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

Résumé : We study the optimal multi-period asset allocation problem with leverage constraints in a persistent, high-inflation environment. Based on filtered high-inflation regimes, we discover that a portfolio containing an equal-weighted stock index partially stochastically dominates a portfolio containing a capitalization-weighted stock index. Assuming the asset prices follow the jump diffusion model during high inflation periods, we establish a closed-form solution for the optimal strategy that outperforms a passive strategy under the cumulative quadratic tracking difference (CD) objective. The closed-form solution provides insights but requires unrealistic constraints. To obtain strategies under more practical considerations, we consider a constrained optimal control problem with bounded leverage. To solve this optimal control problem, we propose a novel leverage-feasible neural network (LFNN) model that approximates the optimal control directly. The LFNN model avoids high-dimensional evaluation of the conditional expectation (common in dynamic programming (DP) approaches). 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. Numerical experiments show that the LFNN model achieves comparable performance to the closed-form solution on simulated data. We apply the LFNN approach to a four-asset investment scenario with bootstrap resampled asset returns. The LFNN strategy consistently outperforms the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the terminal date. These results suggest that during persistent inflation regimes, investors should favor short-term bonds over long-term bonds, and the equal-weighted stock index over the cap-weighted stock index.