Optimal Financial Portfolio Selection

Modern Portfolio Theory (MPT) has been the canonical theoretical model of portfolio selection for over 60 years, yet it faces limited adoption among practitioners. This is because MPT’s main inputs, assets’ expected returns and covariances, are estimated with noise, while the solution to its optimization problem requires the inversion of an ill-conditioned matrix. As a result, MPT often produces unstable portfolios with extreme weights. This study reviews and evaluates several methods for altering MPT’s inputs and optimization problem to produce more stable and diversified portfolios, without discarding MPT’s intuitive assumptions and structure. These methods are: robust estimators and shrinkage estimators of expected returns and covariances, covariances based on statistical models of returns, sparse graphical models of inverse covariance matrices, filtered covariance matrices, portfolio optimization that incorporates uncertainty in expected returns, and portfolio optimization with penalties on weights’ norm. To evaluate competing methods, I construct their respective portfolios using monthly data on 92 assets and 90 rolling training periods of 15-year length. Comparing these portfolios’ out-of-sample performance across several financial metrics and rolling test periods of 6-month length, I find that most alternatives outperform the standard MPT approach. However, I also find that only the L1-norm penalized portfolio marginally outperforms the benchmark equal-weighted portfolio, and owes its good performance to limiting short-sales