Alternative equity indices are a growth industry, with bold claims being made about their superior performance against cap-weighted equivalents. But these indices’ objectives are often vague, and their exposures to classic equity risk factors can be significant. The authors provide a logical framework for building such indices. They show that their three diversification-based approaches are more effective at meeting objectives and often exhibit higher Sharpe ratios than the common characteristics-based approaches of the commercial products. Furthermore, they demonstrate that an initial characteristics-based stock selection can be combined with a diversification-based weighting scheme to build successful alternative equity indices without the risk factor exposures.

Proponents of alternative beta equity indices claim they are more representative and generate superior returns compared with cap-weighted equivalents. The authors explore how the choice of index construction affects the properties and returns of the resulting portfolio. They first demonstrate that across four leading alternative beta indices from Standard & Poor’s (S&P), Morgan Stanley Capital International (MSCI), and the FTSE Group, 50–90% of the outperformance is the result of exposure to known risk factors: small size, low volatility, and high dividend yield.

The authors focus on two steps of index construction: stock selection and stock weighting. They first test whether diversification-based stock weighting schemes, because they account for interaction effects, are superior to their characteristics-based equivalents. They benchmark three diversification schemes—minimum volatility weighting with norm constraints (GMV-NC), efficient maximum Sharpe ratio (EMSR), and maximum decorrelation (MDC)—against their characteristics-based analogs and find that the diversification schemes dominate in terms of meeting their respective objectives.

Next, the authors consider whether stock selection, which is necessarily characteristics based, can complement diversification-based weighting schemes if the value tilts inherent in these schemes are offset. They trisect the S&P 500 Index by volatility, size, and yield and apply each of the three diversification schemes to the three sets of trisections. By initially applying the anti-value stock selection, the authors find that all three diversification schemes lose, and even reverse, their value biases compared with the cap-weighted S&P 500. Additionally, all diversification schemes, except GMV-NC applied to high-volatility stocks, are more successful at achieving their objectives than the cap-weighted index.

The authors apply these proprietary diversification techniques to commercially available defensive and fundamental index stock selections. Among the defensive indices, all diversification schemes are able to reduce the volatility of the S&P 500 Low Volatility Index and the Russell 1000 Defensive Index. The MSCI Minimum Volatility Index has 12% lower volatility when sector constraints instead of stock-level constraints are applied and the GMV-NC is used. For fundamental indexing, the benchmark strategy selects 500 stocks based on a composite firm size measure, which adds 50 bps of annual return over the S&P 500 and weights them by the same measure, adding another 100 bps. But all of the diversification schemes, when applied to fundamental stock selection, achieve more impressive returns and Sharpe ratios than fundamental weighting. The diversification schemes also succeed in improving their individual objective metrics by between 21% and 36%.

For generic strategy testing, the authors use the S&P 500 universe of stocks for January 1959–December 2010. When reengineering commercially available indices, they use the commercial index provider’s universe. The starting points are November 1990, July 1996, January 1999, and January 1984 for the S&P, Russell, MSCI, and fundamental indices, respectively.

The three diversification schemes introduced by the authors are GMV-NC, EMSR, and MDC. GMV-NC minimizes overall portfolio volatility subject to a constraint on the minimum effective number of holdings, and its objective metric is to reduce the portfolio’s volatility. EMSR maximizes the Sharpe ratio by assuming each stock has an expected return proportional to its risk group’s median downside risk, and the objective metric is the ex post Sharpe ratio. MDC minimizes portfolio volatility under the assumption that all stocks have identical volatility; thus, low correlations rather than low volatility are used to reduce risk. Its objective is to maximize a correlation-aware measure of the effective number of stocks.

The authors provide a logical framework for alternative beta index construction (i.e., characteristics-based stock selection followed by diversification-based stock weighting). They demonstrate that weighting schemes can maintain the attractive return characteristics of alternative beta indices, whereas stock selection can be effective in neutralizing the factor tilts often inherent in such indices. The article has very real relevance for the design of alternative beta indices with improved risk–return characteristics, although the improvement is at the expense of more complex construction rules. The research is limited to U.S. stock markets, although the conclusions are likely to be valid more broadly.