The introduction of the S&P 500 Equal Weight Index (EWI) in January 2003 pioneered the subsequent development of non-capitalization weighted indices catering to investors who question market efficiency.

Equal weighting is factor indifferent. It randomizes factor mispricing and is thus an attractive option for proponents of the theory that the market is inefficient and at times misprices factors.

The Equal Weight Index has different properties from the S&P 500, including a lower concentration of individual stocks and slower-changing sector exposures.

The S&P 500 EWI has outperformed the S&P 500 since its inception. The level of outperformance has varied considerably under different market conditions.

The outperformance of the two indices is a result of the differing weighting and rebalancing processes. In terms of risk factor exposures, a complex and dynamic combination of size and style risk factors have contributed to the difference in returns. It may be difficult to replicate S&P 500 EWI return outcomes through a simplistic combination of style and sector indices.

Equal weighting also demonstrates long-term outperformance internationally.

Criticism of equal weighted indices has centered on additional turnover and increased capacity constraints relative to a market capitalization weighted index. While true in abstract theory, neither is a serious hurdle in practice.

THE S&P 500 EQUAL WEIGHT INDEX AND ALTERNATIVE WEIGHTED INDICES

Since the introduction of the S&P 500 in 1957, most indices have been weighted by market capitalization. The theoretical underpinnings for market capitalization weighted indices as a basis for investment lie in the Capital Asset Pricing Model (CAPM) and the Efficient Market Hypothesis. According to the CAPM model, the expected return implicit in the price of a stock should be commensurate with the risk of that stock. However, stocks are subject to two types of risk - systematic risk, resulting from potential movements in market factors, and unsystematic risk, resulting from factors associated with individual assets. Since unsystematic risk can be diversified away stocks should be priced solely based on systematic risk. This also implies that it is optimal to hold a well diversified portfolio in order to minimize unsystematic risk for a given level of expected return. According to the efficient market hypothesis it is impossible to beat the market because prices already incorporate all relevant information. Based on this the most efficient portfolio would be the entire market, and a broad market capitalization index would represent the optimal investment. However, there is much debate as to how efficient the market is in practice. Thus there are countless different strategies being used in an attempt to beat the market. This has led to indices being created based on alternative factors which measure different strategies.

From a methodological standpoint, all equity indices can be thought of as being weighted by a certain factor raised to a power, as shown below:

The factor used can be one of any number of attributes, including market capitalization. If it is desired to amplify the influence of the factor, an exponent can be applied. For instance, to achieve a portfolio with as high a dividend yield as possible, the index could be weighted based on dividend yield squared. In general, however, most indices do not use an exponent and are therefore weighted by a factor or a score derived from several factors. The S&P 500 Equal Weight Index is unique in that its methodology is defined not by the factor used but by the exponent. In an equal weighted index the exponent used is zero. Therefore, regardless of what factor is used the overall score for each component stocks is always one and the weight of each stock in the index is always one divided by the total number of components in the index. Since the index is factor indifferent, it randomizes factor mispricing and is thus an attractive option for proponents of the theory that the market is inefficient and at times overweight or underweight certain factors.

At the time of its release on January 8, 2003 the S&P 500 Equal Weight Index (EWI) represented the first major equity index to use an "alternative" weighting methodology. Since the introduction of the S&P 500 Equal Weight Index, several indices and index families using alternative weighting schemes have been developed, examples of which are shown in Exhibit 1. (It was certainly not the first non-market capitalization weighted index - MSCI GDP weighted indices and GRA wealth weighted indices were published in the 1990's - but it was the first such index to be widely used for index products.)

There has also been strong interest in the S&P 500 EWI itself since the introduction of the index. Assets linked to the index have increased rapidly since the launch of the index, as illustrated in Exhibit 2.

PROPERTIES OF THE S&P 500 EWI

Upon the launch of the S&P 500 EWI it was noted that the S&P 500 EWI has several different properties from the S&P 500, mostly resulting from the nature of an equal weighted index. For instance, the S&P 500 EWI will have a lower stock concentration than the S&P 500, will tend to have a higher turnover due to the quarterly rebalancing of weights back to equal weighted and will have higher liquidity constraints since all stocks in the index are given the same weight regardless of market cap.

Stock Weightings and Concentration

Relative to the S&P 500, the S&P 500 EWI is expected to overweight the smaller market-cap stocks the S&P 500 and underweight the larger market-cap stocks. The size distribution of the market, and thus the S&P 500, tends to be long-tailed, with a few stocks having market caps significantly higher than the mean of the index and many stocks having market caps below the mean. Therefore, the S&P 500 EWI will underweight a few large stocks and overweight a large number of smaller stocks. Exhibit 3 shows the difference in stock weightings between the S&P 500 and S&P 500 EWI based on the market cap of each of the stocks in the index.

