# Optimal Asset Allocation in a High Inflation Regime: a Leverage-feasible Neural Network Approach

**Authors:** Chendi Ni, Yuying Li, Peter A. Forsyth  
**arXiv:** [2304.05297](https://arxiv.org/abs/2304.05297)  
**Date:** 2023-04-11  
**Summary page:** https://www.summarizepaper.com/en/paper/2304.05297v1/

## Key points

- The paper addresses the optimal multi-period asset allocation problem with leverage constraints in a persistent, high-inflation environment.
- During high-inflation regimes, a portfolio containing an equal-weighted stock index partially stochastically dominates a portfolio containing a capitalization-weighted stock index.
- The authors establish a closed-form solution for the optimal strategy assuming asset prices follow the jump diffusion model during high inflation periods.
- They propose a constrained optimal control problem with bounded leverage and introduce a novel leverage-feasible neural network (LFNN) model that approximates the optimal control directly.
- Numerical experiments show that the LFNN model achieves comparable performance to the closed-form solution on simulated data and consistently outperforms passive benchmark strategies by about 200 bps (median annualized return), with greater than 90% probability of outperforming at terminal date.
- Investors should favor short-term bonds over long-term bonds and equal-weighted stock index over cap-weighted stock index during persistent inflation regimes in a four-asset investment scenario with bootstrap resampled asset returns.
- The proposed LFNN model offers an efficient alternative to traditional dynamic programming approaches and shows promising results in both simulated and real world investment scenarios.

## Summary

This paper addresses the optimal multi-period asset allocation problem with leverage constraints in a persistent, high-inflation environment. The authors discover that during high-inflation regimes, a portfolio containing an equal-weighted stock index partially stochastically dominates a portfolio containing a capitalization-weighted stock index. They establish a closed-form solution for the optimal strategy assuming asset prices follow the jump diffusion model during high inflation periods. To obtain strategies under more practical considerations, they propose a constrained optimal control problem with bounded leverage and introduce a novel leverage-feasible neural network (LFNN) model that approximates the optimal control directly. The LFNN model avoids high-dimensional evaluation of conditional expectation common in dynamic programming approaches and can yield solutions arbitrarily close to those of the original optimal control problem with bounded leverage. Numerical experiments show that the LFNN model achieves comparable performance to the closed-form solution on simulated data and consistently outperforms passive benchmark strategies by about 200 bps (median annualized return), with greater than 90% probability of outperforming at terminal date. The authors apply their approach to a four-asset investment scenario with bootstrap resampled asset returns and find that during persistent inflation regimes, investors should favor short-term bonds over long-term bonds and equal-weighted stock index over cap-weighted stock index. They also demonstrate that despite being specifically trained under high-inflation scenarios, their neural network strategy performs admirably well in low-inflation environments. The paper provides insights into optimal asset allocation strategies in persistent high-inflation environments while considering practical constraints such as bounded leverage. The proposed LFNN model offers an efficient alternative to traditional dynamic programming approaches and shows promising results in both simulated and real world investment scenarios.