A Robust Estimator of the Efficient Frontier
16 Pages Posted: 18 Oct 2019 Last revised: 4 Mar 2020
Date Written: October 15, 2016
Convex optimization solutions tend to be unstable, to the point of entirely offsetting the benefits of optimization. For example, in the context of financial applications, it is known that portfolios optimized in-sample often underperform the naïve (equal weights) allocation out-of-sample. This instability can be traced back to two sources: (i) noise in the input variables; and (ii) signal structure that magnifies the estimation errors in the input variables. A first innovation of this paper is to introduce the nested clustered optimization algorithm (NCO), a method that tackles both sources of instability.
Over the past 60 years, various approaches have been developed to address these two sources of instability. These approaches are flawed in the sense that different methods may be appropriate for different input variables, and it is unrealistic to expect that one method will dominate all the rest under all circumstances. Accordingly, a second innovation of this paper is to introduce MCOS, a Monte Carlo approach that estimates the allocation error produced by various optimization methods on a particular set of input variables. The result is a precise determination of what method is most robust to a particular case. Thus, rather than relying always on one particular approach, MCOS allows users to apply opportunistically whatever optimization method is best suited in a particular setting.
Presentation materials are available at: https://ssrn.com/abstract=3469964.
Keywords: Monte Carlo, convex optimization, de-noising, clustering, shrinkage.
JEL Classification: G0, G1, G2, G15, G24, E44
Suggested Citation: Suggested Citation