By definition the S&P 500 EWI will have a lower stock concentration than the S&P 500. The Herfindahl Index is a commonly used measure of concentration that is calculated as the sum of squares of percent weight of each stock in a portfolio.

Exhibit 4 plots the Herfindahl Index for the S&P 500, and the S&P 500 EWI. Since at each rebalancing the weights of the S&P 500 EWI are always .2% for each stock, it will always have a Herfindahl Index of about 20, while the Herfindahl Index for the S&P 500 will track the concentration of large-cap U.S. equities. Over time the level of concentration of the S&P 500 has changed considerably. Unsurprisingly it peaked in 2000 when mega caps dominated the market. Since that time, concentration has decreased.

Sector Weightings

The differences in sector weightings of the S&P 500 EWI versus the S&P 500 have varied markedly over time. The S&P 500 EWI will at any time have different sector exposures than the S&P 500. The S&P 500 is designed to have sector weightings close to those of the large cap market. The weight of each sector in the index at any time is dependent on the total market cap of the stocks in that sector relative to the market cap of the entire index. On the other hand the sector weights of the S&P 500 EWI will be determined at each rebalancing by the number of stocks in each sector in the S&P 500. Therefore, the S&P 500 EWI will be overweight relative to the S&P 500 in sectors that contain stocks that are on average smaller than the average stock in the S&P 500 and will underweight sectors that contain larger than average companies. Exhibits 5 and 6 illustrate how the sector weightings for the two indices have evolved over time.

Since 1998 the S&P 500 EWI has been consistently overweight in certain sectors, such as Utilities and Consumer Discretionary, and underweight in certain sectors, such as Health Care and Telecommunication Services, relative to the S&P 500. However, for other sectors the situation has varied considerably over time. For instance, the S&P 500 EWI was overweight Industrials by at least two percentage points from 1998 through 2002, and often by as many as five percentage points during that time, but is now actually underweight in that sector versus the S&P 500. In fact, even for sectors where the S&P 500 EWI has been consistently overweight or underweight, the difference in concentration between the two indices has altered significantly. For instance, while the S&P 500 EWI has been overweight in Materials since 1998, it had been overweight by over eight percent in 1999 but is now only overweight by two percent.

More important than the differences in sector weights between the two indices is the variance of the sector weights themselves. As can be seen in the exhibits above, the sector weights of the S&P 500 EWI have changed far less than those of the S&P 500. This is unsurprising since hte sector weights of the S&P 500 will vary based both on the number of stocks in each sector in the index as well as the performance of each sector over time, whereas for the S&P 500 EWI it will only vary due to the number of stocks in each sector. Therefore, when a certain sector underperforms or outperforms the market by a large percentage, the sector weights of the S&P 500 will adjust relatively quickly, whereas those for the S&P 500 EWI will not, due to the quarterly rebalancing of the index back to equal weights. The largest change in the relative sector weights of the two indices has been in the Information Technology (IT) sector. During the Internet bubble in the late 1990s the S&P 500 EWI went from being underweight in the sector by only three percent at the start of 1998 to being underweight by close to 20 percent in August 2000. This can be attributed almost entirely to the change in the sector weight of the S&P 500 during this time. While the IT sector weight of the S&P 500 EWI did increase from 10 percent to 15 percent, that of the S&P 500 increased from 13 percent to 33 percent over the same time period.

CRITICISM OF EQUAL WEIGHTED INDICES

Turnover

Since the launch of the S&P 500 EWI, two main concerns have been expressed, primarily from the perspective of investment products based on the index. These are turnover and capacity constraints.

Admittedly, the S&P 500 EWI has higher market capitalization turnover than the S&P 500, due to the rebalancing of the index on a quarterly basis to equal weights. Since the introduction of the index in 2002, average annual turnover for the S&P 500 EWI has been over five times that of the S&P 500 (22.09% and 4.01% respectively). However, the S&P 500 has a very low turnover relative to most indices. The S&P 500 EWI has turnover only 60% greater than that of the S&P MidCap 400 and S&P SmallCap 600 (13.65% and 13.93% respectively) and is in line with other alternatively weighted indices which generally have turnover in the 15% - 30% range. Thus, while turnover for the S&P 500 EWI is somewhat larger than other indices, it is within a reasonable range for indices and is certainly much lower than turnover for most actively managed portfolios, which tend to be in the 50% to 100% range.

