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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.
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