio
optimization
optimization to capture Barra risk factors
One important point is that risk premia appear to exhibit time variation. As shown in Melas, Briand, andUrwin (2011), systematically tilting an equity portfolio towards any one fundamental factor does notguarantee long-term outperformance over the market portfolio. Rather, risk premia are better
combined with one another for diversification.

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Demystifying an Equally Weighted Equity Portfolio
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As seen in Exhibit 1, we categorize equal weighted indices as a risk-based index.1 Later on, we will seethat over the January 1999 to March 2012 time period, equal-weighted versions for MSCI flagshipindices such as the MSCI EAFE and Emerging Markets Indices have historically delivered significantly
enhanced returns over their cap weighted counterparts.

Why Equally Weight Stocks?
Academics and practitioners have long studied the potential benefits of equal weighting.2 The equal
weighting scheme is simple—an investor holds the same dollar value in each stock so that each stock
represents an equal part of the value of the portfolio. Many institutional money managers, for example,
will often equally weight the stocks they select. There are a range of reasons that have been proposed
for why equally weighting a broad universe of stocks may outperform a cap weighted portfolio. The fourmain explanations are:(1) Take advantage of inefficient markets: If investors are irrational and prone to over-optimismwith respect to high-flying stocks, and over-pessimism for beaten-down stocks, then market cap
weighting reflects those inefficiencies through its definition as shares times price. Equal
weighting on the other hand does not suffer from this issue.
(2) Avoid concentrating too much of the portfolio into a few large stocks: Market cap weighting
can result in a large part of the portfolio concentrated in a few names which may not bedesirable from the perspective of concentration risk. Equal weighting, on the other hand, avoids
this issue.
(3) Get more exposure to smaller cap stocks compared to cap weighting: By construction, stocks
with smaller market cap get lower weights in a market cap weighting scheme. This can be good
(as they may be riskier) or bad (as they have historically had stronger performance). Equal
weighting a portfolio assigns more capital to these smaller cap stocks. Conversely, equal
weighting also assigns less capital to larger stocks.
(4) Build in disciplined rebalancing that takes account of mean reversal in stock returns: A market
cap weighted portfolio evolves naturally and in theory never has to be rebalanced (if theportfolio constituents remain constant). Equal weighted portfolios are rebalanced at a chosenfrequency (e.g. daily, weekly, monthly) and tend to sell recent winners and buy recent losers.3 In
between rebalancing dates, stock weights will fluctuate with prices. Thus, an equally weighted
portfolio builds in disciplined rebalancing which takes advantage of mean reversal in stock1

As with all risk premia strategy indices, equal weighted portfolios are a special case of mean-variance optimal portfolios. The assumptions for equal weighted
indices are that the expected returns and volatilities for all stocks are the same and the correlations between all stocks are zero. Melas, Briand, and Urwin (2011)
categorize these indices as risk-based strategy indices because there are no expected return assumptions.
2

Empirical support for the performance of equal weighted portfolios relative to cap weighted indices include Lessard (1976), Roll (1981), Ohlson and Rosenberg(1982), Breen et al. (1989), Grinblatt and Titman (1989), Korajczyk and Sadka (2004), Hamza et al. (2007) and Pae and Sabbaghi (2010). Furthermore DeMiguel et al.
(2007) show the strong performance relative to optimized portfolios.
3

If the portfolio is re-weighted daily, and no names enter or leave the portfolio, then the weight for each stock remains the same. To maintain this constant weight,
shares would have to be sold or bought daily since prices are constantly changing, thus affecting the weight of the stock in the portfolio. Because broker-dealers set
the cost of trading, rebalancing daily in small amounts is generally not efficient so in practice, equal weighted portfolios are not rebalanced daily. They tend to berebalanced at a longer frequency, which forms an implicit contrarian strategy.

