This is a summary of “Enhanced Portfolio Optimization” by Lasse Heje Pedersen, Abhilash Babu, CFA, and Ari Levine, published in the Second Quarter 2021 issue of the Financial Analysts Journal.
Managers can improve the performance of the mean–variance approach by using enhanced portfolio optimization (EPO). EPO accounts for the noise in investors’ estimates of risk–return and, as a result, increases risk-adjusted performance.
What Is the Investment Issue?
The failure of mean–variance optimization (MVO) in practice is well documented. The authors identify the problem with standard portfolio optimization in a principal components space. They define “problem portfolios” as portfolios with the least important principal components. These portfolios tend to have underestimated risk and overestimated returns. The proposed solution, enhanced portfolio optimization (EPO), shrinks the correlations of the underlying assets toward zero, thereby addressing the problem. EPO makes the expected Sharpe ratios more consistent with realized Sharpe ratios. The art is in the size of the shrinkage factor: A shrinkage factor of zero is just MVO unadjusted; a shrinkage factor of 1 removes all correlations and resorts to Fama–French-style factor portfolios. The sweet spot lies somewhere in between.
The article manages to “unify and demystify” some familiar frameworks. Black and Litterman (“Global Portfolio Optimization,” Financial Analysts Journal, 1992) focused on the noise factor in expected returns. The authors state, “Although the EPO solution is seemingly different from Black and Litterman, we show that it is, in fact, equivalent to Black and Litterman. But EPO is simpler to apply and more transparent in how and why it works.”
The authors also build on the work of a slew of researchers who respectively examined variance/covariance shrinkage, factor models, and random matrix theory: “We found that the EPO solution significantly outperforms such approaches because EPO uses a much larger shrinkage to account for noise in estimates of both risk and expected returns.”
The authors link their approach to work on “robust optimization” by Fabozzi, Huang, and Zhou (“Robust Portfolios: Contributions from Operations Research and Finance,” Annals of Operations Research, 2010) and others “by showing how to solve a problem with a general ‘ellipsoidal uncertainty’ set on the mean and by showing, perhaps surprisingly, the exact equivalence between this form of robust optimization and the Bayesian estimator.”
Results from the empirical research “extend and enhance standard factor models—in particular, industry . . . and time-series momentum.” Plus, the authors demonstrate that EPO can be seen as a “ridge regression” in a way similar to viewing MVO as a regression coefficient per Britten-Jones (“The Sampling Error in Estimates of Mean–Variance Efficient Portfolio Weights,” Journal of Finance, 1999).
How Do the Authors Tackle the Issue?
The authors illustrate the implementation and success of the EPO method by developing shrinkage factors for various portfolios and then seeing how those portfolios performed out of sample relative to nonoptimized portfolios.
They calculated what should be the appropriate shrinkage factor using 15 years of historical data from a variety of portfolios and then tested the EPO model against the remaining out-of-sample data.
The historical data come from 11 different portfolio samples, which include eight equity portfolios and three global portfolios (consisting of equities, bonds, currencies, and commodities). The equity data cover the period 1927 through 2018. For the global portfolios, the period is 1970–2018.
The sampling period used to test the EPO method started 15 years after the first data were available. For equities, the backtesting period therefore covers 1942 through 2018, and for the global portfolios, the backtesting covers 1985 through 2018.
The backtesting results of the optimized equity industry momentum portfolios are compared with the monthly returns of the Fama–French five-factor model. The authors also review the returns of optimized time-series momentum portfolios versus a sample of time-series momentum benchmarks.
What Are the Findings?
For the global asset portfolios, the EPO time-series momentum portfolio performs far better than the market portfolio and the 1/N approach. It also does better than such sophisticated portfolio approaches as “volatility-scaled long-only and standard time-series momentum portfolios.” The approach provided a large and statistically significant increase in realized Sharpe ratios and alpha. “These sophisticated benchmarks already deliver high Sharpe ratios,” the authors state. “Yet EPO beat it.”
For all eight equity portfolios, the EPO approach produced realized Sharpe ratios higher than those for the 1/N portfolio, the standard industry momentum approach, and the MVO approach. “This strong outperformance of EPO cannot be explained by exposure to existing factors in the literature, such as the Fama–French factors,” the authors state. As with the global portfolios, the equity portfolio saw statistically significant increases in Sharpe ratios and alpha.
What Are the Implications for Investors and Investment Managers?
Investment managers can realize higher Sharpe ratios and improve on MVO by using EPO with appropriate shrinkage.