Some experts use the mean-variance analysis of Modern Portfolio Theory (MPT), which penalizes large upside volatility, to measure portfolio efficiency. Others use Second-order Stochastic Dominance (SSD) analysis, purer mathematically than MPT but open to unrealistic investor behavior. Is there a better way? In the February 2012 version of his paper entitled “The Passive Stock Market Portfolio is Highly Inefficient for Almost All Investors”, Thierry Post describes and tests a portfolio efficiency measure based on an Almost Second-order Stochastic Dominance (ASSD) that aims to exclude unrealistic investor behaviors. He applies the measure to a market portfolio (value-weighted average of NYSE, AMEX and NASDAQ stocks) and three alternative sets of ten equity portfolios formed using NYSE decile breakpoints for: (1) market capitalization (size); (2) book-to-market ratio; and, (3) past 11-month return with skip month (momentum). He considers investment horizons of one, 12 and 120 months over sample periods of 1926-2011 and 1963-2011. Using monthly value-weighted returns and contemporaneous stock/firm characteristics from July 1926 through December 2011 (1,026 months), along with the contemporaneous one-month Treasury bill yield as the risk-free rate, he finds that:
- MPT mean-variance analysis assigns negative weights to large positive gross returns, penalizing size, value and momentum strategies when they strongly outperform.
- SSD analysis tends to assign very large positive weights to large negative gross returns due elevated correlations among stocks during bear markets, heavily penalizing the downside risk of size, value and momentum strategies.
- ASSD analysis indicates that the market portfolio is highly inefficient on a gross basis relative to portfolios formed based on size, value and momentum strategies. The gross superiority of the active strategies increases with investment horizon.
In summary, evidence from tests on gross returns of U.S. stocks suggest that conventional ways of measuring portfolio efficiency may cause investors to decline attractive strategies.
Cautions regarding findings include:
- While testing includes a 1963-2011 subsample, analysis is largely in-sample. An investor operating in real time on strictly historical data may draw different conclusions.
- As acknowledged in the paper, analyses do not include trading frictions, which may well differ systematically with size, book-to-market and momentum factors in a way that works against findings.
- The market may be adaptive to widespread use of any method of optimizing portfolio efficiency.
