Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment

TL;DR

This paper develops a neural network-based method to optimize multi-period investment strategies under leverage constraints during high inflation, outperforming passive benchmarks with high probability.

Contribution

It introduces a leverage-feasible neural network (LFNN) that transforms constrained portfolio optimization into an unconstrained problem, enabling effective high-inflation investment strategies.

Findings

LFNN strategy outperforms passive benchmark by ~200 bps median annualized return

LFNN achieves over 90% probability of outperforming benchmark

Closed-form solution derived under jump-diffusion model during high inflation

Abstract

Motivated by the current global high inflation scenario, we aim to discover a dynamic multi-period allocation strategy to optimally outperform a passive benchmark while adhering to a bounded leverage limit. To this end, we formulate an optimal control problem to outperform a benchmark portfolio throughout the investment horizon. Assuming the asset prices follow the jump-diffusion model during high inflation periods, we first establish a closed-form solution for the optimal strategy that outperforms a passive strategy under the cumulative quadratic tracking difference (CD) objective, assuming continuous trading and no bankruptcy. To obtain strategies under the bounded leverage constraint among other realistic constraints, we then propose a novel leverage-feasible neural network (LFNN) to represent control, which converts the original constrained optimization problem into an unconstrained optimization problem that is computationally feasible with standard optimization methods. We establish mathematically that the LFNN approximation can yield a solution that is arbitrarily close to the solution of the original optimal control problem with bounded leverage. We further apply the LFNN approach to a four-asset investment scenario with bootstrap resampled asset returns from the filtered high inflation regime data. The LFNN strategy is shown to consistently outperform the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the end of the investment horizon.