Fluctuation-bias trade-off in regularized portfolio optimization
The optimization of a large random portfolio under Expected Shortfall with an L2 regularizer is carried out analytically with methods borrowed from the statistical physics of random systems. The regularizer reins in the large sample fluctuations and the concomitant divergent estimation error, and eliminates the phase transition where this error would otherwise blow up. In the data-dominated region, where the number of different assets in the portfolio is much less than the length of the available time series, the regularizer plays a negligible role, while in the opposite limit, where the samples are small compared to the number of different assets, the optimum is almost entirely determined by the regularizer. Our results suggest that the transition region between these two extremes is relatively narrow, and it is only here that one can meaningfully speak of a trade-off between fluctuations and bias.
This is a joint work with Gábor Papp (Eötvös Lorand University, Institute for Physics (Budapest, Hungary)) and Imre Kondor (Parmenides Foundation (Pullach, Germany) and Department of Investment and Corporate Finance, Corvinus University of Budapest (Budapest, Hungary)).