This repository hosts a quantitative framework for Market Risk Management and Model Validation, developed in R. The objective is to calculate regulatory risk metrics (Value at Risk) and perform independent validation (Backtesting) to assess model performance under stress.
Asset Universe: Energy Select Sector SPDR Fund (XLE) – serving as a proxy for commodity exposure and energy equity risk.
Data Ingestion: Automated data extraction from Yahoo Finance using quantmod.
We implemented a Historical Simulation approach (Full Valuation), which is non-parametric and makes no assumptions about the normality of return distributions.
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Value at Risk (VaR 99%): The quantile of the loss distribution such that:
$$P(L > VaR) = 1 - \alpha$$ (Where $\alpha = 0.99$. We look back 250 trading days). -
Expected Shortfall (ES 99%): The conditional expectation of loss given that the loss exceeds VaR (Tail Risk):
$$ES_{\alpha} = E[L | L > VaR_{\alpha}]$$ (This captures the "severity" of tail events, compliant with Basel III / FRTB standards). -
Model Validation (Backtesting):
- Detection of Breaches (Exceptions) where actual loss exceeds VaR.
- Visual inspection of model performance over time.
The chart below illustrates the model's performance over the 2020-2025 period, capturing the post-COVID recovery and the 2022 Energy Crisis.
- Blue Line: Value at Risk (99% Threshold).
- Orange Line: Expected Shortfall (Average loss when things go wrong).
- Red Dots: Actual market crashes that broke the model limit.
Observations:
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Volatility Clustering (Heteroskedasticity): The graph clearly shows that breaches are not randomly distributed but clustered during stress periods (e.g., 2020 and 2022). This confirms that financial returns exhibit volatility clustering—large changes tend to be followed by large changes.
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Fat Tails (Leptokurtosis): The significant gap between the Blue Line (VaR) and the Orange Line (ES) during high volatility indicates a "Fat-Tailed" distribution. The standard Normal distribution would underestimate these extreme losses. The ES metric proves crucial here, providing a buffer that VaR misses.
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Model Performance:
- Breach Count: 16 breaches over the sample period.
- Breach Rate: 1.27%, which is slightly higher than the theoretical 1.00% target.
- Conclusion: The Historical Simulation is robust but slightly slow to react to sudden regime changes (Ghost Effect). A volatility-weighted approach (e.g., EWMA or GARCH) could improve responsiveness.
- Language: R (v4.0+)
- Libraries:
quantmod,PerformanceAnalytics,ggplot2,dplyr.
Author: Alessandro D'Atria | Risk Management Professional