Efficient Portfolio Selection in a Large Market†

Recent empirical studies show that the estimated Markowitz mean-variance portfolios oftentimes perform rather poorly when there are more than several assets in the investment universe. In this article, we argue that such disappointing performance can be largely attributed to the estimation error incurred in sample mean-variance portfolios, and therefore could be improved by utilizing more efficient estimating strategies. In particular, we show that this “Markowitz optimization enigma” (Michaud, 1998) could be resolved by carefully balancing the tradeoff between the estimation error and systematic error through the so-called subspace mean-variance analysis. In addition to the consistent improvement observed on real and simulated data sets, we prove that, under an approximate factor model, it is possible to use this strategy to construct portfolio rules whose performance closely resemble that of theoretical mean-variance efficient portfolios in a large market.