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

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.