Introduction
The ‘size factor’ is a source of additional return which investors
have long sort to capture in their investm...
State Street Global Advisors 2
IQ Insights | Equal Weighting and Other Forms of Size Tilting
Another way to view evidence ...
State Street Global Advisors 3
IQ Insights | Equal Weighting and Other Forms of Size Tilting
Another approach to capturing...
State Street Global Advisors 4
IQ Insights | Equal Weighting and Other Forms of Size Tilting
Similar analysis can also be ...
State Street Global Advisors 5
IQ Insights | Equal Weighting and Other Forms of Size Tilting
The Equal-Weighted Approach B...
IQ Insights | Equal Weighting and Other Forms of Size Tilting
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2015 Equal Weighting and Other Forms of Size Tilting

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Does equal weighting have some additional exposures or
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2015 Equal Weighting and Other Forms of Size Tilting

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