Can Indexes Generate Alpha?

February 17, 2010

Can Indexes Generate Alpha? There are an increasing number of passive investing strategies available for investors, each offering a slightly different market exposure. While we would expect indexes with the same general market exposure (e.g., domestic large value) to have similar returns, past research by Israelsen [2007], among others, has noted that the returns of indexes can vary widely, even over prolonged time periods. Comparing indexes on returns alone, though, does not account for risk. It could be that a large growth index from one family outperformed another during a historical period just because it was less “large” or more “growth.”

Therefore, the best way to compare indexes from different providers is to do so on a risk-adjusted basis, i.e., determine their respective alphas. While indexes are beta investments by definition—not alpha investments—given their varying returns and construction methodologies, we would expect some to outperform others on a risk-adjusted basis. This “alpha” component of seven different index methodologies (and almost as many providers)—including the Dow Jones, Dow Jones Wilshire (rebranded as the Dow Jones Total Stock Market Indexes as of March 31, 2009), Morningstar, MSCI, Standard & Poor’s, Standard & Poor’s Pure and Russell index families—will be explored in this paper, where alpha is determined using a four-factor regression model (i.e., Carhart model) consisting of the three Fama/French factors and momentum.


Investors choose to invest in an index, or really an investment that tracks an index such as a mutual fund or ETF, in order to capture the return associated with that market exposure without the variability (and often costs) associated with active management. While the major index providers have similar methodologies for their domestic equity indexes (see Appendix I for a summary of the methodologies for the index providers included in the study), there are differences among them. These differences impact the performance and risk attributes for each index, yet make it difficult for the average investor to compare the relative strengths and weaknesses of each strategy.

As a shortcut, many investors simply seek out the most well-known index for investing purposes. For example, according to the 2009 Investment Company Factbook, 58 percent of all assets invested in domestic equity index mutual funds were tracking the S&P 500, despite the fact that many other indexes exist with similar market exposures. A better approach would be to see which indexes actually outperform on a risk-adjusted basis, yet little research has been devoted to this topic. While one may expect that indexes would not generate alpha using traditional risk-adjusted measures (i.e., four-factor alpha), the research conducted for this paper suggests otherwise.

Index Investing Today

As of June 30, 2008, more than 70 percent of assets in index mutual funds and ETFs invested within the nine domestic equity styles boxes (defined as Investment Category by Morningstar) were invested in the large blend category, followed by 7 percent in large growth and 5 percent in large value (making the total large-cap allocation approximately 82 percent). While it is not surprising that the majority of assets are invested in large cap, given that it is generally defined as the largest 70 percent of securities based on market capitalization, it is somewhat surprising that such a large portion is invested in a single style: large blend.

Figure 1 includes the rolling three-year annualized performance for the large blend indexes from each of the six different index methodologies (S&P uses the same blend methodology for both its regular and pure indexes, so the return for the S&P 500 has only been included once) from July 1997 to June 2009. Note that rolling three-year periods were selected because the regression analysis in the following section is based on rolling historical three-year periods (i.e., 36 months).

Can Indexes Generate Alpha Fig 1

As shown in Figure 1, while the rolling annualized three-year returns for the large blend indexes varied across providers, the returns were relatively similar, although significant differences did exist at varying points in time. The maximum range in three-year returns during the entire test period for the six large blend indexes was the three-year period ending September 2001, where the Morningstar large blend index outperformed the MSCI large blend index by 7.51 percent (per year, +6.70 percent vs. -0.81 percent, respectively), while the minimum range was in September 2000, where the Dow Jones large blend outperformed the S&P large blend index by 1.28 percent (per year, +17.72 percent vs. +16.44 percent, respectively).

Figure 2 includes the annualized returns of the indexes for each style from July 1997 to June 2009, or a 12-year period. Note that these returns were calculated by compounding the monthly returns obtained from Morningstar Direct, based on the same values used to create Figure 1.

Can Indexes Generate Alpha Fig 2

The annualized performance differences may not appear large among the indexes in Figure 2, but they are material given the time period (12 years). For example, the annualized performance difference between the best-performing large-cap blend index (Morningstar at 2.78 percent) and the worst-performing large-cap blend index (MSCI at 0.15 percent) may be only 2.63 percent, but over 12 years this would result in a difference of approximately 36 percent (with the investment in the Morningstar large-cap blend being 36 percent larger, ignoring contributions). What is less clear, though, is what the true “alpha” of the strategies is after accounting for their varying market exposures. Using the previous example, it may be that the outperformance of the Morningstar large blend index over the MSCI large blend index is entirely due to the Morningstar index having a higher market weight (i.e., higher beta factor), and once this is adjusted for the difference (or relative alpha), it could become negative. This is what will be explored in the analysis section of the paper.


While it is impossible to know which index group (or really which methodology) will outperform on a risk-adjusted basis in the future, a review of the historical risk-adjusted attributes of each methodology should provide insight as to which methodology does a better job capturing outperformance relative to its market exposure. To determine the “alpha” or risk-adjusted outperformance for each index methodology, a four-factor (i.e., Carhart) regression analysis is performed using the three Fama/French factors, as well as momentum. All data for the beta factors, as well as the risk-free rate, was obtained from Kenneth French’s Web site, and all return data for the indexes was obtained from Morningstar Direct.



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