Does equal weighting have some additional exposures or diversification benefits which investors need to consider?

1. 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.

2. 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.

3. State Street Global Advisors 3
IQ Insights | Equal Weighting and Other Forms of Size Tilting
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.

4. State Street Global Advisors 4
IQ Insights | Equal Weighting and Other Forms of Size Tilting
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.
Past performance is no guarantee of future results.
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.
Past performance is no guarantee of future results.

5. State Street Global Advisors 5
IQ Insights | Equal Weighting and Other Forms of Size Tilting
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.

6. IQ Insights | Equal Weighting and Other Forms of Size Tilting
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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.
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