Pragmatic attitude to large-scale Markowitz’s portfolio optimization and factor-augmented derating

In this paper, we propose a Factor-Augmented Derating (FAD) method for large-scale mean–variance portfolio optimization to further overcome the overprediction phenomenon pointed by Bai et al., (2009). They found out the optimal return obtained by plug-in method was consistently higher than the theoretical optimal return and proposed a bootstrap de-rated optimal return instead based on random matrix theory. Incorporating the widely recognized fact in empirical finance studies that high-dimensional stock returns often conform to factor models, we replace the estimator of the precision matrix with a low-rank estimator in the plug-in optimal return, and further derate it using the correction parameter derived from Bai et al., (2009). We establish theories to verify why the FAD method can more effectively avoid overprediction. In our simulation, we find that derating is requisite and our FAD optimal return is the closest to the theoretical optimal return comparing to plug-in, bootstrap-derated and factor-based optimal returns in high-dimensional situations. We also find that the FAD optimal return is the most credible in our empirical studies on portfolio allocation among 200 component stocks of S&P500. Backtesting results clearly show that the discrepancy of “high expectation-low realization” can be best reduced by using the FAD method, though no real returns can achieve the anticipated optimal returns. More surprisingly, FAD method yields the highest real returns, even with low optimal returns at the decision-making stage.