One number is a guess; a thousand numbers are a forecast
Traditional real estate underwriting often produces a single number: 'this deal returns a 15% IRR' (internal rate of return, a measure of investment return covered elsewhere in this course). That single number comes from a single set of assumptions — one guess for rent growth, one guess for the exit cap rate, one guess for vacancy. But every one of those inputs is genuinely uncertain; nobody knows today exactly what the market cap rate will be five years from now. A single-point estimate hides that uncertainty entirely and hands you false confidence in one specific number.
Monte Carlo simulation (named after the Monte Carlo casino, because it relies on repeated random chance, much like a roulette wheel) solves this by running the same underwriting model not once, but many times — called trials or iterations, often thousands of them in real practice. On each trial, every uncertain input is randomly redrawn from a realistic range of possible values, the model is recalculated using that trial's random inputs, and the output (say, sale price, NOI, or profit) is recorded. After many trials, instead of one number, you have a full distribution of possible outcomes — the same concept introduced earlier in this block — which lets you ask far more useful questions: what's the average outcome? What's the worst realistic case? What's the probability this deal actually loses money?
A simplified simulation, one uncertain input at a time
Real Monte Carlo software runs thousands of trials using continuous probability distributions and a random number generator. To build the intuition by hand, this topic uses a small, simplified number of trials with input values given directly — the same underlying logic, just at a scale you can compute yourself.
Worked example 1. A property's Year-5 net operating income (NOI) is projected with confidence at $500,000. The exit cap rate, however, is uncertain. A simplified 5-trial simulation draws the exit cap rate as 5.5%, 6.0%, 6.5%, 7.0%, and 7.5% — one value per trial. Recall the relationship Sale Price = NOI ÷ Cap Rate (covered in this course's valuation topics). Applying it to each trial:
- Trial 1 (5.5% cap rate): $500,000 ÷ 0.055 = $9,090,909 - Trial 2 (6.0% cap rate): $500,000 ÷ 0.060 = $8,333,333 - Trial 3 (6.5% cap rate): $500,000 ÷ 0.065 = $7,692,308 - Trial 4 (7.0% cap rate): $500,000 ÷ 0.070 = $7,142,857 - Trial 5 (7.5% cap rate): $500,000 ÷ 0.075 = $6,666,667
Summing all five outcomes: $9,090,909 + $8,333,333 + $7,692,308 + $7,142,857 + $6,666,667 = $38,926,074. Dividing by the 5 trials gives a mean simulated sale price of $38,926,074 ÷ 5 ≈ $7,785,215. The outcomes range from a low of $6,666,667 to a high of $9,090,909 — instead of one guess, you now have a full picture of how sensitive the sale price is to where the exit cap rate lands.
You can also extract a probability directly by counting trials: of the 5 trials, 2 produced a sale price above $8,000,000 (Trials 1 and 2). The simulated probability of exceeding $8,000,000 is 2 ÷ 5 = 40%.
Combining multiple uncertain inputs at once
The real power of Monte Carlo simulation shows up when several inputs are uncertain simultaneously, and each trial draws a full random 'scenario' — a value for every uncertain input together, not one input at a time.
Worked example 2. A 100-unit apartment property has fixed annual operating expenses of $200,000. Both occupancy (the percentage of units generating rent) and average monthly rent per unit are uncertain. A 4-trial simplified simulation draws the following paired scenarios, using NOI = (Occupancy × Units × Monthly Rent × 12) − Operating Expenses:
- Trial A (90% occupancy, $1,000/month rent): 0.90 × 100 = 90 occupied units; 90 × $1,000 = $90,000/month; × 12 = $1,080,000 gross collected rent; NOI = $1,080,000 − $200,000 = $880,000 - Trial B (85% occupancy, $950/month rent): 0.85 × 100 = 85 occupied units; 85 × $950 = $80,750/month; × 12 = $969,000; NOI = $969,000 − $200,000 = $769,000 - Trial C (95% occupancy, $1,050/month rent): 0.95 × 100 = 95 occupied units; 95 × $1,050 = $99,750/month; × 12 = $1,197,000; NOI = $1,197,000 − $200,000 = $997,000 - Trial D (80% occupancy, $900/month rent): 0.80 × 100 = 80 occupied units; 80 × $900 = $72,000/month; × 12 = $864,000; NOI = $864,000 − $200,000 = $664,000
Mean simulated NOI: ($880,000 + $769,000 + $997,000 + $664,000) ÷ 4 = $3,310,000 ÷ 4 = $827,500. The simulated NOI ranges from a low of $664,000 (Trial D) to a high of $997,000 (Trial C) — a $333,000 spread driven jointly by occupancy and rent moving together within each trial.
