Factor-based deep reinforcement learning for asset allocation: Comparative analysis of static and dynamic beta reward designs

Traditional asset allocation rules, while effective in stable phases, tend to erode once markets enter volatile regimes or undergo structural breaks. Research in deep reinforcement learning (DRL) has usually emphasized raw-return rewards, leaving aside the role of factor exposures ([Formula: see text]) that shape both risk-adjusted payoffs and adaptive responses. This paper advances a Factor-based Deep Reinforcement Learning for Asset Allocation (FDRL) framework in which [Formula: see text] sensitivities-estimated via rolling regressions on momentum, volatility, deviation, and volume signals-inform both the state representation and the reward design. Five reward variants are examined (Sharpe, Sortino, Static-[Formula: see text], Dynamic-[Formula: see text], Momentum-[Formula: see text]) using PPO, SAC, and TD3 across equities, cryptocurrencies, macroeconomic instruments, and mixed portfolios. Empirically, [Formula: see text]-based rewards generate heterogeneous but interpretable patterns. In equities, Dynamic-[Formula: see text] improves annualized returns from roughly 20% (Sharpe baseline) to 23-24%, with Sharpe rising from 1.04 to about 1.27 across windows. In cryptocurrencies, Dynamic-/Momentum-[Formula: see text] achieve 38-43% annual returns but remain highly regime-sensitive, with drawdowns often exceeding -35%. In macro instruments, Static-[Formula: see text] delivers the most stable behaviour, maintaining volatilities near 8-9% and limiting drawdowns to roughly -18%. In mixed-asset portfolios, Momentum-[Formula: see text] under TD3 produces the strongest gains (cumulative returns above 70-80%), exceeding equal-weight baselines whose CAGR remains near 19-22% with Sharpe ratios around 1.25. All findings were validated through beta-window sensitivity checks (30/60/90/120 days), regime-conditional analysis, and multiple robustness tests including HAC, Wilcoxon, jackknife Sharpe, moving-block bootstrap, and false-discovery-rate adjustments. These diagnostics confirm that the main performance patterns are not driven by window choice or serial dependence. Four contributions follow. First, a reward structure operationalizing time-varying [Formula: see text]. Second, systematic benchmarking of factor-sensitive objectives. Third, evidence on asymmetric outcomes across asset classes. Finally, a framework that reconciles responsiveness with interpretability and risk discipline in allocation.