Portfolio Tail Risk: A Multivariate Extreme Value Theory Approach.

Area of Science:

• Quantitative Finance
• Risk Management
• Econometrics

Background:

• Accurate assessment of portfolio tail risk is crucial for financial institutions.
• Traditional multivariate methods often struggle to model extreme market movements effectively.
• Extreme Value Theory (EVT) offers a robust framework for analyzing tail events.

Purpose of the Study:

• To develop and validate a novel method for portfolio tail risk assessment using EVT.
• To provide closed-form expressions for key risk measures like Value at Risk (VaR) and Expected Shortfall (ES).
• To evaluate the forecasting performance of the proposed method on U.S. stock portfolios.

Main Methods:

• Application of separate univariate estimations within the EVT framework.
• Derivation of closed-form solutions for VaR and ES.
• In-sample goodness-of-fit tests and out-of-sample backtesting across multiple quantiles.
• Numerical simulations to corroborate empirical findings.

Main Results:

• The proposed EVT-based method demonstrates superior performance in portfolio risk modeling compared to multivariate parametric methods, especially during extreme market movements.
• In-sample tests confirm the model's suitability for capturing tail risk.
• Backtesting results indicate that the model is statistically robust, even when including periods of market stress.
• Numerical simulations validate the empirical evidence.

Conclusions:

• The developed EVT-based methodology provides a more accurate and reliable approach to portfolio tail risk assessment.
• The closed-form expressions for VaR and ES simplify practical implementation.
• The model's strong performance in backtesting and simulations suggests its utility for financial risk management in volatile markets.