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Demystifying an Equally Weighted Equity Portfolio
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returns and locks in recent gains/losses.4 Between rebalancing dates, the stocks whose prices go
up by the most tend to expand in weight the most. These recent winners are then sold off at
the next rebalancing date. On the flip side, the stocks whose prices decrease the most tend toshrink in weights the most.5
From the perspective of the risk premia framework, the third rationale above (smaller cap exposure) isthe most well understood and widely accepted, whereas the other three rationale may be capturingtypes of risk premia that are less well documented.6

Historical Performance and Characteristics
Exhibit 2 demonstrates the significant outperformance of the equal weighted versions of the MSCI EAFE
and Emerging Markets Indices. The indices garnered 2.7% and 1.6%, respectively, of additional annual
returns relative to their cap weighted parent indices from December 31, 1998 through May 24, 2012.
Exhibit 2: Select Equal Weighted Indices Have Outperformed Cap Weighted Indices Since 1998
(Cumulative Relative Returns of Equal Weighted Indices Relative to Their Market Cap Weighted Parent
Indices, Gross Daily Returns, December 31, 1998 to May 24, 2012)

Cumulative Relative Returns (Dec 31, 1998 = 100)

170

150

130

110

90

70

50

EAFE Eq Wtd (Rel. to EAFE)

EM Eq Wtd (Rel. to EM)

Exhibit 2 also highlights sub-periods when the MSCI Equal Weighted Indices underperformed andoutperformed their cap weighted parent indices. The periods of underperformance include September
1999 to March 2000, July 2002 to October 2002, March 2008 to October 2008, and September 2011 to
4

The impact of rebalancing has been documented in a number of papers. Perold and Sharpe (1995) examined the benefitsof rebalancing from a strategic asset
allocation perspective. By comparing different strategies, they conclude that a constant-mix (rebalanced) approach tends to outperform a buy-and-hold(unrebalanced) strategy when markets are characterized more by reversals than by trends. Interested readers can also refer to papers by Bernstein (1996a), (1996b)
and Bernstein and Wilkinson (1997).
5

In theory there is an optimal rebalancing frequency that takes into account the natural momentum and reversal cycle in most stocks. Moreover, the rebalancing
frequency should take into account the turnover at each rebalancing date and the cost of trading.
6

For instance, the first rationale may be capturing a risk premia that arises from behavioral biases and is essentially a premium to stocks that have been overboughtor oversold whereas the fourth rationale might be capturing a premium to contrarian stocks over certain frequencies.

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Demystifying an Equally Weighted Equity Portfolio
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December 2011. For the most part these were periods just before and at the onset of major market
corrections. Periods of strong performance immediately followed those above: March 2000 to July
2002, February 2003 to July 2007, and November 2008 to September 2010.
Exhibit 3 summarizes return and additional metrics for the MSCI Equal Weighted Indices and their cap
weighted counterparts.


MSCI Equal Weighted Indices universally outperformed their cap weighted parent indiceshistorically over the last 12+ years with the exception of Latin American Emerging Markets



The volatility (standard deviation) of monthly returns was somewhat higher for most regions but
return-to-risk ratios were significantly higher7



MSCI Equal Weighted Indices tended to have betas and correlations that were close to 1

Exhibit 3:

Performance Summary(Gross Index Monthly Returns, January 29, 1999 to May 31, 2012)
Annualized Return

Annualized Risk

Return-to-Risk
Ratio

Beta of
Equal
Weighted
to Cap
Weighted

Correlation
Btwn Equal
Weightedand Cap
Weighted

Cap Wtd

Equal
Wtd

Cap Wtd

Equal
Wtd

Cap Wtd

Equal
Wtd

ACWI

2.9%

8.6%

17.1%

19.6%

0.17

0.44

1.09

0.95

EAFE

2.4%

5.7%

18.2%

18.7%

0.13

0.30

0.99

0.96

EM

11.4%

13.9%

24.7%

24.8%

0.46

0.56

0.98

0.97

UK

2.0%

3.7%

21.7%

23.4%

0.09

0.16

1.05

0.97

Pacific

2.1%

5.3%

22.0%

20.1%

0.09

0.26

1.07

0.93

Japan

9.8%

12.1%

22.0%

22.3%

0.45

0.54

0.99

0.97

USA

2.5%

6.5%

16.4%

18.7%

0.15

0.35

1.09

0.95

Canada

2.2%

5.6%

16.2%

18.9%

0.13

0.30

1.11

0.95

EM Asia

10.4%

11.1%

22.5%

21.0%

0.46

0.53

0.86

0.92

EM EMEA

9.7%

11.1%

25.8%

26.7%

0.38

0.41

1.00

0.96

EM Latin
America

15.8%

5.7%

29.0%

33.8%

0.55

0.17

0.93

0.80

Europe ex UK

One of the reasons raised by proponents of equal weighting is to circumvent concentration risk, i.e.,holding too much of the portfolio in a single stock or set of stocks. In Exhibit 4, we compare the weightsof the ten largest companies in the market cap weighted versus the equal weighted versions of the MSCIEAFE and Emerging Markets Indices. Large companies such as Nestle and HSBC in EAFE, and Samsung
Electronics and Taiwan Semiconductor in Emerging Markets were allocated significantly smaller weights
in the equal weighted indices as of June 1, 2012.8
7

