2015 Equal Weighting and Other Forms of Size Tilting

Introduction
The ‘size factor’ is a source of additional return which investors
have long sort to capture in their investment portfolios, and is
based on the belief that smaller stocks (as measured by market
capitalization) tend to outperform larger stocks over the long
term. It is worth noting that this opportunity goes beyond just
investing in smaller companies and can be captured within a
large-cap universe such as the S&P500 or the FTSE100 by, for
example, equally weighting constituents rather than using
market-capitalization weights.
Using an equal-weight strategy is probably the most
straightforward way to capture the size effect and is perhaps
the most natural starting point when looking at the risks and
return of this effect, although there are other options, including
diversity weighting. Tilting methodologies, such as State Street
Global Advisors’ (SSGA’s), can also be used to access
the premium.
This article focuses on three main questions:
1. Is there a size premia and why might it exist?
2. How might this be implemented in a portfolio and what
are the challenges which investors should consider? And,
3. Does such a portfolio have some additional exposures or
diversification benefits which investors need to consider?
The Size Factor: A History and Summary
Research by Banz (1981) and Reinganum (1981) first highlighted
that small-capitalization stocks tend to outperform large-
capitalization stocks on a risk-adjusted basis. Fama and French
(1992, 1993) have shown that size along with value and market
beta explain a significant part of the cross-sectional variation
in stock returns. The phenomenon was confirmed in both
developed and emerging markets by Rizova (2006). And this
does not appear to be a short-term anomaly; according to Fama
and French, the smallest 30% of companies have outperformed
the largest 30% of companies by 2.4% per annum over 86 years
in the US (see figure 1). However, this does come with
significantly higher volatility.
IQINSIGHTSEqual Weighting and Other Forms of Size Tilting
by Richard Hannam, Head of GEBS EMEA and
Frederic Jamet, Head of Investments SSGA France
Figure 1: The Long-Term Size Premium
30% Small Cap (%) 30% Large Cap (%)
Return 11.9 9.5
Volatility 34.4 19.6
Sharpe Ratio 35.0 48.0
1000
30% small cap (11.9% per year) 30% large cap (9.5% per year)
0
1
10
10000
100000
1926 1948 1970 1992 2012
100
Source: Fama and French, 1926–2013.
Past performance is no guarantee of future results.

