Ten Thousand Runs of the Wrong Number

No lending program requires a Monte Carlo simulation in a feasibility study. Most of the ones that reach a credit committee should not have been run. What the method can do, what it cannot, and the one question to ask before you ask for the probability.

There is a page in a certain kind of feasibility study, usually near the back, that reads something like this: after 10,000 iterations, the probability that debt service coverage remains above 1.25x is 87.3 percent. A histogram sits under it, roughly bell-shaped, with a red line drawn at 1.25x. The credit officer reads the sentence, looks at the picture, and moves on to the appraisal.

We have written that page. We have also sat on the other side of the table and read it. The sentence is not false. It is an accurate summary of the calculation that was performed. The trouble is that almost nobody asks the only question that would reveal whether the calculation was worth performing: which distributions were used, where were they centered, and who decided that occupancy and room rate could move independently of each other?

This piece is long because the honest answer takes room. The short version is that a Monte Carlo simulation is only as good as three decisions made before the first random number is drawn: where the center of each input sits, how wide and how lopsided each input is allowed to be, and how the inputs move together when the world turns bad. Get the first one wrong and you have simulated the wrong deal ten thousand times. Get the second wrong and you have drawn a bell curve around a hotel that has twice since 2009 lost between a sixth and half of its revenue in a single year. Get the third wrong and you have assumed that the things that fail together will fail separately, which is the assumption that priced the mortgage bonds of 2007.

We build simulations in our own practice. We also decline to build them more often than we build them. The rest of this article explains both decisions.

What the programs actually ask for

Start with the requirement, because a surprising amount of the confusion around simulation comes from a belief that a lender, a guarantor, or an examiner is asking for it. None of them is.

The SBA's operating rules for 7(a) and 504 lending, SOP 50 10 8, do not require a feasibility study for any class of loan. The regulatory basis is a single permissive clause: SBA "may require professional appraisals of the applicant's and principals' assets, a survey, or a feasibility study" (1, 2). Where the SOP does speak to projections, its vocabulary is deterministic throughout. A Standard 7(a) loan above $350,000 must show operating coverage of at least 1.15 to 1 on a historical or projected basis, global coverage of 1.00 to 1, and a 1.10 to 1 floor applies to 7(a) Small Loans from March 1, 2026 (1). We covered the full architecture of that requirement, and the gap between what lenders think it says and what it says, in our piece on the SBA feasibility study requirement that does not exist. The forthcoming SOP 50 10 8.1, effective for applications assigned an SBA loan number on or after October 1, 2026, raises the coverage floor to 1.25x for change-of-ownership transactions and bars reliance on post-closing projections for that test, but it leaves the feasibility framework where it was (3). Neither version contains the words "simulation," "probabilistic," "distribution," or "confidence interval." We checked.

USDA's consolidated guaranteed-loan rule, 7 CFR Part 5001, is more explicit about studies and equally silent on method. It defines a feasibility study as a report by "an independent qualified consultant(s) evaluating the economic, market, technical, financial, and management feasibility of the proposed project," requires one for guaranteed loans above $1,000,000 to a new business, and states that "financial projections must be supported by a list of assumptions showing the basis for the projections" (4). The older feasibility-study guidance that Part 5001 absorbed, preserved as Appendix D to Subpart B of Part 4280, goes one step further and lists "sensitivity analysis" among the financial components a study should address (5). That is the strongest word any federal lending program uses: sensitivity. Not simulation. Readers who want the full enumeration of what USDA does ask for will find it in our annotated walk through the 37 factors of 7 CFR Part 5001.

HUD's multifamily programs handle uncertainty by fixing it in advance. The MAP Guide sizes loans on prescribed debt coverage ratios and vacancy factors that vary by program, and Mortgagee Letter 2025-03 moved several of those ratios in January 2025 (market-rate coverage from 1.176x to 1.15x, for example) without changing the method: a vacancy factor of 3, 5 or 7 percent is the occupancy stress, applied identically to every deal (6). Freddie Mac's multifamily guide applies a refinance test built on a single published forward rate, and waives it altogether where the loan carries an amortizing debt coverage ratio of 1.40x or greater together with leverage at or below the stated loan-to-value threshold (7). Fannie Mae's guide requires lenders to size against an underwriting interest-rate floor and to "assess and stress the cap rate used to determine the Underwriting Value" (8). One rate. One cap rate. One stress.

The bank supervisors are where the language gets closest to what a simulation does, and it is worth reading them precisely. The 2006 interagency guidance on commercial real estate concentrations lists "requirements for feasibility studies and sensitivity analysis or stress testing" among the underwriting standards a CRE lending policy should contain, and expects institutions with concentrations to "perform portfolio-level stress tests or sensitivity analysis to quantify the impact of changing economic conditions on asset quality, earnings, and capital." It then adds a sentence that ought to be framed on the wall of every consultant who sells simulation as compliance: stress testing "may not necessarily require the use of a sophisticated portfolio model," and "may be as simple as analyzing the potential effect of stressed loss rates on the CRE portfolio, capital, and earnings" (9). The OCC's 2012 guidance for community banks says the same thing without the hedge. "The OCC does not endorse a particular stress testing method for community banks. Stress tests do not need to involve sophisticated analysis or third-party consultative support. Effective methods can range from a single spreadsheet analysis to a more sophisticated model" (10).