When daily returns are used instead of monthly returns for calculating standard deviations, over the same period, volatilities are instead lower for equal weighted
indices than cap weighted indices with the exception of the US, UK, and Latin America. This suggests that serial correlation in daily returns can have an important
impact in evaluating the risk of the two types of indices.
8

Whether one wants to underweight these names depends on the investor’s own beliefs. Behavioralists might argue that large weights in these names are risky ifinvestors are irrational and those higher valuations are not permanent.

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Demystifying an Equally Weighted Equity Portfolio
June 2012

Exhibit 4: Equal Weighting Reduces the Concentration in Big Names(Index Constituents as of June 1, 2012)MSCI EAFE Index

MSCI Emerging Markets Index
Weight in Cap
Wtd

Weight in
Eql Wtd

Weight in
Cap Wtd

Weight in
Eql Wtd

NESTLE

2.07%

0.11%

SAMSUNG ELECTRONICS CO

3.48%

0.12%

HSBC HOLDINGS (GB)

1.56%

0.11%

TAIWAN SEMICONDUCTOR MFG

2.15%

0.12%

VODAFONE GROUP

1.47%

0.11%

CHINA MOBILE

1.87%

0.12%

NOVARTIS

1.32%

0.11%

CHINA CONSTRUCTION BK H

1.53%

0.12%

BP

1.28%

0.11%

GAZPROM (RUB)

1.44%

0.12%

ROYAL DUTCH SHELL A

1.26%

0.11%

AMERICA MOVIL L

1.42%

0.12%

GLAXOSMITHKLINE

1.24%

0.11%

PETROBRAS PN

1.22%

0.12%

ROCHE HOLDING GENUSS

1.21%

0.11%

ICBC H

1.21%

0.12%

TOYOTA MOTOR CORP

1.18%

0.11%

VALE PNA

1.12%

0.12%

BHP BILLITON LTD

1.11%

0.11%

ITAU UNIBANCO PN

1.01%

0.12%

Sum

10.99%

0.62%

Sum

16.45%

1.24%

Top 10 Companies

Top 10 Companies

Exhibit 4 also shows the aggregate weights of the ten largest index constituents, highlighting the topheavy characteristic of a capitalization weighted scheme.
Another well-known characteristic of equally weighted portfolios is that they tend to overweight smaller
cap stocks. By construction, equal weighted indices have a lower weighted market cap (a tilt towards
smaller cap stocks) since they give more weight to stocks at the lowest end of the market cap range andless weight to stocks at the highest end of the market cap range. This is illustrated in Exhibit 5 which
compares the weights across the capitalization spectrum resulting from the two weighting schemes.

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Exhibit 5: Equal Weighting Tilts Towards Smaller Cap Stocks(Weights Resulting from Cap Weighting vs. Equal Weighting for MSCI EAFE, June 1, 2012)
2.5%

Weight in Portfolio

2.0%

1.5%

1.0%

0.5%

0.0%

Largest market cap
stocksSmallest market cap
stocks
EAFE Weight

EAFE EW Weight

One reason why the MSCI Equal Weighted Indices performed better over the observed period is becauseof this smaller cap bias. Smaller cap stocks outperformed larger cap stocks over the last decade. For
instance, the MSCI EAFE Small Cap and Mid Cap Indices earned 6.9% and 4.2% annualized returns,
respectively over the period January 1999 to May 2012, while the MSCI EAFE Large Cap Index only
returned 1.9%.9 In the next section, we quantify how much return arises from this effect.

What Drives Performance?
The impact of the tilt towards smaller cap names is strong. Exhibit 6 shows the relative performance ofthe MSCI EAFE Equal Weighted Index alongside the relative returns of smaller over large caps. There is avery high correlation of 0.73 between the relative returns.

9

The MSCI ACWI Small Cap and Mid Cap Indices earned 7.8% and 6.1% annualized returns, respectively during the period January 1999 to May 2012 while the MSCIACWI Large Cap Index returned 2.3%.

