A real estate investment company runs a 12-month cash flow projection. Revenue: $18M. Costs: $15.6M. Projected profit: $2.4M. The board approves the plan. Six months later, three things happened: two homes sat for 90+ days, renovation costs ran 30% over on a batch of older homes, and interest rates moved 75bps. Actual profit: $400K. The CFO says "the market moved." The real answer: the $2.4M was never a prediction — it was the mean of a distribution nobody bothered to compute.
The Problem with Expected Value
A point-estimate P&L computes one number per line item. Revenue is $18M. But revenue depends on sale prices (uncertain), days-on-market (uncertain), volume (uncertain), and market appreciation (uncertain). Each of those has a distribution. The product of their means is not the mean of their product:
And they're not independent. When the market drops, sale prices fall, DOM increases, and volume drops — simultaneously. The point estimate misses the correlation structure entirely.
The Monte Carlo Approach
Instead of one scenario, simulate 10,000. For each simulation draw:
| Variable | Distribution | Correlation |
|---|---|---|
| Market appreciation | Normal(μ=3%, σ=4%) | Base driver |
| Sale price error | Normal(0, σ=5%) | ρ = 0.4 with appreciation |
| Days-on-market | LogNormal(μ=40, σ=25) | ρ = −0.6 with appreciation |
| Renovation cost overrun | LogNormal(μ=0%, σ=15%) | ρ = 0.3 with DOM |
| Volume (deals/month) | Poisson(λ=25) | ρ = 0.5 with appreciation |
| Interest rate Δ | Normal(0, σ=50bps) | ρ = −0.3 with appreciation |
The correlations are the whole point. Use a Gaussian copula to generate correlated draws across all variables simultaneously:
Draw correlated normals , transform to uniform via the CDF , then invert through each variable's marginal distribution . This preserves the rank correlation structure while allowing each variable to have its own distribution shape.
What 10,000 Scenarios Tell You
Monte Carlo output (10,000 trials): Mean profit: $2.38M (close to point estimate — sanity check) Median profit: $2.15M (skewed left — downside is fatter) Std deviation: $1.2M P10 (bad year): $0.8M P5 (rough year): $0.1M P1 (nightmare): -$0.9M Probability of loss: 4.2% Probability < $1M: 14.8% Value at Risk (95%): $0.1M Expected Shortfall: -$0.4M
The point estimate said $2.4M. The simulation says: yes, probably around $2M, but there's a 15% chance you make less than $1M and a 4% chance you lose money. That changes how you set the cash reserve, how aggressively you buy, and whether you hedge the interest rate exposure.
Three Decisions This Changes
1. Cash reserve sizing
Set the reserve to cover the P5 scenario (5th percentile). If P5 is $100K profit, your reserve needs to cover the $2.3M gap between that and your cost base. The point estimate would have sized the reserve at zero — "we're profitable, why hold cash?"
2. Acquisition pace throttling
Run the simulation monthly with updated inputs. When the distribution widens — when exceeds a threshold — slow down acquisitions automatically. This is variance-based risk management, not gut feel.
3. Sensitivity analysis for free
Which variable has the most impact on profit variance? Compute the Sobol index for each:
In practice, DOM and market appreciation dominate — together they explain 70–80% of profit variance. Renovation cost overruns, despite getting the most operational attention, contribute less than 10%. You're optimizing the wrong variable.
| Variable | Sobol index | Operational attention |
|---|---|---|
| Market appreciation | 38% | Low (can't control) |
| Days-on-market | 32% | Medium (pricing + staging) |
| Volume | 12% | High (sales team focus) |
| Reno cost overrun | 9% | Very High (weekly reviews) |
| Interest rate | 6% | Low (treasury hedges) |
| Sale price error | 3% | Medium (AVM tuning) |
The simulation doesn't tell you what will happen. It tells you what could happen — and how much each input matters. A board that sees a distribution makes different decisions than a board that sees a number. One hedges. The other gets surprised.