Even the largest stress-testing exercise in American finance is deterministic. The Federal Reserve's annual supervisory stress test hands the largest banks a small number of named scenarios, each a single path for 28 macroeconomic and financial variables over thirteen quarters. The 2026 severely adverse scenario takes unemployment to a 10 percent peak and commercial real estate prices down by about 40 percent; the Board's own release states that "the scenarios are not forecasts and should not be interpreted as predictions of future economic conditions." Thirty-two banks were run through that one path and the results, published in June, showed more than $708 billion of projected losses (11). There is no distribution. There is a path, chosen by people, defended in public. The one supervisory document that does reach a simulation is not a lending rule at all but the model risk guidance, SR 11-7, which governs any quantitative method a bank relies on, and we return to it at the end because it decides what a lender owes the probability once it has one (12).

The point of the tour is not that simulation is unwelcome. It is that nobody upstream of the consultant asked for it, which means the consultant who includes one is making an analytical claim rather than meeting a requirement. That claim has to stand on its own. The rest of this article is about when it can.

The three ways a simulation goes wrong

A deterministic pro forma has one well-known defect, and it has a name. Sam Savage called it the flaw of averages: for any nonlinear calculation, the output at the average input is not the average output (13). A hotel pro forma is nonlinear in the way that matters. Fixed costs do not fall when occupancy does, so a 10 percent shortfall in revenue produces something closer to a 17 percent shortfall in net operating income at the margins typical of select-service lodging. Plug in average occupancy and average rate and you get a coverage ratio that is systematically too kind, because the bad years cost more than the good years pay.

That defect is the honest case for simulation. It is a real defect and simulation is the right tool for it. But the tool has three failure modes of its own, and in our experience of reading other firms' work (and, early on, our own) they account for nearly every simulation that has misled a lender.

The first is the center. Every input distribution has to be centered somewhere, and the default is to center it on the pro forma value: 70 percent occupancy, a $145 rate, $150,000 per key to build. If those values are optimistic, and the evidence that they usually are is overwhelming, the simulation faithfully explores the neighborhood of a deal that does not exist. Ten thousand draws around the wrong number produce a beautifully smooth distribution of the wrong number.

The second is the width and the shape. A normal distribution with a standard deviation of a few points is the reflex choice, and it is the wrong choice for any variable that has recorded a 2009 or a 2020. Hotel revenue does not wobble symmetrically around a mean. It drifts upward in most years and collapses in a few, and the collapses are large enough that a Gaussian fitted to the calm years assigns them a probability close to zero.

The third is dependence. Occupancy and rate fall together in a recession. Construction cost and financing cost rise together late in a cycle. Cap rates widen when credit tightens, which is when net operating income is also softening. A simulation that draws these independently produces a comfortable left tail because it lets a bad draw on one input be rescued by an average draw on another. In the world, they arrive together.

Each of these is a decision, not a technicality. Each has a literature behind it. And each can be checked by a credit officer with no training in statistics, provided the study discloses what it did. That disclosure is the difference between a simulation that adds information and one that adds a histogram.

Where the center belongs

The most important number in any simulation is not in the simulation. It is the number the analyst chose as the middle of each input, and the right way to choose it is to look outward, not inward.

The inside view, to use the language Daniel Kahneman and Dan Lovallo introduced in 1993, builds the forecast from the specifics of the project: this site, this operator, these bids (14). The outside view asks how projects like this one have actually turned out. Bent Flyvbjerg has spent thirty years assembling the outside view for capital projects, and the results are not close. In the original 258-project study of transport infrastructure, nine out of ten projects ran over budget and the average overrun was 28 percent in real terms; rail averaged 44.7 percent, bridges and tunnels 33.8 percent, roads 20.4 percent, and the authors found that cost escalation "has not decreased over the past 70 years" (15). The database has since grown past 16,000 projects across more than twenty fields. Roughly 91.5 percent go over budget, over schedule, or both. About half a percent come in on budget, on time, and with the promised benefits. Buildings, as a category, carry a mean cost overrun of 62 percent, and 39 percent of building projects land in what Flyvbjerg calls the fat tail, over budget by 50 percent or more, where the average overrun is 206 percent (16).

Those are not numbers to plug into a lender's model unadjusted; they aggregate megaprojects across the world, and a ground-up car wash on a pad site is not a nuclear plant. But governments that fund capital projects have long since stopped treating the pro forma as the center. HM Treasury's Green Book guidance on optimism bias, built on a Mott MacDonald review of large public procurements, instructs analysts to uplift capital cost estimates by a stated percentage that depends on the reference class: for standard buildings the recommended range runs from 24 percent at the outline stage down to 2 percent once risks have been demonstrably mitigated; for non-standard buildings, 51 percent down to 4 percent (17). The UK Department for Transport goes further and expresses the uplift as a percentile: a roads scheme moves from a 15 percent uplift at the median to 32 percent if the sponsor wants only a one-in-five chance of overrun (18). The Australian Commonwealth requires P50 and P90 cost estimates side by side. What all of these have in common is the recognition that the pro forma number is not the expected value. It is the hoped-for value, and the expected value sits somewhere to the right of it.

Commercial real estate has its own outside view, and it says the same thing in the same direction.

John O'Neill's study of 3,699 U.S. hotels that opened between 2001 and 2006 is the best evidence on ramp-up that exists. The average hotel reached stabilization in 3.08 years, which flatters the industry's three-year convention, but only 61.9 percent stabilized inside the two-to-four-year window. In year one the average new hotel ran 55.3 percent occupancy, 76.9 percent of what it would eventually achieve; in year two, 65.5 percent, or 91.1 percent of stabilized (19). Extended-stay hotels ramped faster; luxury, upper-upscale and independent hotels ramped slower. A pro forma that assumes 90 percent of stabilized occupancy in year one is not aggressive by the standards of the pro formas we review. It is also wrong on the evidence by about 9.5 points of occupancy, which in a 100-key hotel is roughly 3,450 room nights in the first year alone.

