Dynamic-Parametric-VaR-Calculation-Backtesting

Overview

This project implements a rolling-window parametric VaR model for an equity portfolio using historical returns and a normal distribution assumption. The model is evaluated through backtesting and exception analysis.

Assets

• Apple (AAPL)
• Microsoft (MSFT)
• Google (GOOGL)

Methodology

• Daily log returns are computed from adjusted prices
• Portfolio returns are calculated using fixed weights
• Mean and volatility are estimated using a rolling window
• VaR is computed at a specified confidence level
• Backtesting is performed by counting VaR exceptions

Diagnostics

• Rolling VaR vs realized returns
• Return distribution with VaR and Expected Shortfall
• QQ plot to assess normality assumptions

How to Run

1. Install dependencies: pip install -r requirements.txt
2. Open the notebook: dynamic_parametric_var.ipynb
3. Run all cells sequentially

Results Summary

• Rolling VaR closely tracks changes in portfolio volatility
• Backtesting shows a small number of VaR breaches
• Exception rate is slightly above the theoretical level, reflecting fat-tailed equity returns
• QQ plot indicates deviations from normality in the tails

Limitations

• Assumes normally distributed returns
• Does not model volatility clustering
• Not intended for regulatory capital calculations

Future Enhancements

• GARCH-based volatility
• Historical and Monte Carlo VaR