Market-Linked Monte Carlo for Private Equity Portfolios

Most Monte Carlo tools for private equity make a fatal assumption: private fund returns are independent of market conditions.

That's not realistic.

When the S&P 500 crashes 30%, your growth equity fund doesn't return 18%. When the Nasdaq rallies 50%, your VC fund doesn't flatline.

Yet most forecasting tools model PE/VC returns as if they exist in a vacuum—generating the same P10/P50/P90 outcomes whether we're in a bull market or the depths of 2008.

This post explains how to fix that.

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The Problem with Independent Simulations

Example: Traditional Monte Carlo

Let's say you're modeling a growth equity fund with:

• Target IRR: 18%
• TVPI: 2.5x
• Deployment period: 5 years
• Exit timing: Years 7-10

A traditional Monte Carlo simulation might work like this:

1. Sample IRR from a distribution (e.g., N(18%, 5%))
2. Sample deployment timing variations
3. Sample exit timing variations
4. Generate 1,000 iterations

Result: P10/P50/P90 outcomes that are identical whether the S&P 500 is at +25% or -30%.

Why This Breaks

Private equity funds—especially growth equity and venture capital—have systematic exposure to public equity markets. Their returns aren't random noise. They're correlated with:

• S&P 500: Large-cap growth exposure
• Russell 2000: Small-cap exposure
• Nasdaq: Tech-heavy VC funds
• Credit spreads: Buyout funds using leverage

When you ignore this, your Monte Carlo simulations produce unrealistic scenarios:

• Bear case (P10) looks too optimistic (ignores market crash impact)
• Bull case (P90) looks too conservative (ignores market rally boost)
• Base case (P50) might be fine, but the tails are wrong

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The Solution: Alpha + Beta Model

Core Formula

Instead of modeling returns as independent, model them as:

r_t = alpha + beta × market_returns_t + epsilon_t

Where:

• alpha = Fund-specific outperformance (manager skill, strategy)
• beta = Systematic market exposure
• market_returns_t = Public market benchmark returns (e.g., S&P 500)
• epsilon_t = Idiosyncratic noise (company-specific risk)

Example: Growth Equity Fund

Let's say your fund has:

• Alpha: 8% (manager outperforms market by 8%)
• Beta: 1.2 (amplifies market moves by 20%)

Bull Market (S&P +20%):

r = 8% + 1.2 × 20% = 8% + 24% = 32%

Bear Market (S&P -20%):

r = 8% + 1.2 × (-20%) = 8% - 24% = -16%

Flat Market (S&P +0%):

r = 8% + 1.2 × 0% = 8%

Now your Monte Carlo simulations produce realistic outcomes that vary with market conditions.

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Implementation: How Nagare Does It

Step 1: Calibrate Alpha to IRR

Given a target IRR (e.g., 18%), we need to find the alpha that preserves this target while modeling market exposure.

Algorithm:

1. Sample market returns from historical data (e.g., S&P 500 1990-2024)
2. Compute expected fund return: E[r] = alpha + beta × E[market]
3. Solve for alpha such that IRR(cashflows) = target_IRR

Example:

• Target IRR: 18%
• Beta: 1.2
• Historical S&P mean: 10%
• Alpha: 18% - 1.2 × 10% = 6%

Step 2: Sample Market Returns

For each Monte Carlo iteration:

1. Sample a market scenario (e.g., S&P 500 path)
2. Apply r_t = alpha + beta × market_t + epsilon_t
3. Build fund cashflows (capital calls + distributions)
4. Compute TVPI, DPI, IRR

Market scenarios:

• P10 (Bear): Worst 10% of historical market paths (e.g., 2008-2009)
• P50 (Base): Median market performance
• P90 (Bull): Best 10% of historical market paths (e.g., 2020-2021)

Step 3: MOIC-First Calibration

Problem: If you just apply alpha + beta × market to NAV growth, you can get unrealistic NAV paths that:

• Collapse to zero in bear markets
• Explode to 10x in bull markets
• Don't preserve the target TVPI

Solution: MOIC-First Approach

1. Fix the amplitude (TVPI): Ensure the fund reaches target TVPI over its life
2. Apply drift via alpha/beta: Adjust timing and path based on market conditions
3. Blend back to deterministic path: Gradually blend NAV growth back to the engine path over blendBackMonths to avoid artifacts

Result: Realistic NAV paths that preserve TVPI while varying with market conditions.