The same group later concluded that hotel feasibility methodology, unchanged for decades, is "grossly inadequate" because it produces "point estimates of future performance" that "do not adequately consider the inherent risk in lodging investments," and recommended that analysts use Monte Carlo simulation (20). We agree, with the caveat that occupies the rest of this article. A second paper by the same lead author found that in 480 hotel CMBS loans originated between 2010 and 2019, 87 percent of the appraisals showed upward bias, a far higher incidence than the residential literature reports, and that the bias predicted subsequent default (21).

The largest sample of all belongs to John Griffin and Alex Priest, who examined 39,522 CMBS loans securitized between 2013 and 2019. Actual net operating income fell short of underwritten income by 5 percent or more in 28 percent of the loans. The share of non-agency loans overstating income by that margin rose from 36 percent in 2013 to 43 percent in 2019. Among 6,820 properties with transaction prices, 92 percent were appraised at or above the price paid, and those appraised more than 10 percent above it were measurably more likely to become distressed (22). The industry's trade association objected that hospitality and retail naturally show wider variance between underwritten and actual than multifamily, which is true and is also the point: the direction of the miss is one-sided.

The small-business side tells the same story in a different register. Across the public analyses of SBA's loan-level FOIA data we have checked, loans to new businesses charge off at two to three times the rate of loans to existing businesses and acquisitions (23). A feasibility study for a start-up that centers its inputs on the operator's projection, without asking what happens to start-ups as a class, is centering on the inside view.

What we do with this in practice is mechanical and, we think, defensible. Before any distribution is drawn, the center of each input is moved to a base-rate-corrected value. Construction cost carries an uplift tied to the reference class and the stage of design, in the spirit of the Green Book table, and reduced only when bids, a GMP contract, or a completed permit set justify it. Year-one and year-two operating levels are set from the ramp evidence for the asset class, not from the sponsor's schedule. Stabilized NOI carries a haircut that reflects the documented gap between underwritten and realized income for that property type. Only then does the simulation begin. The correction is usually small in percentage terms. In the worked example below it is worth more than the entire effect of fat tails and correlation combined.

The width and the shape

Once the center is honest, the question is how far, and in which direction, each input is allowed to move. The reflex is a normal distribution with a standard deviation the analyst finds reasonable. The evidence is that for most operating variables in commercial real estate this is the wrong shape, and for some of them it is very wrong.

Hotels are the clearest case because the record is public and long. In 2020, U.S. hotel occupancy fell 33.3 percent to 44.0 percent, average daily rate fell 21.3 percent to $103.25, and RevPAR fell 47.5 percent to $45.48, the worst year on record on all three measures (24). Eleven years earlier, in 2009, RevPAR fell 16.7 percent to $53.53, at the time the worst decline since STR began tracking the industry in 1987, on roughly equal declines in occupancy and rate (25, 26). Two events of that size eleven years apart are not the signature of a normal process. Fit a Gaussian to the years in between, whose annual RevPAR moves cluster in the low single digits, and the 2009 outcome sits several standard deviations from the mean while the 2020 outcome is, for practical purposes, impossible. A simulation built on that Gaussian will report a reassuring left tail because it has been told the left tail does not exist. Put a number on it: fit a normal to the calm years using the 3.2 percent long-run average annual RevPAR growth that STR itself publishes and a generous 3.5-point standard deviation, and 2009 lands 5.7 standard deviations below the mean, which that curve calls a one-in-150-million-year event. 2020 lands 14.5 standard deviations below, a number with no meaningful return period at all. Both happened, eleven years apart, inside the working life of a single hotel loan. And the calm years are not as calm as they look: 2025 brought the first full-year decline in occupancy and RevPAR since 2020, small in size, driven by demand falling below the prior year without a recession to explain it (27).

The mechanics of those two hotel downturns also tell you how to shape the inputs. Occupancy did more of the falling than rate in both, because operators hold nominal rate and lose room nights first; rate lags on the way down and is slow on the way back. Occupancy is therefore best modeled as a bounded variable (it cannot exceed physical capacity, and it has a floor well above zero for a going concern) with an explicit probability of a large downward jump. Rate is a strictly positive quantity with a long left tail in bad years, which argues for a lognormal or an empirical distribution rather than a symmetric one. Chain scale changes the width but not the shape; our chain-scale analysis of the hospitality market documents how far the luxury and upper-upscale tiers swing relative to economy and extended-stay.

Institutional property indices split the same way. The NCREIF Property Index posted a total return of roughly minus 17 percent in 2009, and nearly all of that loss sat in the appreciation component; the income return stayed positive (28). For a feasibility model this means the stabilized-NOI leg and the exit-value leg have different distributions and should not share one. NOI can often be modeled with a tighter, more symmetric shape. The cap rate that turns NOI into value carries the skew.

Then there are the asset classes whose record justifies a narrow distribution, and it matters to get these right in the other direction, because a consultant who applies hotel-width uncertainty to a self-storage facility is being conservative in a way that costs the borrower loan proceeds for no analytical reason. Public Storage's same-store revenues fell 3.5 percent in the second quarter of 2009, on a 2.9 percent decline in realized rent per occupied square foot and a 1.1 percent decline in occupancy (29). That was the trough of the worst recession in seventy years, and it was a 3.5 percent revenue decline.

Manufactured housing community REITs kept same-property NOI growth positive through 2008 to 2010 (30). Recurring-membership car wash revenue behaves more like a subscription than like retail traffic. For these classes a narrow triangular or PERT distribution, bounded by the observed worst year, is not optimistic. It is what the data say.

