Constituents of the S&P 500 Equal Weight (EW) and S&P 500 are identical, but the EW version is rebalanced quarterly so that every company has equal representation after the rebalance. That often results in significantly different performance between the two indices, because equal weighting gives more representation to smaller stocks and alters the distribution of sector exposure.
Sector representation is different between the indices because the weight of a sector in the EW index is strictly a function of the number of stocks in the sector, whereas cap-weighted sectors depend on company size and company count. The largest sector in the EW index is consumer discretionary, because it has the most companies (85 as of March 31, 2017); however the largest deviation from cap-weighted sectors is in information technology because that sector comprises several mega-cap companies such as Apple, Alphabet (parent of Google), Microsoft, and Facebook. Exhibit 1 shows relative sector weights of the EW index versus its cap-weighted benchmark.

In the 14 years since its launch on Jan. 8, 2003 (counting 2003 as a full year), the S&P 500 EW outperformed the cap-weighted S&P 500 10 times, underperforming in 2007, 2008, 2011, and 2015. The magnitude of outperformance was greatest in 2009 as the market bottomed and then began its recovery from the global financial crisis.
Decomposing performance of the S&P 500 EW relative to the S&P 500, using 2 Factor Brinson Attribution (showing sector allocation and security selection effects) illustrates the historical impact of EW variation relative to the cap-weighted benchmark. Since the set of index constituents are identical, the security selection factor measures only the effect of weight differences between the indices.

In spite of significantly different sector allocations between equal- and cap-weighted indices, most of the value added or detracted by equal weighting comes from variations of individual component weights. In other words, the effect of EW security selection has historically dominated that of EW sector allocation. The value of security selection relative to sector allocation is important because it demonstrates that the S&P 500 EW aligns with a desire to gain access to smaller S&P 500 stocks without necessarily resulting in detraction from sector redistribution. Market participants looking for a simple variation of cap-weighting with a reasonable chance of adding value over time may want to consider investment strategies tracking S&P 500 EW.
[1] GICS stands for Global Industry Classification Standard. Information about GICS is available at http://spindices.com/resource-center/index-policies/.
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What happens to the cumulative returns when the daily returns move in opposite directions? In this case, the magnitude of the returns matters, but not the order. If a market participant were to pursue both strategies, it would likely be a losing proposition in a choppy market. The only way to profit is by picking whether the larger absolute return will be positive or negative and using the standard long index for the larger absolute positive return and the inverse index, which is like a short position, for the larger absolute negative return. If the magnitudes of the opposite consecutive returns are the same, the directional order makes no difference, as shown in the first column of Exhibit 2, and there is a certain loss for both the standard and inverse indices. However, there is a chance to win if opting for only one strategy with a correct bet on the bigger absolute return, regardless of order.
What conclusions can be drawn for 2x leveraged indices when daily returns are compounded? Similar results are observed when comparing the standard indices to the 2x leveraged indices, which double the daily return. The compounded returns when there are two days of consecutive losses or gains show that the 2x leveraged version has a better payoff profile, since it loses less than double the standard index return but gains more than double. If a market participant is sure about commodity trends over time, then the 2x leveraged index may be a winning bet, even if the direction is uncertain.