State Street Global Advisors 2
IQ Insights | Equal Weighting and Other Forms of Size Tilting
Another way to view evidence of the size premium is to start
from an equal-weighted position. With each stock having the
same initial weight, this has the effect of underweighting
large-cap stocks and overweighting small-cap stocks, relative
to the market capitalization. Although over a much shorter
time period, using the MSCI equal-weighted indices across
other regions appears to show a size premium broadly similar
in magnitude to that shown in the US (see figure 2).
The empirical evidence of a size premium appears to be strong
over long time periods and across different geographies; which
begs the question: Why might this be the case? The possible
explanations can broadly be divided into two camps: risk-based
and systematic investor errors or mistakes.
The risk-based theories assume that small companies are
earning a return premium as a result of one or more systematic
risk factors which cannot be diversified away. Suggestions put
forward for these factors include lower liquidity (Amihud
2002), information uncertainty (Zhang 2006), financial
distress (Chan and Chen 1991) default risk (Vassalou and Xing
2004) and generally greater sensitivity to macro-economic
factors (MSCI Paper on Foundations of Factor Investing).
With regard to investors making systematic errors or mistakes,
many of the reasons put forward are based on concepts from
behavioural finance including chasing winners, over-reaction,
overconfidence and loss aversion. There may also be a link back
to the use of indices for benchmarking and the short-term
nature of performance monitoring which is likely to lead
investors to focus on larger-cap names and to get less time for
their active decisions to pay off.
It is also fair to say that investors have a demand for liquidity
in their portfolios and as such are likely to favour large-cap
securities. Smaller-capitalization companies generally have
lower liquidity and as such are more expensive to trade,
suggesting some form of ‘liquidity risk’ premium should
be earned by investors for holding small-cap stocks.
Purchasing the MSCI World Equal-Weighted costs 20bps
(as shown in Figure 4) versus 16bps for the MSCI World Market
Cap (as shown in Figure 3). Spreads, commissions and market
impacts are higher for smaller-capitalization stocks.
Capturing the Size Effect
The size factor can be captured by investors in a number of
different ways.
The most common and straightforward approach involves
splitting the universe into several ‘buckets’ by market
capitalization such as large capitalization, medium
capitalization and small capitalization and then allocating
more to the medium- and small-capitalization buckets
relative to their market capitalization weights.
For example, within its indices MSCI targets a breakdown of
70% for large capitalization, 15% for medium capitalization, 15%
for small capitalization; while FTSE targets 70% for large cap,
20% for medium capitalization, 10% for small capitalization (as
detailed on Figure 6). The ‘standard’ market-cap index is the
combination of the large- and mid-cap universes, while including
large-, mid- and small-cap is the full opportunity set for that
index series (as shown in figure 4).
Figure 4: MSCI Market-Capitalization Breakdown
Minimum Cap
World Large Cap 6683
World Mid Cap 2428
World Small Cap 236
Source: MSCI, 2013, in million USD.
Figure 2: The International Size Premium
 EW Excess
(%)
3.5
2.1
3.2
0
1
2
3
4
5
USA EUROPE PACIFIC WORLD EM
3.7
1.8
Source: MSCI, 1998–2013.
Figure 3: Large Cap vs Small Cap Cost Analysis
 Market Cap (16bps)  Equal Weight (20 bps)
0
5
10
15
20
25
Avg 1/2
Spread
Impact
Cost
Comm Taxes Ticket Chg Total Cost
Source: SSGA, 2013.