The general rule we apply is simple to state. Choose the shape from the tail behavior you can document, and never default to normal for anything that has posted a 2009 or a 2020. Triangular when all you have is a minimum, a most-likely and a maximum from an expert. PERT when you trust the most-likely value more and want the extremes to fade.

Lognormal for anything strictly positive and right-skewed: rents, rates, construction cost, values. Empirical, meaning the historical changes themselves, resampled, when the history is long enough to contain the bad years, which for hotels it is. Nassim Taleb's point about fat-tailed processes applies with full force here: when a single observation can dominate the sample, the historical average understates the risk, and the analyst's job is to make sure the bad observation is in the sample rather than to average it away (31). Flyvbjerg's group has measured the tail-shape parameter across 23 project types and found that for the fattest-tailed classes the variance is not merely large but undefined, which is a normal way of saying that a standard deviation is not a meaningful description of the risk (32).

Dependence, which is where the tail lives

The third decision is the one most often skipped, and the reason it is skipped is that it is hard to see. A simulation with independent inputs and a simulation with correlated inputs produce almost the same mean and almost the same median. They differ in the tail, and the tail is the only part of the distribution a lender is paying for.

The intuition is not complicated. In a normal year, occupancy and rate move for their own reasons, and a weak month for one can coincide with a strong month for the other. In a recession they fall together, because the same absence of travelers drives both.

Construction cost and financing cost rise together in the late stage of a cycle, so a project that is late and over budget is also paying more for the money that carries it. Cap rates widen when credit tightens, and credit tightens when operating income is under pressure, so the exit value falls at the moment the cash flow is least able to support the debt. Draw these independently and the model lets a bad draw on one be rescued by an average draw on another. In the world, they arrive as a package.

Finance learned this lesson at a cost that is still being counted. David Li's 2000 paper introduced a Gaussian copula for pricing the correlation among defaults in a pool of loans; it became the standard tool for rating and pricing collateralized debt obligations, and its central assumption was that the correlation parameter was stable and benign (33). When house prices turned, correlations converged toward one, the diversification the model had assumed evaporated, and Felix Salmon's post-mortem in Wired gave the episode its permanent name: the formula that killed Wall Street (34). The feasibility analogue is exact. The marginal distributions can be perfectly reasonable and the dependence assumption alone can destroy the risk estimate.

The fix is two mechanical steps and one act of judgment. The mechanics: impose the dependence explicitly rather than hoping it emerges, using a method that preserves the skewed shapes chosen in the previous section. The standard technique, due to Iman and Conover, induces a target rank correlation between inputs without changing their individual distributions, and it is what commercial simulation tools use by default (35). Copulas with heavier tails than the Gaussian (a Student-t or a Clayton copula) capture the tendency of variables to move together more in bad states than in good ones, which the Gaussian misses. The judgment: after running the simulation at the correlation you believe, run it again with the correlations pushed toward one, and report the difference. That delta is the single most informative number a simulation can give a credit committee, because it isolates how much of the deal's safety depends on the assumption that bad things happen one at a time.

This lineage in real estate is older than most practitioners assume. Stephen Pyhrr built a simulation model for real estate investment risk in 1973; Larry Wofford applied simulation to the appraisal of income property in 1978; Peter Byrne's treatment of risk in property development dates from the mid-1990s; Kelliher and Mahoney demonstrated Monte Carlo in discounted cash flow for The Appraisal Journal's readership in 2000; and French and Gabrielli, followed by Hoesli, Jani and Bender, formalized probabilistic DCF for valuation in the mid-2000s (36, 37, 38, 39, 40, 41). What that fifty-year literature has not produced is adoption. The reasons the papers themselves cite are the three decisions above: analysts do not know where to center the inputs, cannot defend the widths, and have no data on the correlations. The dominant commercial real estate cash-flow platform offers scenario and sensitivity tables but no native simulation, so probabilistic work happens in spreadsheet add-ins or in code, and a code notebook is not an underwriting exhibit (42). None of that is a reason to abandon the method. It is a description of the work the method requires.

The same deal, four ways

Abstractions about centers and tails persuade nobody. Here is a deal.

A 100-key select-service hotel, upper-midscale, ground-up. Total project cost $15.0 million, or $150,000 per key. Debt of $12.0 million at 80 percent loan-to-cost, blended 6.75 percent, 25-year amortization, which produces annual debt service of $994,913. The sponsor's stabilized pro forma: 70 percent occupancy at a $145 average rate, other revenue at 4 percent of rooms revenue, variable costs (rooms expense, franchise and management fees, marketing, FF&E reserve) at 38 percent of total revenue, fixed costs (property taxes, insurance, administrative, base utilities and maintenance) of $1,000,000 a year. Stabilized NOI of $1,388,823, a 36 percent margin, and a debt service coverage ratio of 1.40x.

That deal passes every program floor in the first section with room to spare. A conventional sensitivity table, of the kind we include in every study, says the following: 10 percent below pro forma on occupancy alone, 1.16x; 10 percent below on rate alone, 1.16x; 10 percent below on both, 0.94x. Break-even occupancy for 1.00x coverage is 58.5 percent; for 1.25x, 65.7 percent. Those numbers are useful, and a credit officer can check them on a calculator. What they cannot say is how likely any of them is.

We ran the deal through four versions of a simulation, 200,000 iterations each, changing one decision at a time. Every input is stated so that the reader can reproduce the result.

