Multi-Asset Portfolio Risk Engine

Live app: multi-asset-portfolio-risk-engine.streamlit.app

A full institutional-style market risk pipeline for an 8-asset, $1M portfolio. Covers data ingestion, three VaR methods, CVaR (Expected Shortfall), statistical backtesting, stress testing across historical crises, GARCH(1,1)-t dynamic volatility modelling, and mean-variance portfolio optimization — all assembled into a single risk research project across 8 notebook phases.

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Portfolio

Asset	Ticker	Role
S&P 500 ETF	SPY	US Large Cap Equity
Nasdaq-100 ETF	QQQ	US Tech Equity
Intl Developed ETF	EFA	International Equity
Gold ETF	GLD	Safe Haven / Inflation Hedge
Long Treasury ETF	TLT	Duration / Flight-to-Safety
Investment Grade Bond ETF	LQD	Fixed Income
ExxonMobil	XOM	Energy / Commodity Exposure
Real Estate ETF	VNQ	Real Estate

Equal-weighted (12.5% each) | $1,000,000 portfolio | 2015–2024 (2,514 trading days)

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Pipeline

Phase 1 → Phase 2 → Phase 3 → Phase 4 → Phase 5 → Phase 6 → Phase 7 → Phase 8
 Data      VaR       CVaR     Backtest   Stress    Dashboard   GARCH-t   Optimizer

Each phase saves results to portfolio_data.pkl which is loaded by the next phase.

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Results

Phase 1 — Portfolio Construction

Diversification confirmed: portfolio annualised volatility (11.7%) is lower than every individual asset.

Asset	Ann. Return	Ann. Vol	Sharpe
SPY	12.29%	17.68%	0.695
QQQ	16.93%	21.88%	0.774
EFA	5.12%	17.38%	0.295
GLD	7.48%	14.13%	0.530
TLT	-1.20%	15.31%	-0.078
LQD	2.23%	8.60%	0.259
XOM	5.67%	27.79%	0.204
VNQ	4.71%	21.02%	0.224
Portfolio	6.66%	11.71%	0.568

Portfolio excess kurtosis = 16.99 — fat tails are present and the normality assumption is violated. This motivates using Historical Simulation and CVaR over parametric methods.

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Phase 2 — Value at Risk (Three Methods)

Method	95% VaR	99% VaR	95% VaR ($)	99% VaR ($)
Historical Simulation	1.061%	1.889%	$10,610	$18,886
Parametric	1.213%	1.716%	$12,132	$17,159
Monte Carlo	1.189%	1.701%	$11,891	$17,007

At 99%, Parametric VaR is lower than Historical Simulation — the normal distribution underestimates tail severity. This gap is model risk.

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Phase 3 — CVaR / Expected Shortfall

CVaR answers the question VaR cannot: given we are already having a bad day beyond VaR, how bad is it on average?

Method	95% VaR ($)	95% CVaR ($)	99% VaR ($)	99% CVaR ($)
Historical Simulation	$10,610	$17,442	$18,886	$31,791
Parametric	$12,132	$15,215	$17,159	$19,659
Monte Carlo	$11,891	$15,127	$17,007	$19,787

Historical CVaR/VaR ratio at 99% = 1.68x vs the theoretical normal ratio of 1.16x. The empirical tail is 45% fatter than normality assumes. Basel III replaced VaR with CVaR (Expected Shortfall) as the regulatory standard for this exact reason.

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Phase 4 — Backtesting (Kupiec + Christoffersen)

Rolling 252-day out-of-sample VaR forecasts tested against actual returns.

99% VaR Backtest Results

Method	Exceptions	Expected	Actual Rate	Kupiec	Christoffersen
Historical Sim	35	22.6	1.55%	FAIL	FAIL
Parametric	50	22.6	2.21%	FAIL	FAIL
Monte Carlo	49	22.6	2.17%	FAIL	FAIL

95% VaR Backtest Results

Method	Exceptions	Expected	Actual Rate	Kupiec	Christoffersen
Historical Sim	123	113.1	5.44%	PASS	FAIL
Parametric	106	113.1	4.69%	PASS	FAIL
Monte Carlo	105	113.1	4.64%	PASS	FAIL

All models pass Kupiec at 95% (correct frequency) but fail Christoffersen at both levels — exceptions cluster. For Historical Simulation at 99%: π11 = 14.3% vs π01 = 1.35% — after a VaR breach, another breach the next day is 10x more likely. Static models have no memory of volatility regimes.

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Phase 5 — Stress Testing

Historical crises and a hypothetical liquidity shock applied to the portfolio, compared against VaR/CVaR thresholds.

Scenario	Worst Single Day	Dollar Loss	vs 99% VaR
COVID Crash (Feb–Mar 2020)	7.81%	$78,102	4.14x
Rate Shock 2022	3.75%	$37,526	1.99x
Hypothetical Liquidity Shock	10.38%	$103,750	5.49x
99% VaR (reference)	1.89%	$18,886	1.00x
99% CVaR (reference)	3.18%	$31,791	1.68x

COVID's worst single day was 4x the 99% VaR. The 2022 rate shock broke the stock-bond negative correlation embedded in the covariance matrix — both TLT and LQD fell alongside equities, invalidating the diversification assumption.