This is also why real Monte Carlo software runs thousands of trials, not 4 or 5: with only a handful of trials, the result is highly sensitive to which particular random values happened to get drawn, and a different set of 4 or 5 draws could produce a noticeably different mean. The law of large numbers — a foundational statistical principle stating that as the number of random trials grows, their average result converges toward the true underlying expected value — is why more trials produce a more stable, more trustworthy distribution. Going from 5 trials to 5,000 trials doesn't change the underlying uncertainty in the inputs, but it does make the simulated output distribution a far more reliable picture of that uncertainty.
Simulated Probability Estimate
P(condition) ≈ (Number of trials meeting the condition) ÷ (Total number of trials)
- P(condition)
- — The estimated probability of a specific outcome, such as a loss or exceeding a target return
- Number of trials meeting the condition
- — A simple count of how many simulated trials produced that outcome
- Total number of trials
- — The total number of iterations the simulation ran
Once a simulation has been run, estimating a probability is just counting: divide the number of trials where the outcome you care about occurred by the total number of trials run. In Worked Example 1, 2 of 5 trials produced a sale price above $8,000,000, giving a simulated probability of 40%.
Reading a simulated distribution: mean, median, and probability of loss
Worked example 3. A 10-trial simulation of a property flip (buy, renovate, resell) produces the following simulated profit outcomes, already sorted from lowest to highest: −$50,000; $20,000; $45,000; $60,000; $75,000; $80,000; $90,000; $100,000; $120,000; $150,000.
- Mean: sum all 10 outcomes: (−50,000) + 20,000 + 45,000 + 60,000 + 75,000 + 80,000 + 90,000 + 100,000 + 120,000 + 150,000 = $690,000. Divide by 10 trials: $690,000 ÷ 10 = $69,000 mean simulated profit. - Median: with 10 values (an even number), the median is the average of the 5th and 6th sorted values: 5th = $75,000, 6th = $80,000; ($75,000 + $80,000) ÷ 2 = $77,500. - Range: from a worst case of −$50,000 (a $50,000 loss) to a best case of $150,000 profit. - Probability of loss: only 1 of the 10 trials produced a negative outcome (the −$50,000 trial). Probability of loss = 1 ÷ 10 = 10%.
That last figure — a 10% simulated probability of losing money — is exactly the kind of insight a single-point-estimate model cannot produce. A deterministic model might have projected one clean profit figure like $70,000 and stopped there, giving no sense of how likely a loss actually is. The simulation instead shows a most-likely range clustered between roughly $60,000 and $120,000, a realistic (if unlucky) downside near −$50,000, and a concrete, countable probability attached to that downside.
Point-estimate (deterministic) model vs. Monte Carlo simulation
| Point-estimate (deterministic) model | Monte Carlo simulation |
|---|---|
| Uses one single value for each input (e.g., one exit cap rate) | Uses a range or distribution of possible values for each uncertain input |
| Produces one output number (e.g., one IRR) | Produces a full distribution of possible output values across all trials |
| Cannot show the probability of a loss or of missing a target | Can directly estimate probabilities by counting trials (e.g., 'probability of loss') |
| Fast to build and easy to communicate | Requires more setup (defining ranges/distributions) and many trials to be reliable |
| Hides how sensitive the result is to the uncertain assumptions | Shows exactly how much the output swings as the uncertain inputs vary |
Small samples mislead, and a mean output is not a promise
Two traps catch beginners here. First, the toy 4-, 5-, and 10-trial examples in this topic are for building intuition by hand — they are far too small to be a reliable Monte Carlo simulation in practice. A handful of random trials is noisy: rerun 5 trials with a different set of random draws and you could easily get a meaningfully different mean or probability. Real simulations lean on the law of large numbers and typically run at least 1,000 to 10,000+ trials before the results are considered stable. Second, even a properly large simulation's mean or median output is not a guarantee of the actual future outcome — it is a summary of a distribution built from your assumed input ranges. If those input ranges are wrong or too narrow (for example, assuming rent growth can never be negative, when in a downturn it can), the simulation will confidently produce a distribution that is wrong in exactly the same way. A simulation only reflects the quality of the assumptions fed into it.
Module Check
A 10-trial simulation of a property flip produced the following simulated profit outcomes: -$50,000; $20,000; $45,000; $60,000; $75,000; $80,000; $90,000; $100,000; $120,000; $150,000. Based on these 10 trials, what is the simulated probability of a loss (a negative profit outcome)?