Another approach to capturing the size factor is size tilting.
The SSGA Size-Tilted approach uses a 20 sub-portfolio
framework and a proprietary tilting methodology to allocate
more assets to smaller companies and less assets to larger
companies, when compared to a standard market-cap index.
The portfolio is rebalanced on an annual basis. The annualised
return for each sub-portfolio for the period 1989–2012 for the
MSCI World universe is shown in figure 5. With the smallest
companies in the sub-portfolios to the left (1–5) and the largest
companies in the sub-portfolios to the right (16–20) these
figures support the evidence of a size premium. It is also
interesting that these sub-portfolios generate higher returns
with lower volatility.
The third approach is a simple construct which involves giving
an equal weight to each stock in the universe. For example,
for the S&P500 Equal-Weight Index, each stock has a weight
of 1/500 or 0.2%. As individual stock prices move after each
rebalance stock weights drift away from their initial equal
weight, and the index is no longer equally weighted. As such
it is necessary to rebalance on a regular basis. Quarterly
rebalancing is accepted as a reasonable frequency by both
MSCI and S&P.
It seems a priori that the equally weighted approach is adding
value by its buy low/sell high effect (or selling outperformers,
buying underperformers) at each rebalance. This rebalancing
effect has been analysed by Bernstein Wilkinson (1997)
through the following formula:
Rebalancing effect = ½[∑wi
vii
-∑wi
wj
vij
] + [∑wi
(1+ri
)-(∑wi
(1+ri
)N
)1/N
]
(where wi are portfolio weights, vii
are covariance matrix of
stock returns and ri
are the average stock returns.)
The first term is the contrarian effect. It represents the
short-term reversal and is always positive. The second term is
the dispersion effect. It represents the long-term trend and is
always negative. The rebalancing effect of the equally weighted
strategy is therefore positive if the contrarian effect (short-term
reversal) is larger than the dispersion effect (long-term trend).
It is worth noting that this effect is not systematically positive
and depends on the universe, on the period and on the
rebalancing frequency. However this effect has been positive for
the S&P500 Equal-Weight Index (as shown in figure 6).
It is interesting to compare the S&P500 Equal-Weight index to
the standard S&P500 market-cap index and the S&P100 index
(which is made up of the 100 largest market-capitalization
stocks of the S&P 500). The S&P100 can be considered to be a
large-capitalization index. The performance, volatility, and
Sharpe ratio are provided in Figure 7. The S&P500 Equal
Weight outperforms the S&P 500, and the S&P 500
outperforms the S&P 100, although in both cases with higher
volatility. However, both have a higher Sharpe ratio than the
large-cap S&P100 index.
Figure 5: SSGA Size Tilted vs MSCI World
SSGA Size
Tilted (%)
MSCI World
(%)
Difference
(%)
Return 7.8 6.5 1.2
Volatility 15.8 15.5 2.9
Sharpe Ratio 49.3 42.0 7.3
Figure 6: S&P500 Equal-Weight Rebalancing Effect
Monthly
(%)
Quarterly
(%)
Yearly
(%)
Buy Hold
(%)
Return 5.8 5.9 5.9 4.7
Volatility 22.1 21.9 21.3 21.1
Contrarian Effect 5.7 5.7 5.4 —
Dispersion Effect -4.5 -4.4 -4.2 —
Rebalancing Effect 1.2 1.3 1.2 —
Source: S&P, Ossiam, 1999–2013.
Past performance is not a guarantee of future results.
The index returns are unmanaged and do not reflect the deduction of any fees or
expenses. The index returns reflect all items of income, gain and loss and the
reinvestment of dividends and other income.
0
2
4
6
8
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Sub — Portfolios (High cap to the right)
Size-Sorted Returns for the SSGA Size-Tilted Portfolio (%)
Source: SSGA. Data is from April 1989 through December 2012.
Sub-Portfolios (High cap to the Right)
Size-Sorted Voaltility for the SSGA Size-Tilted Portfolio (%)
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Source: SSGA, 1989–2012, Universe is MSCI World, in USD.
Past performance is not a guarantee of future results.
The index returns are unmanaged and do not reflect the deduction of any fees or
expenses. The index returns reflect all items of income, gain and loss and the
reinvestment of dividends and other income.

