Paper: arXiv 2602.03903

Authors: Marc Schmitt

Abstract

Risk forecasts drive trading constraints and capital allocation, yet losses are nonstationary and regime-dependent. This paper studies sequential one-sided VaR control via conformal calibration. I propose regime-weighted conformal risk control (RWC), which calibrates a safety buffer from past forecast errors using exponential time decay and regime-similarity weights from regime features. RWC is model-agnostic and wraps any conditional quantile forecaster to target a desired exceedance rate. Finite-sample coverage is established under weighted exchangeability, and approximation bounds are derived under smoothly drifting regimes. On the CRSP U.S.\ equity portfolio, time-weighted conformal calibration is a strong default under drift, while regime weighting can improve regime-conditional stability in some settings with modest conservativeness changes.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a solid theoretical framework for regime-weighted conformal risk control with explicit finite-sample coverage and approximation bounds under nonstationarity. It complements the theory with a practical, algorithmic pipeline and empirical validation on U.S. equity portfolio data.

Research Flowchart

  flowchart TD
    A["<b>Research Goal</b><br/>Ensure valid portfolio VaR coverage under nonstationary financial regimes"] --> B["<b>Inputs & Features</b><br/>Base quantile forecasts & regime features (CRSP U.S. Equity Data)"]
    
    B --> C["<b>Regime-Weighted Conformal Risk Control (RWC)</b><br/>Compute past forecast errors (pinball loss/exceedances)"]
    
    C --> D["<b>Conformal Calibration Process</b><br/>Apply exponential time decay & regime-similarity weighting"]
    
    D --> E["<b>Output Strategy</b><br/>Wrap base forecaster with dynamically calibrated safety buffer"]
    
    E --> F["<b>Key Outcomes & Findings</b><br/>• Time decay provides strong default under drift<br/>• Regime weighting enhances regime-conditional stability<br/>• Guarantees valid finite-sample VaR coverage"]

Cited References (32)

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  2. A Tutorial on Conformal Prediction (2008)
  3. Conformalized Quantile Regression (2019)
  4. Conformal Prediction Under Covariate Shift (2019)
  5. The Limits of Distribution-Free Conditional Predictive Inference (2021)
  6. Conformal Prediction Beyond Exchangeability (2023)
  7. Adaptive Conformal Inference Under Distribution Shift (2021)
  8. Conformal Inference for Online Prediction with Arbitrary Distribution Shifts (2024)
and 24 more
  1. Conformal PID Control for Time Series Prediction (2023)
  2. Conformal Risk Control (2024)
  3. Conformal Prediction Interval for Dynamic Time-Series (2021)
  4. Sequential Predictive Conformal Inference for Time Series (2023)
  5. Adaptive Conformal Predictions for Time Series (2022)
  6. Practical Adversarial Multivalid Conformal Prediction (2022)
  7. Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction (2023)
  8. Class-Conditional Conformal Prediction with Many Classes (2023)
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  11. How Accurate Are Value-at-Risk Models at Commercial Banks? (2002)
  12. Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices (2001)
  13. Procyclical Leverage and Value-at-Risk (2014)
  14. Optimization of Conditional Value-at-Risk (2000)
  15. CAViaR : Conditional Autoregressive Value at Risk by Regression Quantiles (2004)
  16. Techniques for Verifying the Accuracy of Risk Measurement Models (1995)
  17. Evaluating Interval Forecasts (1998)
  18. Generalized Autoregressive Conditional Heteroskedasticity (1986)
  19. Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach (2000)
  20. Minimum Capital Requirements for Market Risk (2019)
  21. LightGBM : A Highly Efficient Gradient Boosting Decision Tree (2017)
  22. Volatility-Managed Portfolios (2017)
  23. EX-DRL : Hedging Against Heavy Losses with EXtreme Distributional Reinforcement Learning (2024)
  24. Fusing Narrative Semantics for Financial Volatility Forecasting — → 2510.20699

1 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.