📊 Backtesting and evaluating Value-at-Risk (VaR) models and risk-aware portfolio strategies using US technology equities.
End-to-end pipeline combining VaR estimation, statistical backtesting, loss forecasting, and portfolio risk decomposition.
- Objective: Evaluate the robustness of standard VaR models and investigate alternative methods for tail-risk measurement.
- Motivation: While VaR is widely adopted for regulatory reporting, its reliability depends heavily on distributional assumptions. High-volatility assets often violate Gaussian assumptions, motivating more robust approaches such as Expected Shortfall and bootstrap methods.
- Scope:
- VaR estimation and backtesting (90% & 99% confidence)
- Multi-day loss forecasting (5–50 days)
- Portfolio risk decomposition across six US tech stocks
- Data: Daily returns of six US technology stocks (2014–2024).
- VaR estimation models:
- Parametric: Gaussian, Student’s-t, EWMA
- Non-parametric: Historical Simulation, Standard Bootstrap, Filtered Block Bootstrap (GARCH)
- Backtesting:
- Kupiec POF (unconditional coverage)
- Christoffersen Conditional Coverage
- Probability Integral Transform (PIT) tests
- Portfolio optimisation:
- Equally Weighted, Risk Parity (parametric & non-parametric), Maximum Diversification
- Risk decomposition by marginal VaR contribution
- VaR backtesting:
- At 90% confidence: Bootstrap produced 268 violations vs Gaussian 261 (expected 250).
- At 99% confidence: Gaussian underpredicted tail risk (78 violations vs expected 25; only 37 observed under bootstrap).
- Portfolio performance:
Strategy Sharpe Max Drawdown 95% VaR Violations Cumulative Return Equally Weighted 1.25 -36.35% 7 0.406 Risk Parity (Param) 1.32 -13.2% 8 0.425 Maximum Diversification 1.30 -13.8% 8 0.418 Risk Parity (Non-Param) 1.28 -14.0% 7 0.412 - Loss forecasting: Both Gaussian and bootstrap methods converged to ~17.5% probability of >5% portfolio loss over a 50-day horizon.
- Standard Gaussian VaR fails in high-volatility tech portfolios, underestimating extreme losses at 99% confidence.
- Bootstrap and block bootstrap methods better capture fat tails and regime dependence.
- Risk-aware portfolios (Risk Parity, Maximum Diversification) achieve higher Sharpe ratios and reduced drawdowns relative to naïve equal weighting.
- Expected Shortfall is more coherent than VaR, especially in capturing tail behaviour under stress.
MATLAB (Statistics & Econometrics Toolboxes); dependencies noted in Task.pdf.
- Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk.
- Christoffersen, P. (2012). Elements of Financial Risk Management.
- Basel Committee on Banking Supervision. International Convergence of Capital Measurement and Capital Standards.