Similar analysis can also be carried out using the MSCI World
Equal-Weighted index against the standard MSCI World
market-cap index and the two size segments (Large and Mid cap)
which make this up. Not only does this show the equally weighted
index outperforming over time but it goes beyond the binary
overweight of the mid-cap segment (as shown in Figure 8).
In terms of sectors, the sector weight in an equal-weight index
is proportional to the number of stocks in that sector and as
such, is overweight sectors like Industrials and Materials,
which have more small and mid-cap names and underweight in
sectors like Healthcare and Energy which tend to have a higher
concentration of large companies (as shown in Figure 9).
In terms of countries, the main difference is an overweight to
Japan, due to the fragmentation of the Japanese stock market
and the underweight of United States, due to its concentration
in mega-cap stocks (as shown on figure 10).
While an equally weighted approach leads to a less concentrated
portfolio than a cap-weighted one, this will be at a cost of lower
liquidity and higher transactions costs, which is important
considering the regular requirement to rebalance back to the
equal-weight position. As a result, Fernholz et al proposed
Diversity Weighting as an option for index construction. This
can perhaps be seen as a hybrid between equal weight and cap
weight, with a maximum stock weight being set and any weight
above this being redistributed equally amongst the remaining
constituents. The higher the maximum weight, the closer the
diversity weighted index will be to the market-cap index while
the lower the ceiling, the closer it will be to equal weight.
Figure 7: S&P Equal-Weight Performance
S&P 500 Equal
Weight (%)
S&P 100 Equal
Weight (%)
S&P 500
(%)
Return 12.7 10.6 11.1
Volatility 15.7 15.4 14.7
Sharpe Ratio 81.0 69.0 75.0
Source: S&P, 1990–2013 in USD.
Figure 9: MSCI World Equal-Weighted Sector
Sector
Equal
Weighted World Difference
Consumer Discretionary 14.9 12.0 3.0
Consumer Staples 7.7 10.6 -2.9
Energy 7.3 9.7 -2.4
Financials 21.1 20.8 0.3
Health Care 7.6 11.3 -3.7
Industrials 15.9 11.0 4.8
Information Technology 9.3 11.7 -2.4
Materials 7.9 5.6 2.3
Telecommunication Services 2.9 3.7 -0.8
Utilities 5.2 3.4 1.8
Source: MSCI, 2013.
Figure 10: Top 10 MSCI World Equal-Weighted Countries
Country Equal Weight World Difference
United States 38.0 54.8 -16.8
Japan 20.7 9.3 11.4
United Kingdom 6.5 8.9 -2.4
Canada 5.8 4.2 1.6
France 4.3 3.9 0.5
Australia 4.1 3.3 0.8
Germany 3.0 3.5 -0.5
Hong Kong 2.5 1.2 1.2
Switzerland 2.3 3.8 -1.5
Sweden 1.9 1.3 0.6
Source: MSCI, 2013.
Countries are as of the date indicated, are subject to change, and should not be relied
upon as current thereafter.
Figure 8: MSCI World Equal-Weighted Performance
Equal
Weighted (%)
Large Cap
(%)
Mid Cap
(%)
World
(%)
Return 7.0 2.8 6.6 3.4
Volatility 17.5 16.1 17.9 16.2
Sharpe Ratio 40.0 17.4 36.7 20.8
Equal Weight (7.0% per year)
Mid Cap (6.6% per year) World (3.4% per year)
Large Cap (2.8% per year)
0.5
1.0
1.5
2.0
2.5
3.0
Dec
1998
2002 2006 2010 Jun
2013
Source: MSCI, 1998–2013 in USD.

The Equal-Weighted Approach Beyond the Size Factor
While adopting an equally weighted approach provides the
investor with desired exposure to the size factor, a by-product
of this will be exposures to other factors such as value and also
increased diversification.
One way to highlight the increased diversification of the equally
weighted approach is to use the inverse of the Herfindahl-
Hirschman index,* which gives an effective number of stocks.
Using this measure the equal-weighted portfolio has the
maximum possible effective number of stocks whereas the
market-cap portfolio is more concentrated than suggested by
the actual number of stocks (as shown in Figure 11).
Regarding exposure to value, the equal-weighted portfolio is
likely to have some positive value exposure in that the equal
weights drift away due to market movement and have to be
re-adjusted back to the equal-weight position on a regular basis.
When the portfolio is re-adjusted back to equal weights, the
trades consist of selling stocks that have outperformed (and
thus are more expensive than they were) and buying stocks that
have underperformed (and are thus cheaper than they were).
This regular re-adjustment creates a slight positive value bias.
The positive exposure to value, although small, can be seen
through the correlation with the value premium, where the
value premium is measured by MSCI Value minus MSCI
Growth (as shown in figure 12). However as one would expect,
this is much smaller than the correlation between the equal
weight index and the size premium, measured by MSCI Midcap
minus MSCI Large Cap.
Conclusion
Exposure to the size factor seems to provide an opportunity for
investors to outperform the market cap index. It has a long
history — close to 90 years; seems to provide a reasonable
premium — up to 2–3% of outperformance; and can be found
globally, regionally and in individual markets.
It is not really a surprise that the small-cap premium exists given
higher trading costs, higher systematic risk, lower liquidity,
information uncertainty, default risk and behavioural biases.
This can be seen in the outperformance of cap-weighted indices
such as MSCI World and S&P 500 by their equal-weight
equivalents over the medium to long term.
Interestingly, it appears that the equal-weighted strategy goes
beyond merely capturing small-cap exposure — it offers some
diversification features by the reduction of specific risk, and it is
slightly biased toward value through the systematic
readjustment process.
*
The Herfindahl-Hirschman index is a commonly accepted measure of diversification, calculated
by squaring the market share of each firm competing in a market and summing the resulting
numbers. The resulting HHI number can range from almost zero to 10,000, with a high
score indicating a market as being close to a monopoly and a low score indicating many
competing firms.
Figure 11: Effective Number of Stocks
World Equal Weight
Official Number of Stocks 1610 1610
Effective Number of Stocks 381 1610
Source: MSCI, 2013.
Figure 12: Diversification and Value with the MSCI World
Equal Weighted
Correlations World (%) Value-Growth (%) Mid-Large (%)
Equal Weighted 96 9 34
Source: MSCI, 1998–2013.
The correlation coefficient measures the strength and direction of a linear
relationship between two variables. It measures the degree to which the deviations
of one variable from its mean are related to those of a different variable from its
respective mean.

