Building The Best Index

January 01, 2006

Market capitalization is currently the most popular weighting method for indexes. Its methodology is straightforward: Each stock in an index is weighted based on the total value of its outstanding shares (with some minor alterations, e.g., free float). Although using market capitalization makes sense from a total value perspective, it is only one method to capture the returns of a given asset category.

Market capitalization indexes, by virtue of their very nature, skew performance towards the larger stocks. For example, GE and Cisco Systems are both considered large-cap stocks, but GE's weighting in any market-capitalization-based index would be more than double Cisco's. An alternative methodology that could be used to construct an index would be to weight its constituents equally and then rebalance according to some preset schedule, in order to keep the weightings relatively constant.

There are a number of additional costs associated with the equal-weighting concept when compared to a simple market-capitalization-weighted alternative. The expense ratio of an equal-weighted index exchange-traded fund (ETF) or mutual fund is likely to be higher than its market capitalization peers, and increased turnover will reduce an investor's net returns both implicitly (through the commissions paid by the fund during rebalancings) and explicitly (through the possible tax implications). Although the tax effect would be eliminated if such an investment were held in an IRA or tax-deferred account, it would still remain a concern to some investors.

Currently, the most widely known equally weighted index is the S&P 500 Equal Weight Index. Rydex offers an ETF that tracks this index, which trades under the ticker RSP. The S&P 500 Equal Weight Index's benchmark is the plain vanilla S&P 500; this is an inadequate benchmark, though, because the S&P 500 Equal Weight Index holds a disproportionate number of small- and mid-cap stocks, skewing performance in favor of those asset classes. Therefore, it's not a fair test to compare the two indexes.

A relatively straightforward method that can be used to test the equal-weighted concept would be to historically test the 30 stocks that currently comprise the Dow Jones Industrial Average and compare them on both an equal-weighted and market-capitalization-weighted basis. These are all large-cap companies that represent the U.S. economy as a whole. Selecting the Dow also reduces the possibility of data mining, and using only its current stocks, as opposed to modifying its composition over time, eases the analysis because mergers, additions and deletions do not need to be considered.

The Dow, of course, is a price-weighted index, so that is another interesting aspect of this study. We'll be looking at only market-cap and equal weighted versions of the Dow.

The test period for analysis will be the previous 15 calendar years, and will compare three different portfolios:

1.   A portfolio that is equal-weighted at inception and is not rebalanced (EW NO RE);
2.   An equal-weighted portfolio that is rebalanced quarterly, which ignores transaction costs and tax impacts (EW); and,
3.   A portfolio weighted by market capitalization (Mkt Cap).

The performance for the three portfolios will be tested on both a total-return (dividends included) and a stock-return basis (dividends not included). Average shares outstanding will be used, and outstanding shares will be considered to be issued and repurchased evenly throughout the year.

There will be two separate data tests: The first will be the total previous 15 calendar years (January 1990 to December 2004) and the second will be the three five-year periods that combine to create those 15 years. Risk will be determined by both standard deviation (because it is the most popular definition) and by a downside-risk measure. The downside-risk measure will be the sum of the negative returns squared, using a Minimum Acceptable Return (MAR) of 1.5 percent per quarter. To calculate the MAR, this number is multiplied by its downside potential ratio (the percent of total quarters in which the return was below zero) for the period. The risk-free rate is viewed as that of a domestic (U.S.) investor and is defined as the average yield on five-year Treasury Notes over the corresponding period .1 The risk-adjusted returns will be measured by the Sharpe Ratio (period return minus period risk-free return divided by standard deviation) and by the Sortino Ratio (period re turn minus period risk-free return divided by downside risk). The Sharpe and Sortino ratios will be "modified" to allow for negative excess returns by raising the denominator (which is either standard deviation or downside risk) to the -1 power when the excess return for the period is negative.


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