Risk-Analysis

📉 SMM272 – Risk Analysis Coursework (2024/25)

Abstract
This project investigates financial risk modelling through Value-at-Risk (VaR) forecasting, portfolio construction techniques, and bond risk estimation using both analytical and simulation-based methods. We address Questions 1, 2, and 3 from the Risk Analysis coursework, implementing parametric, non-parametric, and Monte Carlo frameworks using Python. Key outputs include VaR backtesting using Christoffersen tests, comparative performance of Risk Parity vs Diversification strategies, and delta-gamma based bond risk measures. The work critically evaluates the limitations of model assumptions and the robustness of alternative risk estimation approaches.

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✅ Covered Questions

📊 Question 1 – Portfolio VaR Modelling

• Assets: AAPL, MSFT, IBM, NVDA, GOOGL, AMZN (2014–2024)
• Tasks:
  • Return statistics and distributional tests (skewness, kurtosis, Jarque-Bera)
  • VaR forecasts using:
    • Parametric (Normal)
    • Parametric (t-Distribution)
    • Delta-Gamma Approximation
    • Non-Parametric Bootstrap
    • Bottom-Up Monte Carlo (RiskMetrics)
  • Backtesting:
    • VaR Violations Count
    • Unconditional & Conditional Coverage Tests
    • Distributional Test (transformed probability histogram)
• Insights:
  • Normal distribution underestimates tail risk
  • Bootstrap VaR captures leptokurtic behaviour but lags recent volatility
  • Monte Carlo with EWMA provides adaptive risk estimation

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📈 Question 2 – Risk Parity and Portfolio Construction

• Portfolios:
  • Risk Parity Portfolio (RPP)
  • Maximum Diversification Portfolio (MDP)
  • Equally-Weighted Portfolio (EWP)
• Steps:
  • Component VaR and Conditional VaR using parametric and non-parametric methods
  • Out-of-sample backtesting using:
    • Sharpe Ratio
    • Maximum Drawdown
    • VaR Violations
    • Skewness & Excess Kurtosis
• Insights:
  • MDP has highest Sharpe ratio but largest drawdowns
  • RPP shows more balanced risk allocation
  • EWP has high simplicity but suboptimal tail risk control

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💵 Question 3 – Bond VaR Estimation

• Bond Parameters:
  • Face Value: 100 | Maturity: 10 years | Coupon: 5% | Current Price: 99
  • YTM volatility: σ = 0.006 (daily, i.i.d. normal)
• VaR Methods Compared:
  1. Exact (Full Revaluation)
  2. Delta Approximation
  3. Delta-Gamma Approximation
  4. Monte Carlo (Delta / Delta-Gamma / Full)
• Expected Shortfall: Estimated via Monte Carlo Full Revaluation
• Insights:
  • Delta-Gamma improves curvature estimation but underestimates tail losses over long horizons
  • Full revaluation captures convexity effects more accurately

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📁 Repository Structure

risk-analysis-cw/
├── Question1.ipynb             # Portfolio VaR modelling & backtesting
├── Question2.ipynb             # Portfolio construction and performance evaluation
├── Question3.ipynb             # Bond VaR and ES via analytical and simulation methods
├── DataQ2.xlsx                 # Data used in portfolio optimisation (Q2)
├── Risk_Analysis_Report.pdf # Final coursework report
├── CourseWork_QF_MTF_FM_QF_2024_25-3.pdf # Official coursework instructions
├── README.md                   # Coursework overview (this file)

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👨‍👩‍👦‍👦 Authors

• Gael Chen
• Theo Cadier
• Lorenzo Rossi
• Stéphane Leboyer

City, University of London – MSc Quantitative Finance

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📚 Key References

• Jorion, P. (2012). Value at Risk: The New Benchmark for Managing Financial Risk
• Ballotta & Fusai (2017). A Gentle Introduction to Value at Risk
• Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering
• Christoffersen, P. (2003). Elements of Financial Risk Management

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