© 2015 State Street Corporation. All Rights Reserved.
ID2846-EUMKT-3739 0615 Exp. Date: 30/06/2016
ssga.com
For institutional use only. Not for use with the public.
State Street Global Advisors EMEA Entities
Belgium: State Street Global Advisors Belgium, Chausse de La Hulpe 120, 1000
Brussels, Belgium. T: +32 2 663 2036, F: +32 2 672 2077. SSGA Belgium is a branch
office of State Street Global Advisors Limited. State Street Global Advisors Limited
is authorised and regulated by the Financial Conduct Authority in the United Kingdom.
Dubai: State Street Bank and Trust Company (Representative Office), Boulevard
Plaza 1, 17th Floor, Office 1703 Near Dubai Mall & Burj Khalifa, P.O Box 26838, Dubai,
United Arab Emirates. T: +971 (0)4 4372800. F: +971 (0)4 4372818. France: State
Street Global Advisors France. Authorised and regulated by the Autorité des Marchés
Financiers. Registered with the Register of Commerce and Companies of Nanterre
under the number: 412 052 680. Registered Office: Immeuble Défense Plaza, 23-25
rue Delarivière-Lefoullon, 92064 Paris La Défense Cedex, France. T: +33 1 44 45 40 00.
F: +33 1 44 45 41 92. Germany: State Street Global Advisors GmbH, Brienner
Strasse 59, D-80333 Munich. T: +49 (0)89 55878 100. F: +49 (0)89 55878 440.
Ireland: State Street Global Advisors Ireland Limited is regulated by the Central
Bank of Ireland. Incorporated and registered in Ireland at Two Park Place, Upper
Hatch Street, Dublin 2. Registered Number: 145221. Member of the Irish Association
of Investment Managers. T: +353 (0)1 776 3000. F: +353 (0)1 776 3300. Italy: State
Street Global Advisors Limited, Milan Branch (Sede Secondaria di Milano) is a branch
of State Street Global Advisors Limited, a company registered in the UK, authorised
and regulated by the Financial Conduct Authority (FCA ), with a capital of GBP
71’650’000.00, and whose registered office is at 20 Churchill Place, London E14 5HJ.
State Street Global Advisors Limited, Milan Branch (Sede Secondaria di Milano), is
registered in Italy with company number 06353340968 - R.E.A. 1887090 and VAT
number 06353340968 and whose office is at Via dei Bossi, 4 - 20121 Milano, Italy.
T: +39 02 32066 100. F: +39 02 32066 155. Netherlands: State Street Global
Advisors Netherlands, Adam Smith Building, Thomas Malthusstraat 1-3, 1066 JR
Amsterdam, Netherlands. T: +31 (0)20 7181701. State Street Global Advisors
Netherlands is a branch office of State Street Global Advisors Limited. State Street
Global Advisors Limited is authorised and regulated by the Financial Conduct
Authority in the United Kingdom. Switzerland: State Street Global Advisors AG,
Beethovenstrasse. 19, Postfach, CH-8027 Zurich. T: +41 (0)44 245 70 00. F: +41 (0)44
245 70 16. United Kingdom: State Street Global Advisors Limited. Authorised and
regulated by the Financial Conduct Authority. Registered in England. Registered
Number: 2509928. VAT Number: 5776591 81. Registered Office: 20 Churchill Place,
Canary Wharf, London, E14 5HJ. T: +020 3395 6000. F: +020 3395 6350.
Companies with large market capitalizations go in and out of favor based on market
and economic conditions. Larger companies tend to be less volatile than companies
with smaller market capitalizations. In exchange for this potentially lower risk,
the value of the security may not rise as much as companies with smaller
market capitalizations.
Investments in small/mid-sized companies may involve greater risks than in those of
larger, better known companies.
Investing in foreign domiciled securities may involve risk of capital loss from
unfavorable fluctuation in currency values, withholding taxes, from differences in
generally accepted accounting principles or from economic or political instability in
other nations.
Investments in emerging or developing markets may be more volatile and less liquid
than investing in developed markets and may involve exposure to economic
