This project explores portfolio risk management using Parametric Monte Carlo Simulation applied to a portfolio of three major Indian banks: SBI, PNB, and BOB.
We assess portfolio return, standard deviation, and compute Value at Risk (VaR) across multiple confidence levels and time horizons to quantify downside risk and highlight diversification benefits.
Thanks to Mehul Mehta for the insightful lecture series that laid the foundation for this simulation-based approach.
- Total Investment: ₹100,000
- Weights:
- SBI: 30%
- PNB: 40%
- BOB: 30%
We used Parametric Monte Carlo Simulations grounded in the following three risk assessment methods:
Description:
- Assumes returns are normally distributed
- Uses mean and standard deviation of portfolio returns
- Considers covariance matrix for diversification effect
Process:
- Calculate portfolio mean and variance using asset weights and covariance matrix
- Estimate potential losses for different confidence intervals using Z-scores
Implications:
- Quick, reliable for portfolios with normally distributed returns
- Highlights tail risk (extreme losses) and diversification impact
Description:
- Simulates thousands of possible portfolio returns using random samples from a normal distribution defined by mean and SD
- Parametric, as it assumes normality but introduces randomized variability
Process:
- Generate random returns based on portfolio’s statistical parameters
- Aggregate results to estimate probability distribution of losses
- Calculate empirical VaR from simulation results
Implications:
- Captures non-linear risk dynamics
- More robust under uncertain future scenarios
- Enables stress testing over multiple horizons (1-day, 10-day, 1-month)
Description:
- Scales 1-day VaR to longer time frames (10-day, 1-month) using the square root of time rule
Formula:
Implications:
- Simple and intuitive for projecting risk over time
- Assumes returns are i.i.d. (independent and identically distributed)
- Practical for operational risk forecasting and compliance
| Metric | Value |
|---|---|
| Mean Return | 0.20% |
| Portfolio SD | 0.96% |
| Time Horizon | 99% CI | 95% CI | 90% CI |
|---|---|---|---|
| 1-Day | ₹-2,022.28 | ₹-1,370.31 | ₹-1,022.97 |
| 10-Day | ₹-6,395.01 | ₹-4,333.31 | ₹-3,234.90 |
| 1-Month | ₹-11,076.49 | ₹-7,505.52 | ₹-5,603.02 |
- Risk Estimation: Parametric VaR is crucial for identifying exposure under normal market conditions.
- Diversification Effect: Covariance analysis confirms that a balanced mix of SBI, PNB, and BOB reduces total portfolio risk.
- Decision-Making Tool: Monte Carlo Simulations empower investors to plan for extreme loss events and optimize portfolio allocation.
- Python (NumPy, Pandas, Matplotlib)
- Statistical Modeling
- Monte Carlo Engine
- Portfolio Theory
- Lecture Series by Mehul Mehta
- J.P. Morgan’s RiskMetrics™
- Hull, J. (Options, Futures, and Other Derivatives)
Feel free to explore, fork, or contribute to this project. For discussions on portfolio risk modeling or advanced simulations:
📧 rkchs07@gmail.com]
🔗 [https://www.linkedin.com/in/rohit-kumar-38a121284/]