Title: Sparse portfolio selection via the sorted $L_1$ norm
Authors: Malgorzata Bogdan - University of Wroclaw (Poland) [presenting]
Philipp Johannes Kremer - EBS Universitaet fuer Wirtschaft und Recht (Germany)
Sandra Paterlini - European Business School Germany (Germany)
Sangkyun Lee - Hanyang University (Korea, South)
Abstract: A financial portfolio optimization framework is introduced that allows us to automatically select the relevant assets and estimate their weights by relying on a sorted $L_1$-Norm penalization, henceforth SLOPE. Our approach is able to group constituents with similar influence on the overall portfolio risk. We show that depending on the choice of the penalty sequence, 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 sparse equally weighted SLOPE-EW portfolio, can be developed to exploit the data-driven detected similarities across assets.