Sparse Portfolio Selection via the sorted $\ell_{1}$-Norm

TL;DR

This paper introduces SLOPE, a portfolio optimization method using sorted $ ext{l}_1$-Norm penalization that automatically groups assets, improves stability, and enhances out-of-sample performance.

Contribution

The paper presents a novel SLOPE-based framework for portfolio selection, including an efficient algorithm and new strategies leveraging automatic asset grouping.

Findings

SLOPE effectively groups assets with similar properties.

Portfolios optimized with SLOPE show improved out-of-sample risk and return.

SLOPE reduces portfolio turnover and enhances stability.

Abstract

We introduce a financial portfolio optimization framework that allows us to automatically select the relevant assets and estimate their weights by relying on a sorted $\ell_1$-Norm penalization, henceforth SLOPE. Our approach is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. We show that by varying the intensity of the penalty, SLOPE can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. Our empirical analysis shows that SLOPE yields optimal portfolios with good out-of-sample risk and return performance properties, by reducing the overall turnover through more stable asset weight estimates. Moreover, using the automatic grouping property of SLOPE, new portfolio strategies, such as SLOPE-MV, can be developed to exploit the data-driven detected similarities across assets.