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Exhibit 6: The Performance of Equal Weighted Indices Is Tied to the Performance of Smaller Cap Stocks(Relative Monthly Gross Returns, January 1999 to May 2012)

Cumulative Relative Returns (Dec 98 = 100)

170
160
150
140
130
120
110
100
90

Oct-11

May-12Mar-11

Jan-10Aug-10

Jun-09

Nov-08Apr-08

Sep-07

Feb-07

Jul-06

Dec-05

May-05

Oct-04Mar-04Aug-03Jan-03Jun-02

Apr-01

Nov-01

Sep-00Jul-99Feb-00Dec-9880

Relative performance of smaller caps over large caps*
Relative performance of EAFE Equal-Weighted Index* Relative returns are (1) the returns of the EAFE Equal Weighted Index minus the returns of the EAFE Index; and (2) the returns of the EAFE
Large Cap Index minus the returns of the EAFE Mid Cap Index. The MSCI EAFE and EAFE Equal Weighted Indices contain only large and mid caps
(defined according to the MSCI Global Investable Market Index (GIMI) methodology) thus explaining why we use the EAFE Mid Cap Index(instead of the EAFE Small Cap Index) as a comparison to large caps.

Since the correlation between the two series shown in Exhibit 6 is not perfect (equal to 1), clearly there
are other drivers of return at work in equal weighted indices. Using a factor model to attribute sourcesof return is a well-established way to understand the return drivers of a portfolio or index. Moreover, if
there is an explicit factor capturing the effect of market cap size, we can quantify precisely how much
return is derived from the smaller cap tilt. Exhibit 7 shows the annualized 10-year return of the MSCIEAFE Equal Weighted Index broken down into various component factors. (Note that the components
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Exhibit 7: Sources of Return (Annualized Return From Each Source Using Barra Global Equity Model, April
2002 to April 2012)MSCI EAFE Equal-Weighted
Index
8.65%
MSCI EAFE Index

2.19%

Active Return

Currencies
StylesCountries
Industries

0.48%
0.36%
0.14%
-0.04%

Size/Size-Nonlinearity
Momentum
Financial Leverage
GrowthLiquidity
Value
Volatility

0.74%
0.39%
0.04%
0.02%
0.01%
-0.31%-0.53%

6.46%

Specific (Non-Systematic)

1.25%

Within each type, return driven primarily from:
Underweight to EUR/GBP and overweight to JPY
Mid Cap Tilt, Small Cap Tilt
Underweight to Europe
Underweight to Financials

The MSCI EAFE Equal Weighted Index outperformed the MSCI EAFE Index by 2.19% annually over thisperiod. Of that 219 basis points of annual outperformance (the active return shown in Exhibit 7), morethan half of it (125 bps) could not be explained by the sources of systematic return in the model (labeled“Specific” in Exhibit 7). Systematic sources of return encompass different types: “Currencies”, “Styles”(representing well-known stock characteristics known to be priced10), “Countries”, and “Industries”.
While tilts to different currencies, countries, industries and styles all contributed positively to return,they made up less than half of the return. Meanwhile, bundled under the category “Styles”, the cap tilts
accounted for 74 bps of outperformance. This was a substantial contribution; however it was offset byother style tilts such as an underweight to value stocks. 11
Ultimately it is the 125 basis points of non-attributable return that remains most intriguing. It is not justthat equally weighting stocks picks the right currencies, countries, industries, etc., or that it is capturing
a small cap premium in a different way. There appears to be some attribute unique to equal weightingthat generates outperformance, perhaps related to one of the other three reasons cited for investing inequally weighted indices or portfolios. This subject deserves further study and is a prime candidate for
future research.

10

The Barra Global Equity Model identifies 8 main style factors: Momentum, Volatility, Value, Growth, Size, Size-Nonlinearity, Leverage, and Liquidity.

11

Over time, the MSCI EAFE Equal Weighted Index has sometimes shown a greater tilt towards value stocks than the cap weighted parent index, MSCI EAFE: in
2002-2003 and briefly in November 2008 to April 2009. The rest of the time during the April 2002-April 2012 period, it was less tilted towards value stocks.

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Research Insight
Demystifying an Equally Weighted Equity Portfolio
June 2012Conclusion
Equal weighting is one of the earliest alternative weighting schemes to market capitalization weighting.
Despite (or because of) the simplicity of the approach, over the January 1999 to March 2012 period,
equal weighted versions for MSCI flagship indices such as the MSCI EAFE and Emerging Markets Indiceshistorically delivered significantly enhanced returns over their cap weighted counterparts. Moreover,their volatilities were only slightly higher, producing extremely attractive return-to-risk ratios over thesame period. Proponents of equal weighting suggest there are various reasons for these benefits thatinvestors may want to consider. Equal weighting may make sense for investors who wish to takeadvantage of market price inefficiencies, reduce concentration in their portfolio, get more exposure tosmaller cap stocks, and/or build in a disciplined rebalancing process.

