Do somewhat abstract risk-based portfolio strategies translate to familiar stock/firm characteristic tilts? In their September 2011 paper entitled “Demystifying Equity Risk-Based Strategies: A Simple Alpha plus Beta Description”, Raul Leote de Carvalho, Xiao Lu and Pierre Moulin investigate how the following five risk-based equity allocation strategies relate to four common portfolio factors.

- Equal Weight – long only, same portfolio weight for each stock.
- Equal Risk Budget – long only, same portfolio weight times volatility for each stock.
- Equal Risk Contribution – long only, similar to equal-risk budget, but tilted toward stocks with low market correlations (low beta).
- Minimum Variance – long only or long-short, limited to stocks with the extreme volatilities and market correlations.
- Maximum Diversification – long only or long-short, limited to stocks with extreme market correlations.

They map these five strategies to market capitalization (size), book-to-market ratio (value), market beta and residual (idiosyncratic) volatility factors based on quarterly rebalancing for empirical tests. Using weekly total returns for the stocks in the MSCI World Index of developed countries and the one-month U.S. Treasury bill yield during January 1997 through December 2010, *they find that:*

- All the risk-based strategies except Equal Weight are defensive, with lower volatility than the market index.
- The Equal Weight, Equal Risk Budget and Equal Risk Contribution strategies all overweight small-capitalization stocks, with the latter two also overweighting low-beta stocks. These three strategies:
- Invest in all stocks in the selected universe.
- Overlap by more than 80% in holdings.
- Exhibit excess return correlations around 90% with each other.
- Exhibit relatively low portfolio turnover.
- The defensive Minimum Variance and Maximum Diversification strategies overweight low-beta stocks and underweight small-capitalization stocks, with the former also overweighting low idiosyncratic volatility stocks. These two strategies:
- Invest in only about 120 stocks for long-only versions, overlapping by 61%.
- Are long (short) about 60% (40%) of the stocks in the selected universe for long-short versions.
- Are more statistically diversified than the other three strategies (especially the long-short version).
- Exhibit excess return correlations over 90% with each other.
- Exhibit relatively high portfolio turnover (especially the long-short version).
- All five strategies earn higher gross excess returns than the market index over the sample period, and all except Equal Weight have lower volatility. All five strategies beat the market based on gross Sharpe ratio, paced by the long-short versions of Minimum Variance and Maximum Diversification, which also have the smallest drawdowns.
- Book-to-market ratio (value) plays only a marginal role in explaining the risk-based strategies, and momentum is not relevant.
- Results are robust to regional subsamples, risk modeling approaches, data sampling frequencies and risk estimation windows. However, while the risk-based strategies generate positive gross returns during the bull market from the mid-1990s through March 2000, they all underperform the market index during this subperiod.
- Because they tilt toward small-capitalization stocks, the Equal Weight, Equal Risk Budget and Equal Risk Contribution strategies likely face elevated per-trade frictions and may not be practical for large (institutional) investors.

In summary, *these five widely used risk-based equity allocation strategies translate into tilts toward stocks with small capitalizations, low betas and/or low idiosyncratic volatilities.*

Note that the risk-based strategies essentially ignore value and momentum, suggesting combination strategies.

Cautions regarding findings include:

- Returns and Sharp ratios are gross, not net. Including reasonable trading frictions would reduce them.
- As noted by the authors, the higher trading frictions generally associated with small-capitalization stocks would impact the Equal Weight, Equal Risk Budget and Equal Risk Contribution strategies.
- Also, the Minimum Variance and Maximum Diversification strategies have relatively high portfolio turnover, elevating compounded trading frictions (with shorting costs for long-short versions).