The Fundamental Structure of Risk: From Characteristics to Covariance

Battle Count: 55

Directly addresses core quantitative trading infrastructure: covariance estimation for portfolio construction (GMV, ERC), factor model construction, and risk management. The zero-shot onboarding capability is highly practical for live trading systems where new assets enter/exit universes. The interpretable factor structure aids in strategy design and risk attribution. The characteristic-driven approach reduces dependency on noisy return data, which is valuable for robust risk models. The Stein loss objective directly targets the risk geometry used in portfolio optimization. However, it is a risk model rather than a return/alpha prediction model, so it supports rather than drives trading decisions.

The architecture involves multiple components: FT-Transformer-style tabular encoding (per-feature affine maps, categorical embeddings, concatenation, MLP), two linear heads (membership with softmax, loading with bias), factor return construction (market + long-short with L1 normalization), EWMA factor covariance, idiosyncratic variance estimation, and a learned scale parameter. End-to-end training with Adam, mini-batching over timesteps, early stopping on validation Stein loss. The fast covariance inversion via Woodbury identity (Appendix A) is essential for tractability. Hyperparameter tuning includes latent dimension D, number of factors K (via Marcenko-Pastur), loss weight α, EWMA half-life, lookback window, and forward horizon. Moderate to high complexity due to the multi-component architecture and careful training protocol.

Code is publicly available on GitHub (https://github.com/alexouadi/CD-DFM). Detailed hyperparameters are provided in Appendix B (Table 8). Training algorithm is fully specified (Algorithm 1). Fast covariance inversion derivation in Appendix A. However, the underlying data (S&P Global Compustat Xpressfeed, RavenPack Edge) are proprietary and not freely available, limiting full reproducibility. Results are reported as 5-seed means for CD-DFM and GKX, single fits for others. Chronological train/val/test splits with embargo are described.