Market Risk: VaR & Expected Shortfall Pipeline

A complete, production-style market risk pipeline implemented from scratch in Python.
Built as a quantitative finance portfolio project targeting buy-side and sell-side risk roles.

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Portfolio

ETF	Exposure	Asset Class
SPY	30%	US Large-Cap Equity
TLT	20%	US Long-Term Treasury
GLD	25%	Gold (Inflation hedge)
EEM	15%	Emerging Market Equity
LQD	10%	US Investment Grade Credit

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Methods

Method	Type	Notes
Historical Simulation	Non-parametric	Rolling 252-day window
Normal (Parametric)	Parametric	Gaussian tails
Student-t	Parametric	MLE ν via 3-param joint optimization
Monte Carlo	Simulation	N = 50,000, Normal innovations
GARCH(1,1)-t	Conditional	Volatility-adaptive, Student-t innovations

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Key Results (2018–2024 sample)

Metric	Value
Annualised Return	5.90%
Annualised Volatility	10.80%
Excess Kurtosis	9.48 (Gaussian rejected, JB p ≈ 0)
MLE ν̂	4.11 CI 95%: [3.50, 4.71]
VaR 99% Historical	1.60%
VaR 99% Student-t	1.78%
Diversification benefit (VaR 99%)	~43%
GARCH: α + β	0.9808 (vol half-life ≈ 36 days)

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Backtesting (OOS 2019–2024, α = 99%)

Model	Violations	Kupiec	Basel Zone
Historical	23	PASS	Green (k = 3.0)
Normal	27	FAIL	Green (k = 3.0)
Student-t	19	PASS	Green (k = 3.0)
GARCH(1,1)-t	23	PASS	Green (k = 3.0)

All models fail Christoffersen CC (violation clustering during COVID-19 / 2022).
This is a model-class limitation, not a single-model failure: no static VaR handles regime shifts.

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Stress Scenarios

Event	Period	Cumulative Loss	Peak / VaR 99%
COVID-19 crash	Feb–Mar 2020	−16.2%	3.7×
2022 Rate Shock	Jan–Oct 2022	−22.7%	2.0×
Aug 2015 Flash Crash	Aug 18–26, 2015	(requires 2014+ data)	—

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Repository Structure

market-risk-var-es/
├── VaR_ES_Market_Risk.ipynb   ← Narrative notebook (render document)
├── var_es_pipeline.py         ← Pure Python pipeline (executable)
├── download_data.py           ← Data fetch from Yahoo Finance
├── generate_notebook.py       ← Regenerates the .ipynb from scratch
├── requirements.txt
├── .gitignore
└── data/                      ← CSV files (not tracked in git)

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Quick Start

# 1. Install dependencies
pip install -r requirements.txt

# 2. Download historical data (2014–2024)
python download_data.py

# 3. Run the pipeline
python var_es_pipeline.py

# 4. Or open the narrative notebook
jupyter notebook VaR_ES_Market_Risk.ipynb

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Technical Highlights

• MLE for ν: 3-parameter joint optimization (ν, μ, σ) with profile Hessian CI.
  Fixing σ=1 on standardized returns is a common pitfall — it biases ν̂ upward by 2–3×.
• No look-ahead bias: rolling VaR uses .shift(1) before aligning with OOS returns.
• GARCH-t: arch library, GARCH(1,1) with Student-t innovations.
  α + β < 1 ensures covariance stationarity.
• Basel II zones: exception counts scaled to T=250, multiplier k ∈ {3.0, 3.40, …, 4.0}.
• Christoffersen CC: includes explicit power caveat for T≈1500, α=99%.

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Extensions (Planned)

• GJR-GARCH (leverage effect: σ↑ more after negative returns)
• Filtered Historical Simulation (FHS) — Basel FRTB IMA standard
• DCC-GARCH (dynamic correlations — resolves 2022 SPY/TLT breakdown)
• EVT/GPD (Extreme Value Theory beyond 99% quantile)
• t-Copula Monte Carlo (non-linear tail dependence)

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Author

Tancrede G · github.com/tancredeg