References
Bernstein, W. J. (1996a) “The Rebalancing Bonus: Theory and Practice.” The Efficient Frontier.
http://www.EfficientFrontier.com.
Bernstein, W. J. (1996b). “When Doesn’t It Pay to Rebalance?” The Efficient Frontier.
http://www.EfficientFrontier.com.
Bernstein, W.J., and D. Wilkinson (1997). “Diversification, Rebalancing, and The Geometric Mean
Frontier.” The Efficient Frontier. http://www.EfficientFrontier.com.
Breen, W., L. R. Glosten, and R. Jagannathan (1989). “Economic significance of predictable variations instock index returns.” The Journal of Finance 44, 1177-1189.
DeMiguel, V., L. Garlappi, and R. Uppal (2007). “Optimal versus naïve diversification: How inefficient is
the 1/n portfolio strategy.” The Review of Financial Studies 22(5): 1915-1953.
Grinblatt, M. and S. Titman (1989). “Mutual fund performance: An analysis of quarterly portfolio
holdings.” The Journal of Business 62, 393-416.
Hamza, Olfa, Mohamed Kortas, Jean-Francois L’Her, and Mathieu Roberge (2007). “International Equity
Indices: Exploring Alternatives to Market Cap-Weighting.” Journal of Investing 16(2): 103-118.
Korajczyk, R. A. and R. Sadka (2004). “Are momentum profits robust to trading costs?” The Journal of
Finance 59, 1039-1082.
Lessard, D. R. (1976). “World, country and industry relationships in equity returns.” Financial Analysts
Journal 32(1): 32-41.
Melas, D., R. Briand, and R. Urwin (2011). “Harvesting Risk Premia with Strategy Indices: From Today’s
Alpha to Tomorrow’s Beta.” MSCI Research Insight, September 2011.
Ohlson, J. and B. Rosenberg (1982). “Systematic risk of the CRSP equal-weighted common stock index: A
history estimated by stochastic-parameter regression.” The Journal of Business 55, 121-145.
Pae, Yuntaek and Navid Sabbaghi (2010). “Why do equally weighted portfolios outperform value
weighted portfolios?” Working paper, Lewis University College of Business and Illinois Institute ofTechnology.
Perold, A.F., and W. F. Sharpe (1995). “Dynamic Strategies for Asset Allocation.” Financial Analyst
Journal, Vol. 51, No. 1, pp. 149–160.

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Roll, R. (1981). “A possible explanation of the small firm effect.” The Journal of Finance 36, 879-888.

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ISS Corporate Services, Inc., which provides tools and services to issuers. MSCI ESG Research materials, including materials utilized in any MSCI ESG Indices or other products, have notbeen submitted to, nor received approval from, the United States Securities and Exchange Commission or any other regulatory body.
 Any use of or access to products, services or information of MSCI requires a license from MSCI. MSCI, Barra, RiskMetrics, ISS, CFRA, FEA, and other MSCI brands and product names are
the trademarks, service marks, or registered trademarks of MSCI or its subsidiaries in the United States and other jurisdictions. The Global Industry Classification Standard (GICS) was
developed by and is the exclusive property of MSCI and Standard & Poor’s. “Global Industry Classification Standard (GICS)” is a service mark of MSCI and Standard & Poor’s.

About MSCIMSCI Inc. is a leading provider of investment decision support tools to investors globally, including asset managers, banks, hedge funds and pension funds. MSCI
products and services include indices, portfolio risk and performance analytics, and governance tools.
The company’s flagship product offerings are: the MSCI indices with approximately USD 7 trillion estimated to be benchmarked to them on a worldwide basis1;
Barra multi-asset class factor models, portfolio risk and performance analytics; RiskMetrics multi-asset class market and credit risk analytics; MSCI ESG(environmental, social and governance) Research screening, analysis and ratings; ISS governance research and outsourced proxy voting and reporting services; FEA
valuation models and risk management software for the energy and commodities markets; and CFRA forensic accounting risk research, legal/regulatory risk
assessment, and due‐diligence. MSCI is headquartered in New York, with research and commercial offices around the world.
1

As of June 30, 2011, based on eVestment, Lipper and Bloomberg data.

MSCI Research© 2012 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document

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