Paper Reading: STABLE – A Robust Portfolio Allocation Method Using Conditional Diffusion Estimates

Background

In dynamic financial markets where regimes shift, portfolio decisions must balance high returns with controlled volatility and drawdown. Existing methods face three challenges: (1) difficulty jointly modeling macro and firm‑specific factors, (2) uncertainty of factor influence over time and assets, and (3) inadequate risk diversification when assets are correlated.

Traditional optimization relies on historical returns and performs poorly under regime changes, while deep‑reinforcement‑learning approaches tend to over‑fit macro signals and ignore stock‑level idiosyncrasies.

Problem Definition

Given macro conditions m_{\tau}, single‑stock conditions c^{s}_{\tau}, a prior window \nu, prior mean \mu_{prior,\tau} and covariance \Sigma_{prior,\tau} computed from the most recent \nu trading days, and an investment horizon l, the goal is to find portfolio weights that maximize expected return while satisfying the budget constraint:

Method

Conditional Diffusion Generator (CDG)

Regime‑aware Sampling STABLE uses a Denoising Diffusion Implicit Model (DDIM) conditioned on macro and firm signals to generate stock‑level return trajectories. The forward process adds Gaussian noise to a log‑return random walk, and the reverse process learns to denoise, producing trajectories consistent with the given market and company state.

Input Refinement At each rebalancing time \tau, macro features m_{\tau} are linearly transformed by W_{m}. Firm‑specific features c^{s}_{\tau} concatenate a time‑stock embedding \beta^{s}_{\tau}, the last normalized adjusted close price, and daily log‑return, then pass through W_{c} to obtain refined stock‑level conditions.

Time‑Stock Embedding A Kalman filter estimates a time‑varying coefficient \beta^{s}_{\tau} by regressing stock log‑returns on macro vectors, yielding a robust embedding that captures each stock’s sensitivity to macro factors over time.

Conditional DDIM Synthesis The conditional denoiser updates the latent state according to multi‑level conditions, following the DDIM recursion.

Training Objective STABLE minimizes diffusion MSE across all stocks, rebalancing times, and DDIM steps, adding an l_2 penalty to mitigate over‑fitting.

Multi‑Level Guidance (MLG)

For each (\tau, s), noise is decomposed into shared macro influence and stock‑specific residual. A stock‑specific gate z^{s}_{\tau} balances the two, reflecting that macro impact varies over time and differs across stocks.

The joint optimization minimizes diffusion MSE while the gate adapts to the macro‑level signal h^{s}_{f,\tau}. The resulting loss is:

Black‑Litterman‑based Mean‑Variance Optimizer (BL‑MVO)

STABLE feeds the time‑series forecasts from CDG+MLG into the Black‑Litterman framework to obtain posterior expected returns and covariances, then solves a mean‑variance optimization to produce the final portfolio weights.

The weights that maximize the Sharpe ratio are derived by minimizing the negative log‑posterior:

Experiments

Experimental Setup

Datasets: Four region‑balanced equity datasets – US S&P 500, China CSI 300, Europe EUROSTOXX, and Korea KOSPI 200.

Baselines: Portfolio allocation methods – equal‑weight (CRP), classic mean‑variance (MVO), momentum (MOM), RL‑based DeepTrader, MetaTrader, AlphaMix. Time‑series prediction baselines – Diffusion‑TS, AEC‑GAN, KoVAE.

Metrics: Portfolio performance – annualized Sharpe ratio (ASR), relative max drawdown (RMDD), annualized volatility (AVol). Forecasting – mean‑squared error (MSE) and dynamic time warping (DTW).

Hyper‑parameters: Grid‑searched window length l, encoder widths, DDIM steps, number of guided paths k, noise scale \eta, gate cap z_{max}, BL prior window \nu, and l_2 weight \beta.

Results

Portfolio Management (Q1)

STABLE ranks first on ASR, RMDD, and AVol across all regions, delivering higher risk‑adjusted returns while reducing drawdown and volatility. Traditional methods are sensitive to regime shifts; DeepTrader performs worst, and AlphaMix is the strongest competitor. STABLE’s advantage stems from its time‑varying Kalman beta embeddings and stock‑level regime adaptation.

Time‑Series Forecast Accuracy (Q2)

STABLE achieves the lowest MSE and DTW in every market, indicating the most accurate conditional return forecasts. Diffusion‑TS is the strongest baseline but still lags behind STABLE, which benefits from separating system and idiosyncratic noise and dynamically weighting them per stock and time.

Stock Embedding Quality (Q3)

Nearest‑neighbor analysis on representative US stocks shows that STABLE’s dynamic embeddings track market shifts: Tesla’s neighbors move from large‑cap tech in 2021 to AI‑related firms by end‑2024, while Bank of America’s neighbors remain stable, confirming the method captures sector‑level relationships.

Multi‑Market Regime Performance

During the COVID‑19 crisis and zero‑interest‑rate policy periods, STABLE consistently attains the best ASR, RMDD, and AVol across markets, demonstrating strong resilience to extreme regime changes.

Ablation Study

Removing any component (Kalman‑beta embedding, MLG, or BL‑MVO) degrades performance; the BL‑MVO module has the largest impact, with its removal causing the greatest ASR drop in every market.

Hyper‑parameter Analysis

Sensitivity analysis shows that k = 50 (guided paths per stock) yields peak ASR with diminishing returns beyond that, and \beta = 0.001 provides the best trade‑off between regularization and performance; larger values over‑regularize and hurt results.

Conclusion

STABLE demonstrates that coupling a conditional diffusion generator with a Black‑Litterman optimizer and multi‑level guidance yields a robust, style‑aware portfolio allocation method. It substantially improves Sharpe ratios, reduces drawdowns, and delivers state‑of‑the‑art time‑series forecasts across diverse equity markets.

Paper link: https://openreview.net/pdf?id=VltZQpfarw

Code repository: https://github.com/iclr26stable