Capacity Constraints

Another concern regarding the S&P Equal Weighted Index and equal weighted indices in general is capacity constraints. Since all constituents are held at equal weights regardless of their market capitalization, an investment product tied to the index will have relatively large holdings in the smallest stocks in the index. This could produce liquidity pressures at rebalancing. However, deeper investigation shows that this concern is true only in theory.

As of the end of 2006, the smallest stock had a market cap of $1.41 billion. Applying the 10.34% ratio to this it can be estimated that at least $145 million can be linked to the smallest stock in the S&P 500 EWI without resulting in capacity issues. Since each stock in the index represents .2% of the index, this implies that $72.8 billion can be linked to the index without any optimization. If stocks below $2 billion in market capitalization (currently only 5 stocks) are optimized, the capacity reaches $100 billion. However, as noted above, there were only $8.5 billion in assets linked to the index as of the end of 2006, suggesting that assets can increase by tenfold before reaching the level of index effect seen in S&P 500 index changes.

PERFORMANCE OF THE S&P 500 EWI

Exhibit 7 illustrates the performance of the S&P 500 EWI relative to that of the S&P 500. Since inception in 1990 the S&P 500 EWI has outperformed by 1.5% per year. However, the level of outperformance or underperformance has varied considerably over time in line with different market cycles. The S&P 500 EWI outperformed in the early 1990s but lagged the S&P 500 for six straight years from 1994 through 1999, significantly underperforming during the technology bubble of the late 1990s. The S&P 500 EWI significantly outperformed during the correction from 2000 through 2002 and beat the S&P 500 for seven consecutive years through 2006. Although the historical data for the S&P 500 EWI comprises only one major bull market and correction, the performance of the index over this time suggests that equal weighting may underperform relative to market cap weighting during strong markets but will correspondingly hold up better during bear markets.

Exhibits 8 and 9 graph the historical volatility of the S&P 500 EWI and the S&P 500 and the correlation between the two indices. The volatility of the S&P 500 EWI, as measured by rolling three-year annualized standard deviations, exceeded that of the S&P 500 from 1992 through 1995, although the difference in volatility decreased over that period. For the next five years the volatilities of the two indices were very similar. However, the volatility of the S&P 500 EWI spiked relative to the S&P 500 in late 2002 and has remained between 1.5% and 3.5% higher than that of the S&P 500 since that time.

The correlation between the two indices, as measured by rolling 36-month returns, has for the most part consistently stayed between 93% and 96%. The one major exception to this was the technology bubble of the late 1990s and the following correction. During this time correlation was much lower between the two indices than during the rest of the history of the S&P 500 EWI. It reached a low of 84% in late 2001.

Risk Factor Attribution

The question arises as to where the outperformance of the S&P 500 EWI is derived from. Exhibit 10 shows a style map of the S&P 500 and S&P 500 EWI. The map exhibits the influence of both style and size on the relative performance of the two indices. The performance of the S&P 500 EWI, while consistently in the large cap half of the chart, tends to fall somewhere between the S&P 500 and S&P 400 style indices, thus showing an influence on its return by movements in mid-size stocks. Also, the S&P 500 EWI varies between being more heavily influenced by growth or value factors. However, in the majority of periods it falls on the value side of the chart. Thus, over the last five years the S&P 500 EWI has been influenced both by the size factor and the value factor relative to the S&P 500. This suggests that equal weighting results in unique exposure to a complex and dynamic combination of size and style risk factors. It may be difficult to replicate S&P 500 EWI return outcomes through a simple combination of style and sector indices.

Looking at attribution by sectors also yields results mostly in line with expectations. Exhibits 11 and 12 show attribution by sector for two periods - 1995 through 1999, the major period of significant underperformance for the S&P 500 EWI, and 2000 through 2007, a period of significant outperformance for the S&P 500 EWI.

As would be expected, the majority of the underperformance of the S&P 500 EWI during the late 1990s can be attributed to the Information Technology sector which contributed 42.34% of total underperformance, close to half of total underperformance of 91.39%. During this time Information Technology had the largest return of any sector in both the S&P 500 and S&P 500 EWI. However, the S&P 500 EWI had both a lower weight in this sector and a lower sector return. Health care and Telecommunication Services were also large contributors to underperformance. For the time period from 2000 through 2007 the largest contributors to outperformance were Information Technology and Consumer Discretionary sectors. During this period the attribution was much more spread out between sectors. In fact, all of the sectors attributed positively to the outperformance of the S&P 500 EWI during this time.

