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Taming Tail Risk in Financial Markets: Conformal Risk Control for Nonstationary Portfolio VaR

Marc Schmitt

TL;DR

This work tackles tail-risk control in nonstationary financial time series by wrapping any base quantile forecaster with Regime-weighted Conformal Risk Control (RWC). RWC calibrates a safety buffer using a weighted quantile of past conformity scores, combining recency weighting and regime-similarity kernels to stabilize VaR exceedances across recurring market states. Theoretical results include exact finite-sample coverage under weighted exchangeability and approximate regime-conditional bounds under smoothly drifting regimes, with an explicit effective sample size analysis. Empirically, time-weighted calibration (TWC) serves as a strong default under drift, while regime weighting (RWC) can improve regime-conditional stability in settings with slower base-model adaptation, as demonstrated on CRSP US equity data. Overall, the approach provides a modular, model-agnostic reliability layer for risk forecasting pipelines that can adapt to nonstationarity and regime structure while offering finite-sample guarantees.

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.

Taming Tail Risk in Financial Markets: Conformal Risk Control for Nonstationary Portfolio VaR

TL;DR

This work tackles tail-risk control in nonstationary financial time series by wrapping any base quantile forecaster with Regime-weighted Conformal Risk Control (RWC). RWC calibrates a safety buffer using a weighted quantile of past conformity scores, combining recency weighting and regime-similarity kernels to stabilize VaR exceedances across recurring market states. Theoretical results include exact finite-sample coverage under weighted exchangeability and approximate regime-conditional bounds under smoothly drifting regimes, with an explicit effective sample size analysis. Empirically, time-weighted calibration (TWC) serves as a strong default under drift, while regime weighting (RWC) can improve regime-conditional stability in settings with slower base-model adaptation, as demonstrated on CRSP US equity data. Overall, the approach provides a modular, model-agnostic reliability layer for risk forecasting pipelines that can adapt to nonstationarity and regime structure while offering finite-sample guarantees.

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.
Paper Structure (55 sections, 2 theorems, 28 equations, 2 figures, 7 tables, 1 algorithm)

This paper contains 55 sections, 2 theorems, 28 equations, 2 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Background and related work
  4. Problem setup: sequential portfolio risk control
  5. Timing convention (causality).
  6. Base quantile forecaster.
  7. Conformity scores.
  8. Method: Regime-weighted conformal calibration
  9. Regime representation and weighting
  10. Preprocessing of regime features.
  11. Weighted conformal inference.
  12. Weighted conformal quantile
  13. Calibration index set.
  14. Weighted quantile threshold.
  15. Finite-sample correction (optional).
  16. ...and 40 more sections

Key Result

Theorem 5.2

Under Assumption ass:weighted_exch, the RWC bound $U_t = \hat{q}_t + \hat{c}_t$ with $\hat{c}_t$ defined in eq:ct_def satisfies

Figures (2)

  • Figure 1: Rolling 1-year exceedance rate for 99% VaR ($\alpha=0.01$) on the CRSP value-weighted index (GBDT base). The dashed horizontal line indicates the target exceedance level. The dotted vertical line marks the start of the test period. Shaded regions indicate the 2008--2009 financial crisis and the 2020 COVID shock.
  • Figure 2: Rolling 1-year exceedance rate for 99% VaR ($\alpha=0.01$) on the CRSP value-weighted index (HS base). The dashed horizontal line indicates the target exceedance level. The dotted vertical line marks the start of the test period. Shaded regions indicate the 2008--2009 financial crisis and the 2020 COVID shock.

Theorems & Definitions (2)

  • Theorem 5.2: Finite-sample weighted coverage
  • Theorem 5.4: Approximate regime-conditional coverage under smooth drift (informal)