Version one is the naive model, and it is the model behind most of the histograms we see. Occupancy normally distributed around 70 percent with a standard deviation of 3.5 points; rate normally distributed around $145 with a standard deviation of 5 percent; fixed costs normally distributed around $1.0 million with a standard deviation of 5 percent; no construction overrun; all inputs independent. The result: mean coverage 1.40x, a 20.7 percent probability of coverage below 1.25x, and a 1.1 percent probability of coverage below 1.00x. This is the page from the introduction. Nearly four in five chance the deal clears 1.25x, the level USDA lenders customarily underwrite to; one in a hundred that it fails to cover. A lender would be forgiven for reading it as reassurance.

Version two changes only the center. Stabilized occupancy moves down 1.5 points to reflect the documented gap between underwritten and realized income; fixed costs move up 2 percent; construction cost carries a lognormal overrun with a mean of 6 percent and a 10 percent standard deviation, roughly the Green Book's standard-building range after partial mitigation, and half of any overrun is financed with additional debt on the same terms. Nothing else changes: still normal, still independent. Mean coverage falls to 1.28x. The probability of coverage below 1.25x rises from 20.7 percent to 45.0 percent. The probability of coverage below 1.00x rises from 1.1 percent to 6.0 percent. A one-and-a-half-point occupancy correction and a modest cost uplift, both of which the evidence in the previous sections supports as conservative, more than doubled the chance of falling below 1.25x and multiplied the chance of a coverage failure by five. This is the finding we would ask any reader to take away if they take away one thing: the center moves the whole distribution, and the center is a choice the pro forma made before the simulation started.

Version three keeps the corrected center and replaces the normal distributions with the shapes the record supports. Occupancy and rate are drawn from a three-regime mixture. In 92 percent of years the shocks are modest, with standard deviations of 3 points on occupancy and 4 percent on rate. In 6.5 percent of years the deal experiences a 2009: occupancy down 6 points and rate down 9 percent, which is what STR recorded at the industry level. In 1.5 percent of years it experiences a 2020: occupancy down 22 points and rate down 21 percent. Those regime probabilities imply roughly one 2009-type year in fifteen and one 2020-type year in sixty-five, which is if anything generous given the last two decades. Inputs remain independent. Mean coverage barely moves, 1.24x. The probability of coverage below 1.25x rises only from 45.0 to 48.5 percent. But the probability of coverage below 1.00x rises from 6.0 to 10.4 percent, and the fifth-percentile coverage falls from 0.98x to 0.88x. The shape changed the tail and left the middle alone, which is exactly what the previous section predicted.

Version four adds dependence. Within the calm regime, occupancy and rate now carry a rank correlation of 0.6; construction overrun and fixed costs carry 0.4. Mean and median move by less than a hundredth. The probability of coverage below 1.25x barely moves, from 48.5 to 49.3 percent. The probability of coverage below 1.00x rises from 10.4 to 13.5 percent. Push the correlations toward one, 0.9 and 0.7, and it rises to 15.1 percent. Set them to zero, and it falls back to 10.4. The entire effect of the dependence assumption is concentrated in the region below 1.00x, which is the region the guaranty exists for.

Two further readings of the full model are worth a lender's attention.

The first is where the failures come from. Of the outcomes below 1.00x in the fully specified model, half occur in ordinary years, with no recession in the draw at all; 38 percent occur in the 2009-type regime and 11 percent in the 2020-type regime. The catastrophic year is not the main way a 1.40x hotel fails to cover. The main way is an ordinary year that lands a few points of occupancy and a few dollars of rate below a pro forma that was a few points too high to begin with. That is a finding about the center, not the tail, and it is why the second version of the model did most of the work.

The second is what drives the variance. Decomposed, occupancy accounts for about 44 percent of the variation in coverage, rate for 43 percent, construction overrun for 8 percent and fixed costs for 6 percent. This is the number that tells a credit committee what to negotiate. An interest reserve does nothing about occupancy risk. A completion guaranty addresses 8 percent of the problem. The instruments that address 87 percent of it live on the operating side: a franchise with demonstrated ramp performance in comparable markets, a management agreement with performance tests, and a debt sizing that leaves room for the years the ramp study says will come.

And that ramp is the last thing the deterministic pro forma hides. Applied to the simulated deal, O'Neill's observed year-one level (76.9 percent of stabilized occupancy, with rate at 97 percent) produces a median year-one coverage of 0.68x; the year-two level (91.1 percent, rate at 99 percent) produces a median of 1.03x, and coverage in year two is below 1.00x in 43 percent of runs. A pro forma that assumes 90 percent of stabilized occupancy in year one shows 1.16x. The gap between 1.16x and 0.68x is not a stress case. It is the base case, and it is the size of the interest reserve and working capital line that the study should be recommending. We built the cost side of that argument in our piece on the construction loan feasibility study; the operating side is here.

The same 1.40x, seven asset classes

The hotel example makes a second question unavoidable. If the same pro forma coverage ratio carries that much hidden risk in lodging, what does it carry elsewhere? We built a cleaner test to answer it: the same 1.40x stabilized coverage, the same three-regime structure with the same regime probabilities, no center correction and no construction overrun, so that the only things that differ across asset classes are the width of the revenue distribution, the size of the recession and extreme shocks, and the operating leverage of the property type. Each of those inputs is stated in the emblem, with the empirical anchor that justifies it, so a reader who disagrees with a parameter can see exactly what would change.

The result is the table we would most like lenders to argue with.

