Multi-Period Integer Portfolio Optimization Using a Quantum Annealer

Abstract

For large portfolio managers, a sequence of single-period optimal positions is rarely multi-period optimal. In particular, transaction costs can prevent large portfolio managers from monetizing most of their forecasting power. The solution is to compute the trading trajectory that comes sufficiently close to the single-period optima while minimizing turnover costs.

Computing a trading trajectory in general terms is a NP-Complete problem. This note illustrates how quantum computers can solve this problem in the most general terms.

Keywords: Integer programming, multi-period optimization, np-complete, quantum computer, quantum annealer

JEL Classification: G0, G1, G2, G15, G24, E44