3D Portfolio Risk Simulator — Correlated Monte Carlo VaR

2-Asset Portfolio (3D)

Weight — Asset A 55%

Correlation ρ(A,B) 0.3

Volatility σ_A 24%

Volatility σ_B 9%

Confidence level

Trials run

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Mean return

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VaR (loss)

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Expected Shortfall

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Std dev

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P(loss)

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How it works

Every trial simulates two correlated assets instead of one. Each day's shocks are drawn from independent standard normals (Z₁, Z₂) and combined through a Cholesky decomposition so the two return streams carry the requested correlation ρ — the way a real equity/bond book moves together (or apart) under stress.

Z_B' = ρ·Z_A + √(1−ρ²)·Z_B
R_A, R_B = terminal simple returns of each asset's GBM path
R_p = w·R_A + (1−w)·R_B   (portfolio return)
VaR_α = −Quantile(R_p, 1−α),  ES_α = −mean(R_p | R_p ≤ −VaR_α)

Each outcome marker is one simulated trial, placed on a growing grid; its height is the trial's portfolio return — positive returns rise in teal, losses drop in red.
The amber plane marks the VaR level; the red plane below it marks Expected Shortfall — the average of everything that fell through the VaR floor.
Correlation ρ is the key 3D-only lever: push it toward +1 and losses in A and B start co-occurring, fattening the portfolio's own loss tail even though neither asset's individual volatility changed — diversification stops helping.

Real-world relevance: correlation breakdown between "diversified" assets during market stress is exactly what turns a well-hedged book into a concentrated one — this is the mechanism risk desks stress-test for.

Gain trial Loss trial VaR plane ES plane

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