Interpretable Allocation and Model-Predictive Rebalancing of Equity Portfolios, Tested on Real and Synthetic Markets

Abstract

A live equity portfolio poses three problems: which stocks to hold, when to trade, and whether the strategy holds up beyond the observed market. We built one system for all three and tested it on 373 US equities, calibrated on 2014-2024 and traded from January 2025 to September 2026. A selection rule chose stocks by score, by a bandit, or at random, and one of seven weighting rules, four consumer-theory utilities, and three standard portfolios, set share counts under limits on budget, single-stock weight, portfolio volatility, and turnover, with each stock's preference weight a bounded score of its trend, market beta, and the market's recent direction. A model-predictive controller forecasts portfolio value with a multi-asset geometric Brownian motion and re-planned at its horizon, when the value left its forecast band, or at a drawdown stop. To probe deeper declines than the real window held, we also ran the system on simulated markets from per-asset hidden Markov generators with jumps, linked by market and sector factors. On real prices, the stocks chosen mattered more to terminal wealth than the weighting rule, and the early re-plans shrank the worst drawdown in most rule combinations against a fixed calendar without consistently raising wealth. In the deepest simulated declines, every combination, random picks included, ended above simulated SPY and the equal-weight universe in the median, even without early re-plans, so the margin came from shared parts of the system, not from stock selection or re-plan timing. A market hedge that tightened a beta cap as the market weakened cost wealth on real prices but paid off in the most sustained simulated declines, and the generator's persistent trends favored score-based selection more than the real market did, which suggests a synthetic test judges stock selection fairly only if its generator does not build in that persistence.