Portfolio construction with optimal denoising matrix in L1 minimization approach

Abstract

In this paper, we investigate the mean-variance (MV) portfolio problems that is constructed from the L1 minimization approach that can estimate the eff ective parameters of the MV strategies. Speci cally, we will study the properties of models constructed from the Dantzig Selector (DS) such as the optimality of the denoising matrix in the DS. Our primary interest is to extend some of the existing models proposed in studies to the DS (CDS) and DS with optimal denoising matrix (OD-LPO and OD-CDS), which is inspired by the study conducted by Liu et al. (2016). The advantage of using the DS framework is that the algorithms proposed can be transformed into linear programming problems and e fficiently implemented by numerous mature solvers. Subsequently, we will implement the models to construct MV portfolios and investigate their performance. Simulations are performed to compare the performance of the approaches to the oracle MV portfolios. An empirical study is then conducted to investigate the practical performance of the proposed approaches which found that the optimal denoising matrix has an stabilizing e ffect on the estimated portfolio weights in OD-CDS.