Multi-Period Portfolio Optimization with Cone Constraints and Discrete Decisions

Abstract

In this study, we consider multi-period portfolio optimization model that is formulated as a mixed-integer second-order cone programming problems (MISOCPs). The Markowitz (1952) mean/variance framework has been extended by including transaction costs, conditional value-at-risk (CVaR), diversification-by-sector and buy-in thresholds constraints. The model is obtained using a binary scenario tree that is constructed with monthly returns of the stocks from the S&P 500. We solve these models with a MATLAB based Mixed Integer Linear and Nonlinear Optimizer (MILANO). Numerical results show that we can solve small to medium-sized instances successfully, and we provide a substantial improvement in runtimes using warmstarts in outer approximation algorithm.