A select-service hotel at 1.40x has a 26.6 percent probability of falling below 1.25x in a given stabilized year and a 5.9 percent probability of falling below 1.00x; a 16.6 percent revenue decline puts it at break-even. A quick-service restaurant, whose revenue is steadier but whose 16 percent margin gives it the highest operating leverage in the set, sits at 17.4 percent and 1.3 percent, and only 12.0 percent of revenue stands between it and 1.00x. An express car wash with a membership base: 13.2 percent and 0.09 percent. An RV park: 11.9 percent and 0.02 percent. Self-storage: 1.9 percent, multifamily 1.6 percent and a manufactured housing community 0.5 percent, all three under 0.01 percent at the 1.00x line.

Measured the way a sensitivity table measures them, several of those deals look identical: the RV park and the manufactured housing community both break even on a 17.9 percent revenue decline, and self-storage looks safest of all at 20.2 percent. Break-even distance tells you how far a deal can fall. It says nothing about how far it is likely to fall, and on that second question the RV park is roughly twenty-four times more exposed than the manufactured housing community. The spread between the top and the bottom of the table is a factor of fifty at the 1.25x line. It is the same 1.40x. It means something completely different depending on what stands behind it, and no deterministic ratio, floor, or sensitivity table conveys the difference. The lending programs know this in a rough way, which is why hotels are treated as special-purpose property, why collateral discounts differ, and why an experienced credit officer prices a 1.40x hotel differently from a 1.40x apartment building. What the simulation adds is the size of the difference, stated in the same units the credit policy uses.

Two cautions about reading it. First, these are annual probabilities for a stabilized year, not lifetime default rates; a loan lives through many years, some of which will be the bad ones, and a lender should read the hotel row as "one stabilized year in seventeen fails to cover," not as a 6 percent chance of loss. Second, the parameters are ours. The restaurant and car wash rows in particular rest on franchise comparable-sales behavior and membership economics rather than on a long public index, and the RV park row treats 2020 as the boom year it was for outdoor recreation while allowing for a different shock of the same size. A lender with a portfolio of its own losses in any of these classes has better parameters than we do, and should use them.

What the lender owes the number

Suppose a study does all of this properly and lands a probability on the credit officer's desk. What is the credit officer supposed to do with it? The supervisory answer is more demanding than most consultants who sell simulation acknowledge, and it changes how we deliver.

SR 11-7, the Federal Reserve and OCC guidance on model risk management, defines a model as "a quantitative method, system, or approach that applies statistical, economic, financial, or mathematical theories, techniques, and assumptions to process input data into quantitative estimates" (12). A Monte Carlo simulation that turns assumptions and volatility ranges into a distribution of coverage ratios is a model under that definition, and the guidance is explicit that its provenance does not matter: validation "applies equally to models developed in-house and to those purchased from or developed by vendors or consultants." The bank that relies on a simulation's output for a credit decision inherits the guidance's expectations: an evaluation of conceptual soundness, "review of documentation and empirical evidence supporting the methods used and variables selected"; ongoing monitoring; outcomes analysis against realized results; and documentation "sufficiently detailed to allow parties unfamiliar with a model to understand how the model operates, as well as its limitations and key assumptions" (12). The rigor scales with materiality. It does not disappear.

A deterministic sensitivity table sits differently. It is transparent arithmetic that a reviewer can recompute on a calculator, and examiners do not ask community banks to validate one. A simulation that arrives as a histogram and a probability, with the distributions buried in an appendix or not disclosed at all, hands the lender a model it cannot open and an obligation it did not ask for.

So the delivery rule we follow is this. Every feasibility study carries the deterministic base case, the named downside case, the sensitivity tables and the break-even analysis that the programs and the supervisors actually ask for. Those stand on their own and satisfy the file without the simulation. Where a simulation is warranted, it is a layer on top, and it ships with the four things a lender needs to treat it as a model rather than a picture: the center of every input and the base-rate evidence for it; the shape and bounds of every input and the historical record for it; the correlation matrix and the stressed-correlation rerun; and the raw output, so the lender's own reviewer can recompute any figure in the text. The probability is the least important line in that package. The disclosures are the deliverable.

When is it warranted? Our rule is short. A simulation earns its place when the deal is large enough that the credit decision turns on the tail rather than the base case; when the asset class has a documented fat-tailed operating history, which across our thirty-plus classes means lodging, restaurants, and any operating business whose revenue is discretionary; when institutional or participating capital will review the file under its own model governance; or when the borrower's structure creates operating leverage that a sensitivity table cannot express, such as a ground-up project with a long ramp and a thin interest reserve. It is not warranted for a stabilized multifamily refinance, a self-storage acquisition, or any deal where the table above says the 1.40x is what it appears to be. In those cases the histogram is decoration, and decoration that arrives with SR 11-7 obligations attached is worse than none.

The question to ask

We began with a page near the back of a study and a credit officer who did not ask about it. Here is the question, in the form we would want a lender to put to any consultant, including us.

Not "what is the probability?" Instead: where did you center each input, and against what base rate? What shape did you give it, and which year in the record justifies that shape? What correlation did you assume, and what happens to the tail when you push it toward one? A consultant who can answer those three questions in a page has built a simulation that adds information. A consultant who cannot has drawn a bell curve around a hope and run it ten thousand times.

Monte Carlo simulation is not required by any program a lender in this country uses, and it is not a substitute for the sensitivity analysis that every one of them expects. Done badly, it is the most persuasive way ever devised to present the wrong number. Done well, it is the only method that can tell a credit committee that two loans with the same coverage ratio carry risks a factor of fifty apart, and say by how much. The difference between the two is not the software or the iteration count. It is three decisions, made in the open, before the first random number is drawn. That is where the work is, and it is the work we are asking lenders to insist on. Our methodology page describes how it is applied, and we are glad to walk any credit team through a live model. Request a feasibility study when the deal calls for one.