Interestingly, looking at the sector attribution also further clarifies the importance of the differences in constituent weights due to equal weighting. For the 1995 through 1999 period the S&P 500 EWI not only underperformed as a whole but also in eight out of 10 sectors. Conversely, for the period of 2000 through 2007, the S&P 500 EWI outperformed in every sector and every sector had a positive attribution. This implies that most of the outperformance is due not to differences in sector weightings but to the sector index returns of the S&P 500 and S&P 500 EWI. However, since the stocks in the indices, and thus in each of the sectors, are the same, the differences are caused solely by the different weighting and rebalancing schemes of the two indices.

DOES EQUAL WEIGHTING WORK INTERNATIONALLY?

It would be interesting to see if equal weighting an international portfolio results in similar differences to the risk/return characteristics of the portfolio as it does when equal weighting a U.S. portfolio. To provide some insight into this issue, a backtest was run for an equal weighted version of the S&P International 700, with the same methodology and rebalancing schedule as that of the S&P 500 EWI. The S&P International 700 is the international equivalent of the S&P 500. It is comprised of 700 of the largest, most liquid stocks from outside the United States. The S&P International 700 and the S&P 500 together comprise the S&P Global 1200.

To construct the international equal weighted index, we equal weight constituents of each of the following regional indices - S&P Europe 350, S&P TOPIX 150 for Japanese stocks, S&P/TSX 60 for Canadian stocks, S&P/ASX 50 for Australian stocks, S&P Asia 50 representing Asia ex-Japan stocks and S&P Latin America 40. These equal weighted regional indices are then GDP weighted to arrive at the composite international equal weighted index. We adopt this process to ensure that each region's weight is driven by its economic output, and not the count of stocks in its benchmark index.

Our results suggest equal weighting does seem to work in international markets as well. Similar to the S&P 500 EWI, the S&P International 700 EWI outperforms relative to its market weighted equivalent, has somewhat higher volatility, particularly in recent years, and over time has become increasingly correlated to its market weighted equivalent.

The S&P International 700 EWI has significantly outperformed the S&P International 700, by a greater margin than the S&P 500 EWI has outperformed the S&P 500. In fact, while the S&P 500 EWI has outperformed in certain market cycles and underperformed in others, the S&P International 700 EWI has consistently outperformed.

Exhibit 14 shows the style map for the S&P International 700 EWI relative to the a benchmark international index (S&P/Citigroup BMI Global Ex U.S.) using S&P/Citigroup international style indices. Here too, one notices a complex, time varying style map that suggests that international equal weighted strategy has a different set of style and size exposures compared to a benchmark index.

Exhibits 15 and 16 graph the historical volatility of the S&P International 700 EWI and the S&P International 700, and correlation between the two indices. The volatility of the S&P International 700 EWI, as measured by rolling three-year annualized standard deviations, was lower than that of the S&P International 700 from 1992 through 1995. However, starting after 1997 its volatility has been consistently higher than that of the S&P International 700, with the relative difference peaking in 1999 through 2000 and again in 2003 through 2004. Similar to the relative volatility of the S&P 500 EWI and the S&P 500, the volatility of the S&P International 700 EWI has recently exceeded that of the S&P International 700 by around 1.5% - 2.0%.

The correlation between the market cap and equal weighted versions of the international index has grown in recent times, consistent with the S&P 500 and S&P 500 EWI. Since 2003, it has been between .96 and .98. Unlike the U.S. indices, however, correlations have been stable in the 90% to 98% range over time.

Conclusions

Often, the most powerful investment ideas are simple. The simple concept of equal weighted indexing has gained billions of dollars in assets in last five years. While the headline cause of asset flows has been outperformance over market capitalization indices, sophisticated investors have realized that equal weighting creates a different set of risk factor exposures versus market capitalization weighting that seem to work over the long term. Further, the concept randomizes factor mispricings in the market. As trading costs shrink globally, and as investors realize that turnover of equal weighted indexing is only about a fifth of active managers, we expect the concept to gain ground. Equal weighting has been used in fixed income indexes to a certain degree, and given our results of it working in international markets, we would not be surprised to see interest in equal weighted international products.

The opinions and forecasts expressed are those of Srikant Dash and Keith Loggie, Standard & Poors' researchers, as of April 2008, and may not actually come to pass. This information is subject to change at any time, based on market and other conditions and should not be construed as a recommendation of any specific security or strategy.

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