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Phase 6 — Risk Dashboard

All results assembled into a single publication-quality figure (risk_dashboard.png) with 6 panels: cumulative return and drawdown, VaR/CVaR summary table, rolling VaR vs actual returns, exception timeline, stress test bar chart, and backtesting results table.

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Phase 7 — GARCH(1,1) with Student-t Innovations

Why static VaR models fail

Phase 4 revealed two distinct failure modes in all three models:

1. Wrong frequency (Kupiec) — too many exceptions at 99%, because normal-distribution-based thresholds underestimate how large tail losses actually are
2. Clustered exceptions (Christoffersen) — after one VaR breach, another is 10x more likely the next day (π11 = 14.3%). Static windows are blind to volatility regimes

The fix: GARCH(1,1)-t

GARCH(1,1) models time-varying conditional volatility:

σ²_t = ω + α·ε²_{t-1} + β·σ²_{t-1}

After a large shock, σ_t rises — so the next day's VaR threshold automatically widens. Pairing this with Student-t innovations (instead of normal) adds fat-tailed quantiles that reflect the portfolio's actual excess kurtosis of 16.99.

Results

Method	Exceptions	Expected	Act. Rate	π11	Kupiec	Christoffersen
Hist Sim (static)	35	22.6	1.55%	0.1429	FAIL	FAIL
Parametric (static)	50	22.6	2.21%	0.1200	FAIL	FAIL
MC (static)	49	22.6	2.17%	0.0816	FAIL	FAIL
GARCH-Normal	43	22.6	1.90%	0.0465	FAIL	FAIL
GARCH-t	24	22.6	1.06%	0.0417	PASS	PASS

GARCH-t is the only model that passes both regulatory tests. The progression shows what each assumption costs:

• GARCH-Normal fixed clustering (π11: 0.143 → 0.047) but not frequency — dynamic vol alone isn't enough when the tail distribution is wrong
• GARCH-t fixed both — 24 exceptions vs 22.6 expected, and π11 collapsed to near the unconditional rate

This mirrors the industry's own trajectory: pre-2008 banks used parametric VaR with normal distributions, underestimated tail risk, and failed backtests they didn't run. Basel III's response was to mandate CVaR and more robust volatility models.

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Phase 8 — Efficient Frontier & Portfolio Optimization

Phases 1–7 treated equal-weighting as given. Phase 8 asks: given the same 8 assets, what is the optimal allocation?

The mean-variance optimization problem is solved with long-only constraints (no shorting) across 60 target return levels to trace the efficient frontier, then three specific portfolios are extracted:

Minimum Variance — minimises portfolio variance, ignoring return. Dominated by LQD (lowest individual vol at 8.6%), GLD and TLT (low correlation with equities). Equities (SPY, QQQ, XOM) receive minimal allocation. Result: significantly lower vol and tail risk than equal-weight, at the cost of return.

Maximum Sharpe — the tangency portfolio, maximising return per unit of risk. Concentrates in QQQ (Sharpe 0.774) and SPY (Sharpe 0.695). TLT receives near-zero weight due to its negative Sharpe over the period. Result: highest return and Sharpe, but carries more equity concentration.

Equal Weight (benchmark) — sits inside the frontier, confirming it is mean-variance inefficient. Both optimised portfolios dominate it on a risk-adjusted basis.

Portfolio comparison across all three:

Portfolio	Ann. Return	Ann. Vol	Sharpe	99% VaR ($)	99% CVaR ($)
Equal Weight	6.66%	11.71%	0.568	$18,886	$31,791
Min Variance	lower	lower	comparable	lower	lower
Max Sharpe	higher	higher	higher	higher	higher

The key finding: portfolio construction choices directly affect tail risk, not just normal-times volatility. Minimum variance reduces 99% VaR and CVaR materially — meaningful in a risk management context. Maximum Sharpe improves the return-risk tradeoff but accepts higher tail exposure as a consequence of equity concentration.

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Interactive App

The research has also been packaged into an interactive Streamlit app that lets you run the full analysis on any set of tickers, date range, and portfolio weights in real time — VaR/CVaR across all three methods, rolling backtests with Kupiec and Christoffersen results, GARCH-t conditional volatility forecasting, and mean-variance portfolio optimization with the efficient frontier.

Live: multi-asset-portfolio-risk-engine.streamlit.app

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Setup

git clone <repo-url>
cd "VaR CVaR"

python -m venv .venv
# Windows
.venv\Scripts\activate
# Mac/Linux
source .venv/bin/activate

pip install -r requirements.txt

Running the Notebooks

Run notebooks in order — each phase saves to portfolio_data.pkl which the next phase loads:

notebooks/phase_1.ipynb
notebooks/phase_2.ipynb
notebooks/phase_3_VaR_ES.ipynb
notebooks/phase_4_backtest_kupiek.ipynb
notebooks/phase_5_stress_testing.ipynb
notebooks/phase_6_risk_dashboard.ipynb
notebooks/phase_7_GARCH.ipynb
notebooks/phase_8_efficient_frontier.ipynb