2021/12/13 by Andrew Butler, Roy H. Kwon, Butler, Andrew +1 · 1 citation
Decision Sciences · Engineering · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Reservoir Engineering and Simulation Methods #Risk and Portfolio Optimization #Stock Market Forecasting Methods
paper · pdf · doi:10.48550/arxiv.2112.07016
openalex publication_date 2021/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mean-variance optimization (MVO) is known to be sensitive to estimation error in its inputs. Norm penalization of MVO programs is a regularization technique that can mitigate the adverse effects of estimation error. We augment the standard MVO program with a convex combination of parameterized L1 and L2-norm penalty functions. The resulting program is a parameterized quadratic program (QP) whose dual is a box-constrained QP. We make use of recent advances in neural network architecture for differentiable QPs and present a data-driven framework for optimizing parameterized norm-penalties to minimize the downstream MVO objective. We present a novel technique for computing the derivative of the optimal primal solution with respect to the parameterized L1-norm penalty by implicit differentiation of the dual program. The primal solution is then recovered from the optimal dual variables. Historical simulations using US stocks and global futures data demonstrate the benefit of the data-driven optimization approach.