Project 2:
A Monte Carlo simulation of a $100m multi-asset portfolio's one-day P&L, calibrated on real historical volatility, used to estimate Value at Risk (VaR) and Expected Shortfall (CVaR) — the two headline numbers a bank's market risk committee reports daily.
| Metric | 95% Confidence | 99% Confidence |
|---|---|---|
| Value at Risk (VaR) | $1,888,542 | $2,734,152 |
| Expected Shortfall (CVaR) | $2,404,020 | $3,145,086 |
Worst simulated 1-day loss: -$5,341,289 · Best simulated 1-day gain: $5,602,188
Full write-up: Market\_Risk\_Memo\_VaR\_CVaR.docx
| Constituents | AAPL (30%), MSFT (30%), JPM (20%), BARC.L (20%) |
| Notional | $100,000,000 |
| Calibration window | 2 years of daily historical closing prices |
| Simulation | 100,000 draws from Normal(mean, vol), calibrated on real historical returns |
The portfolio includes Barclays (BARC.L) alongside two US tech names and a US bank, both for relevance to this portfolio's theme and as a sanity check against a name with well-understood volatility.
market-risk-var-engine/
├── market\_risk\_var\_engine.ipynb # main analysis notebook
├── market\_risk\_var\_engine.py # standalone script version
├── Market\_Risk\_Memo\_VaR\_CVaR.docx # 1-page risk committee memo
├── output/
│ └── var\_pnl\_distribution.png # P\&L distribution chart
├── requirements.txt
├── .gitignore
└── LICENSE
Note: output/var\_simulation.csv (the raw 100,000-row simulated P&L output) is generated by
running the notebook/script and is not committed — see .gitignore.
python -m venv venv
source venv/bin/activate # venv\\Scripts\\activate on Windows
pip install -r requirements.txt
jupyter notebook market\_risk\_var\_engine.ipynbRequires an internet connection to download price history from Yahoo Finance via yfinance.
Results will vary slightly from the figures above as market data updates — the notebook is
calibrated on a live 2-year rolling window, not a fixed historical snapshot.
Monte Carlo simulation · real market data calibration (yfinance) · Value at Risk (VaR) ·
Expected Shortfall (CVaR) · historical-simulation sanity checking · NumPy · Pandas
- Returns are modelled as Normally distributed; real returns are typically fat-tailed, so this VaR/CVaR is best read as a lower bound on tail risk. A Student's-t or historical-simulation approach is a natural extension.
- 1-day horizon only; regulatory capital calculations typically require 10-day VaR, commonly approximated via the square-root-of-time rule.
- Correlation between constituents is captured only implicitly through the blended historical portfolio-return series, not as an explicit covariance matrix — sufficient for portfolio-level VaR, but not for single-asset what-if stress testing.
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