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Case Study: 2008 Crash vs 2020 Rally

Hypothetical example illustrating market-linked simulation behavior:

Let's model a growth equity fund with:

• Vintage: 2019
• Target IRR: 18%
• TVPI: 2.5x
• Alpha: 8%
• Beta: 1.2

Scenario 1: 2008-Style Crash

Market conditions:

• S&P 500: -37% (2008)
• Recession: 18 months

Fund outcomes (P10):

• IRR: 9% (vs 18% target)
• TVPI: 2.1x (vs 2.5x target)
• Capital calls delayed: 6-9 months (liquidity crunch)
• Exits delayed: 12-18 months (no buyers)

Scenario 2: 2020-Style Rally

Market conditions:

• S&P 500: +18% (2020), +27% (2021)
• Growth stocks soar

Fund outcomes (P90):

• IRR: 28% (vs 18% target)
• TVPI: 3.2x (vs 2.5x target)
• Capital calls accelerated: Faster deployment into hot market
• Exits accelerated: IPO window opens early

Scenario 3: Base Case

Market conditions:

• S&P 500: +10% annual average

Fund outcomes (P50):

• IRR: 18% (on target)
• TVPI: 2.5x (on target)
• Capital calls on schedule
• Exits on schedule

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Technical Details

Correlation Matrix

For portfolios with multiple funds, model cross-fund correlations:

             Growth PE    VC Tech    Credit
Growth PE        1.0        0.7       0.3
VC Tech          0.7        1.0       0.2
Credit           0.3        0.2       1.0

Why it matters:

• In a tech crash, VC and growth PE both suffer (correlation = 0.7)
• Credit funds are less affected (correlation = 0.3)

Bounded Calibration

To avoid extreme outcomes, apply bounds on alpha calibration:

alpha_min = -5%
alpha_max = +15%

Why:

• Prevents unrealistic scenarios (e.g., alpha = 50%)
• Keeps model sensible even with weird IRR targets

Forward-Looking vs Historical

Historical mode: Sample from past market data (e.g., 1990-2024) Forward-looking mode: Use forward P/E ratios, credit spreads to model future distributions

Nagare supports both.

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Results: Realistic vs Unrealistic Outcomes

Unrealistic (Independent Simulations)

Problem: Bear case ignores market crash. Bull case ignores market rally.

Realistic (Market-Linked Simulations)

Better: Tails properly reflect market conditions.

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When to Use Market-Linked vs Independent

Use Market-Linked When:

• Modeling growth equity, VC, or public-like PE strategies
• Portfolio has systematic exposure to public markets
• You need realistic downside stress tests

Use Independent When:

• Modeling real estate, infrastructure, or truly idiosyncratic strategies
• Returns are driven by project-specific cashflows (e.g., toll roads)
• No clear market correlation

Default: Use market-linked for most PE/VC funds.

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Summary

Traditional Monte Carlo for PE:

• Assumes returns are independent of markets
• Produces unrealistic P10/P90 tails
• Misses downside risk in crashes, upside in rallies

Market-Linked Monte Carlo:

• Models r_t = alpha + beta × market_t + epsilon_t
• Calibrates alpha to preserve target IRR
• Uses MOIC-first approach to avoid NAV collapse
• Produces realistic outcomes tied to market conditions

Result: P10/P50/P90 outcomes you can actually trust.

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Try It Yourself

Nagare's Monte Carlo engine supports market-linked simulations out of the box:

• 1,000+ iterations in seconds
• Correlate with S&P 500, Russell 2000, Nasdaq
• MOIC-first calibration with NAV anchoring
• Snapshot-pinned market data for reproducibility

Start Free →

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Related Reading:

• Blending Public and Private Portfolios
• MOIC-First Calibration: Fixing the NAV Collapse Problem
• Market Data Platform