Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning

Abstract-- We investigate the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two stocks and one risk-free asset. The stocks follow the Cointelation model recently introduced [7]. The proposed optimization methods are twofold. In what we call an Stochastic Differential Equation approach, we compute the optimal weights using mean-variance criterion and power utility maximization. We show that dynamically switching between these two optimal strategies by introducing a triggering function can further improve the portfolio returns. We contrast this with the machine learning clustering methodology inspired by the band-wise Gaussian mixture model [9]. The first benefit of the machine learning over the Stochastic Differential Equation approach is that we were able to achieve the same results though a simpler channel. The second advantage is a flexibility to regime change.