Conformal Prediction for Portfolio Risk: Beyond VaR

Overview

A distribution-free, mathematically rigorous alternative to standard Value at Risk (VaR) models. This article covers conformal prediction mechanics, Conformal Risk Control (CRC), and Regime-Weighted Conformal (RWC) for adaptive capital allocation. Based on Marc Schmitt's research on "Taming Tail Risk in Financial Markets".

The Failure of Traditional VaR

• Distributional Assumptions: Assumes normal distributions, underestimating tail risks.
• Stationarity Assumption: Assumes the future resembles the past, which breaks during regime changes.
• Model Risk: Parametric models (GARCH, EVT) rely heavily on precise parameter specification.

Conformal Prediction Fundamentals

Conformal prediction guarantees finite-sample validity without assuming a specific distribution.

• It uses a calibration set to compute "nonconformity scores" (how unusual an observation is).
• It calculates the (1 - α) quantile of these scores to construct valid prediction intervals under the exchangeability assumption.

Conformal Risk Control (CRC)

CRC extends conformal prediction to bound the expected loss rather than just interval coverage.

• Uses online learning to adjust prediction intervals dynamically in real-time.
• Ensures finite-sample validity for any sample size, unlike asymptotic models.

Regime-Weighted Conformal (RWC)

Standard conformal prediction assumes stationarity (exchangeability), which fails during market regime shifts.

• RWC assigns time-varying weights (e.g., via exponential decay or volatility-based metrics) to historical data.
• It identifies regimes (using VIX or HMMs) and weighs recent or similar-regime data heavier when computing the quantile of nonconformity scores.

Building an Adaptive Capital Allocation System

1. Data Preparation: Gather returns and regime indicators.
2. Base Model Selection: Choose a base model (even naive models work because the conformal layer corrects misspecification).
3. Nonconformity Score Design: Absolute or normalized residuals.
4. Regime Weighting: Implement decay parameters.
5. Risk Control Integration: Define loss function and target risk level α.
6. Capital Allocation: Use conformal VaR for dynamic stop-losses and leverage scaling.

Advantages & Limitations

• Advantages: Distribution-free, valid for finite samples, adapts to regimes automatically, model-agnostic, and optimizes true expected loss (CRC).
• Limitations: Still requires some intra-regime stationarity, needs large calibration sets for extreme tail estimation (e.g., 99% VaR), is highly dependent on accurate regime detection, and can be computationally expensive for high-frequency updates.