structures that are generally less diverse and mature and to political systems which
have less stability than those of more developed countries.
This communication is directed at professional clients (this includes eligible
counterparties as defined by the Appropriate EU Regulator) who are deemed both
knowledgeable and experienced in matters relating to investments. The products
and services to which this communication relates are only available to such persons
and persons of any other description (including retail clients) should not rely on
this communication.
The whole or any part of this work may not be reproduced, copied or transmitted or
any of its contents disclosed to third parties without SSGA’s express written consent.
These investments may have difficulty in liquidating an investment position without
taking a significant discount from current market value, which can be a significant
problem with certain lightly traded securities.
All the index performance results referred to are provided exclusively for comparison
purposes only. It should not be assumed that they represent the performance of any
particular investment.
The views expressed in this material are the views of Richard Hannam and Frederic
Jamet through the period ended 31 March 2015 and are subject to change based on
market and other conditions. The information provided does not constitute investment
advice as such term is defined under the Markets in Financial Instruments Directive
(2004/39/EC) and it should not be relied on as such. It should not be considered a
solicitation to buy or an offer to sell any investment. It does not take into account any
investor’s or potential investor?s particular investment objectives, strategies, tax
status, risk appetite or investment horizon. If you require investment advice you
should consult your tax and financial or other professional advisor. All material has
been obtained from sources believed to be reliable. There is no representation or
warranty as to the accuracy of the information and State Street shall have no liability
for decisions based on such information. This document contains certain statements
that may be deemed forward-looking statements. Please note that any such
statements are not guarantees of any future performance and actual results or
developments may differ materially from those projected. Past performance is not a
guarantee of future results.
Investing involves risk including the risk of loss of principal.
Source: MSCI. The MSCI data is comprised of a custom index calculated by MSCI for,
and as requested by, SSgA. The MSCI data is for internal use only and may not be
redistributed or used in connection with creating or offering any securities, financial
products or indices. Neither MSCI nor any other third party involved in or related to
compiling, computing or creating the MSCI data (the ?MSCI Parties?) makes any
express or implied warranties or representations with respect to such data (or the
results to be obtained by the use thereof), and the MSCI Parties hereby expressly
disclaim all warranties of originality, accuracy, completeness, merchantability or
fitness for a particular purpose with respect to such data. Without limiting any of the
foregoing, in no event shall any of the MSCI Parties have any liability for any direct,
indirect, special, punitive, consequential or any other damages (including lost profits)
even if notified of the possibility of such damages.
Risk associated with equity investing include stock values which may fluctuate in
response to the activities of individual companies and general market and
economic conditions.
Standard & Poor’s (S&P) S&P Indices are a registered trademark of Standard & Poor’s
Financial Services LLC.

2015 Equal Weighting and Other Forms of Size Tilting

More Related Content

What's hot (18)

Similar to 2015 Equal Weighting and Other Forms of Size Tilting (20)

Recently uploaded (20)

2015 Equal Weighting and Other Forms of Size Tilting