Frequently asked questions

Is Monte Carlo simulation required for an SBA or USDA feasibility study? No. SOP 50 10 8 and the forthcoming 8.1 do not require a feasibility study for any class of loan (SBA "may require" one under 13 CFR 120.160) and contain no reference to simulation. USDA's 7 CFR Part 5001 requires an independent feasibility study for guaranteed loans above $1,000,000 to a new business and requires projections "supported by a list of assumptions"; the legacy component guidance lists sensitivity analysis. No federal program references probabilistic methods.

What is the difference between sensitivity analysis, scenario analysis and Monte Carlo simulation? Sensitivity analysis moves one input at a time and reports the effect on the output, typically as a table. Scenario analysis moves several inputs together to a named case (base, downside, severe). Monte Carlo simulation draws every input from a distribution thousands of times, with specified correlations, and reports the distribution of the output. The first two are what lending programs and bank supervisors ask for. The third adds a probability, but only if the distributions and correlations are defensible.

Why does the center of the input distribution matter more than its width? Because a simulation explores the neighborhood of whatever value it is centered on. In the worked example, correcting the center by 1.5 points of occupancy, 2 percent of fixed costs and a 6 percent mean construction overrun moved the probability of coverage below 1.25x from 20.7 percent to 45.0 percent. Adding fat tails and correlation afterward moved it only to 49.3 percent. The center is a choice the pro forma made before the simulation started.

What is a probabilistic DSCR? A distribution of debt service coverage outcomes rather than a single ratio, from which a probability of falling below a threshold (1.25x, 1.15x, 1.00x) can be read. It is only meaningful when the inputs are centered on base rates, shaped by the asset class's historical record, and correlated as they are observed to move together.

Does the same DSCR mean the same risk across asset classes? No. At an identical 1.40x pro forma coverage, our model gives a select-service hotel a 26.6 percent annual probability of falling below 1.25x and a manufactured housing community 0.5 percent, a fifty-fold difference driven by revenue volatility, the size of recession shocks, and operating leverage.

How many iterations does a real estate Monte Carlo need? Enough that the tail estimates stop moving; for a single-asset coverage model 10,000 is usually sufficient and 100,000 costs nothing. The iteration count is the least important choice in the model. The center, the shape, and the correlation of the inputs determine the answer.

Does a Monte Carlo simulation in a feasibility study create model risk obligations for the lender? Under SR 11-7 and OCC 2011-12, a quantitative method that processes input data into quantitative estimates is a model, and validation "applies equally to models developed in-house and to those purchased from or developed by vendors or consultants." A lender that relies on a simulation's output should expect to document its conceptual soundness, key assumptions and limitations, scaled to materiality. A deterministic sensitivity table does not carry the same burden.

When does MMCG include a simulation? When the credit decision turns on the tail rather than the base case, when the asset class has a documented fat-tailed operating history (lodging, restaurants, discretionary operating businesses), when institutional or participating capital will review the file under its own model governance, or when operating leverage and ramp-up cannot be expressed in a sensitivity table. Every study carries the deterministic base case, downside case, sensitivity and break-even analysis regardless.

September 6, 2026 by Michal Mohelsky, principal of MMCG Invest, LLC, a national SBA and USDA feasibility study consultancy

Request a Feasibility Study https://calendar.app.google/EJzWEz3GCqLY2jU86

Michal Mohelsky, J.D. | Principal | mmcginvest.com 

Contact: michal@mmcginvest.com

Phone: (628) 225-1125

Disclaimer: This report is provided for informational purposes only and does not constitute investment, legal, or tax advice. Data presented herein is derived from proprietary MMCG databases and third-party sources believed to be reliable; however, MMCG Invest makes no representation as to the accuracy or completeness of such information. Figures from third-party industry databases have been independently verified and, where appropriate, adjusted to reflect MMCG's proprietary analytical methodology. Statutory and regulatory references are provided for context and must be verified with counsel before reliance. Past performance is not indicative of future results.

