Market-linked stochastic simulation for private markets. How we model correlation, dynamic pacing, and realistic risk assessment.
Most private market Monte Carlo tools sample outcomes independently:
TVPI[i] ~ LogNormal(μ, σ)
IRR[i] ~ Normal(μ, σ)
// Each fund independent - WRONG
Problem: Private markets correlate with public markets. When S&P crashes, PE/VC funds don't stay independent. Capital calls slow, exits delay, marks compress.
Evidence: Korteweg & Sorensen (2010) show VC returns have β ≈ 1.4 vs public equity. Gompers et al. (2008) show investment drops 30-50% in bear markets.
Layer 1 (Economic): Correlated market paths (equity + bonds linked)
Layer 2 (Accounting): NAV smoothing and reporting lag (private marks lag public)
Layer 3 (Liquidity): Cash buffer constraints (realistic capital deployment)
Correlation Matrix:
Σ = [ σ²_equity ρ·σ_equity·σ_bond ]
[ ρ·σ_equity·σ_bond σ²_bond ]
Where ρ ≈ -0.2 (equity-bond correlation)
Cholesky Factor L (such that Σ = LL^T):
L = [ 1 0 ]
[ ρ √(1-ρ²)]
Algorithm:
1. Draw independent standard normals: z₁, z₂ ~ N(0,1)
2. Apply Cholesky: [r_equity, r_bond]^T = L × [z₁, z₂]^T
3. Scale to monthly returns:
R_equity(t) = μ_equity/12 + (σ_equity/√12) × r_equity
R_bond(t) = μ_bond/12 + (σ_bond/√12) × r_bond
Default Parameters:
• Equity: μ = 8% annual, σ = 18% annual
• Bonds: μ = 4% annual, σ = 6% annual
• Correlation: ρ = -0.2 (negative, flight to safety)
→ Why this matters: Realistic correlation means downside scenarios show funds moving together (like 2008), not independently. Better risk assessment.
Observation:
GPs slow capital calls in bear markets, accelerate in bull markets. Exits follow same pattern (Axelson et al., 2009).
Model:
Capital Call(t) = Base Call(t) × (1 + β_call × R_equity(t))
Distribution(t) = Base Dist(t) × (1 + β_dist × R_equity(t))
β_call = 0.4 (calls slow 40% in -100% crash)
β_dist = 0.5 (exits slow 50% in -100% crash)
Example Scenarios:
Bull Market (+20% equity): Calls +8%, Exits +10%
Normal (0%): Base schedule (no adjustment)
Bear (-30% equity): Calls -12%, Exits -15%
→ Why this matters: In downturns, all funds call capital together AND distributions slow. Realistic liquidity planning accounts for this.
1. Industry-Calibrated Exit Timing
Exit curves calibrated to Cambridge Associates and Preqin benchmarks (not arbitrary distributions).
PE Buyout: 5.8y median (4.9% error vs industry target)
Growth Equity: 6.2y median (1.9% error vs benchmark)
Early Venture: 7.7y median (industry-calibrated)
2. Realistic Cash Settlement Overlays
Models escrows, lockups, and trailing payments (not instant proceeds at exit).
Buyout exits: 95% at close, 5% over 18 months (escrows)
Growth IPOs: 90% at close, 10% over 24 months (lockups)
Venture exits: 85-90% at close, 10-15% trailing
3. Small-N Exit Realism (Lines Layer)
For small portfolios (<50 companies), models lumpy exits via correlated exit times (not smooth averaging).
12-company buyout: Top 2 exits = 58% of value ✓
Gaussian copula: ρ = 0.3 (realistic clustering)
Auto-enabled: Buyouts, Growth Equity, Venture <50 lines
4. Markov Regime Switching
Proper state propagation (π_t+1 = π_t × P) instead of expected multiplier. Exits cluster in bull markets, slow in bear markets.
Open regime: 1.6× hazard (bull market)
Shut regime: 0.4× hazard (bear market)
Persistence: p_OO=0.85, p_SS=0.75
Why This Matters:
1. Mean Matching
Sample mean converges to parameter mean (Law of Large Numbers). Error <0.05% over 10,000 iterations.
2. Variance Matching
Sample variance matches theoretical variance. Error <3% (within statistical bounds).
3. Correlation Preservation
Cholesky decomposition produces correct correlation. Measured ρ within ±0.05 of target.
4. Convergence Rate
Standard error decreases as σ/√N. Validates proper sampling.
5. Benchmark Comparison
Exit timing within 5-15% of Cambridge Associates/Preqin benchmarks (PE Buyout: 4.9% error vs 5.8y median). TVPI/IRR derived from calibrated timing and growth assumptions.
→ Bottom line: Use Monte Carlo when uncertainty really matters. For routine forecasting, deterministic is faster and clearer.
Schedule a technical discussion with our team or explore the engine yourself.