Estimating large Markowitz portfolios’ spanning set

Date : Mardi | 2022-12-06 à 12h30
Lieu : Salle des thèses

Rosnel Sessinou (HEC Montréal)

Estimating large Markowitz portfolios implies estimating high-dimensional moments of stock returns,whose large number increases estimation errors. Thus, managing such large portfolios can be burdensomeas their transaction costs increase with estimation errors. Nevertheless, researchers have recently providedempirical evidence of the sparsity of the mean-variance efficient frontier of the U.S. stock market. Thisresult pleads for applying the canonical parsimony principle in the estimation of Markowitz portfolios.However, there is no formal statistical test in the literature of the null hypothesis of sparse stock marketmean-variance efficient frontier. The existing feasible test statistics require constructing non-overlappingsub-portfolios. Nonetheless, we show that this pre-processing step introduces an aggregation bias andleads to misleading conclusions. The objective of this paper is to propose a desegregate test. First, wepresent a general framework for valid portfolio and model selection in high dimensions, using momentconditions with type I error control. We introduce a significance test for high-dimensional linear statisticsbased on subseries methods and a robust p-value aggregation method. Finally, we illustrate the relevanceof the new framework on simulated and real data.