Sources

(1) U.S. Small Business Administration, SOP 50 10 8, Lender and Development Company Loan Programs, effective June 1, 2025, issued via Information Notice 5000-868665. (2) 13 CFR 120.160(b), Loan conditions. (3) U.S. Small Business Administration, Information Notice 5000-880695, SOP 50 10 8.1, effective for applications assigned an SBA loan number on or after October 1, 2026. (4) 7 CFR Part 5001, OneRD Guaranteed Loan Program, sections 5001.3 (definitions of feasibility study and qualified consultant), 5001.303(b)(4)(iii), 5001.304(a)(4)(i), 5001.306(a)(3)(i); 85 FR 42518, July 14, 2020. (5) 7 CFR Part 4280, Subpart B, Appendix D, Feasibility Study Components. (6) U.S. Department of Housing and Urban Development, Multifamily Accelerated Processing (MAP) Guide, 2020 edition with subsequent revisions; Mortgagee Letter 2025-03, January 8, 2025. (7) Freddie Mac Multifamily Seller/Servicer Guide, Refinance Test provisions, 2026 update. (8) Fannie Mae Multifamily Selling and Servicing Guide, Refinance Risk Analysis and Form 4660 Underwriting Interest Rate Floor. (9) Office of the Comptroller of the Currency, Board of Governors of the Federal Reserve System, Federal Deposit Insurance Corporation, Concentrations in Commercial Real Estate Lending, Sound Risk Management Practices, 71 FR 74580, December 12, 2006. (10) Office of the Comptroller of the Currency, Bulletin 2012-33, Community Bank Stress Testing: Supervisory Guidance, October 18, 2012. (11) Board of Governors of the Federal Reserve System, 2026 Stress Test Scenarios, February 4, 2026; 2026 Stress Test Results, June 24, 2026; Policy Statement on the Scenario Design Framework for Stress Testing, 12 CFR Part 252, Appendix A. (12) Board of Governors of the Federal Reserve System and Office of the Comptroller of the Currency, Supervisory Guidance on Model Risk Management, SR 11-7 and OCC Bulletin 2011-12, April 4, 2011. (13) Savage, Sam L., The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty, John Wiley and Sons, 2009. (14) Kahneman, Daniel, and Dan Lovallo, Timid Choices and Bold Forecasts: A Cognitive Perspective on Risk Taking, Management Science 39(1), 1993. (15) Flyvbjerg, Bent, Mette K. Skamris Holm and Søren L. Buhl, How Common and How Large Are Cost Overruns in Transport Infrastructure Projects?, Transport Reviews 23(1), 2003; and Underestimating Costs in Public Works Projects: Error or Lie?, Journal of the American Planning Association 68(3), 2002. (16) Flyvbjerg, Bent, and Dan Gardner, How Big Things Get Done, Penguin Random House, 2023, base-rate appendix. (17) HM Treasury, Supplementary Green Book Guidance: Optimism Bias, based on Mott MacDonald, Review of Large Public Procurement in the UK, 2002; guidance dated April 21, 2013. (18) UK Department for Transport, Procedures for Dealing with Optimism Bias in Transport Planning, Guidance Document, prepared by Bent Flyvbjerg in association with COWI, June 2004. (19) O'Neill, John W., Hotel Occupancy: Is the Three-Year Stabilization Assumption Justified?, Cornell Hospitality Quarterly 52(2), 2011. (20) O'Neill, John W., Benjamin Bloom and Amit Sharma, Toward Improving Hotel Prognostications Through the Application of Probabilistic Methodologies, Cornell Hospitality Quarterly 61(4), 2020. (21) Singh, Amrik, and John W. O'Neill, Appraisal Bias in the Lodging Sector: Evidence from CMBS Transactions, International Journal of Hospitality Management 106, 2022. (22) Griffin, John M., and Alex Priest, Is COVID Revealing a Virus in CMBS 2.0?, The Journal of Finance, 2023; working paper version, SSRN 3671162, 2020. (23) U.S. Small Business Administration, 7(a) and 504 loan-level FOIA data, quarterly release as of March 31, 2026, and public analyses of charge-off rates by business status derived from it. (24) STR, year-end 2020 U.S. hotel performance release, January 2021 (occupancy 44.0 percent, ADR $103.25, RevPAR $45.48). (25) STR, year-end 2009 U.S. hotel performance release (RevPAR $53.53, down 16.7 percent). (26) CBRE Hotels Research, U.S. Hotels: Changes in RevPAR and Profits During Historical Recessions, April 2020. (27) CoStar, U.S. hotels report first full-year occupancy, RevPAR declines since 2020, press release, January 20, 2026. (28) NCREIF, NCREIF Property Index, historical annual total, income and appreciation returns, 2009. (29) Public Storage, Form 8-K, quarter ended June 30, 2009, Same Store Facilities results. (30) Equity LifeStyle Properties, Form 10-K for fiscal years 2008 through 2010, core portfolio operating results. (31) Taleb, Nassim Nicholas, Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications, STEM Academic Press, 2020; and The Black Swan, Random House, 2007. (32) Flyvbjerg, Bent, Alexander Budzier, Jong Seok Lee, Mark Keil, Daniel Lunn and Dirk W. Bester, The Empirical Reality of IT Project Cost Overruns: Defining, Understanding, and Mitigating Fat Tails, Journal of Management Information Systems, 2022; and Flyvbjerg et al., The Uniqueness of IT Cost Risk: A Cross-Group Comparison of 23 Project Types, 2025. (33) Li, David X., On Default Correlation: A Copula Function Approach, Journal of Fixed Income 9(4), 2000. (34) Salmon, Felix, Recipe for Disaster: The Formula That Killed Wall Street, Wired, February 23, 2009. (35) Iman, Ronald L., and W. J. Conover, A Distribution-Free Approach to Inducing Rank Correlation Among Input Variables, Communications in Statistics, Simulation and Computation 11(3), 1982. (36) Pyhrr, Stephen A., A Computer Simulation Model to Measure the Risk in Real Estate Investment, AREUEA Journal 1(1), 1973. (37) Wofford, Larry E., A Simulation Approach to the Appraisal of Income Producing Real Estate, AREUEA Journal 6(4), 1978. (38) Byrne, Peter, Risk, Uncertainty and Decision-Making in Property Development, second edition, E and FN Spon, 1996. (39) Kelliher, Charles F., and Lois S. Mahoney, Using Monte Carlo Simulation to Improve Long-Term Investment Decisions, The Appraisal Journal 68(1), 2000. (40) French, Nick, and Laura Gabrielli, The Uncertainty of Valuation, Journal of Property Investment and Finance 22(6), 2004; and Discounted Cash Flow: Accounting for Uncertainty, Journal of Property Investment and Finance 23(1), 2005. (41) Hoesli, Martin, Elion Jani and André Bender, Monte Carlo Simulations for Real Estate Valuation, Journal of Property Investment and Finance 24(2), 2006. (42) Altus Group, ARGUS Enterprise product documentation, scenario and sensitivity analysis features; Lumivero, @RISK for Excel; Oracle, Crystal Ball.