Industry: Real Estate Product: ModelRisk Application: Real Estate Forecasting
A development firm forecasting a metro house-price index ran the standard plan: compound 3.5% a year, arriving at index 119 in year 5 and 141 in year 10 from a base of 100. The probabilistic re-run in ModelRisk — 40,000 ten-year paths built from drift, annual volatility, and a mean-reverting property cycle — kept that median trajectory but exposed what the straight line concealed: by year 5 the index spans P10 = 94 to P90 = 147, by year 10 it spans 94 to 207, and there is an 18% chance the index is actually below today's level in five years. The forecast was not wrong about the center. It was silent about the cone — and the cone is where the financing decisions live.
A compound-growth line treats every year as the same calm step. Real property markets do not behave that way: they have momentum. A soft year tends to be followed by another soft year, and a hot run tends to overshoot before it reverts. That serial autocorrelation is precisely what a single growth rate cannot represent — and it is what makes the forecast cone fan out far wider than a sum of independent annual shocks would.
The consequence is concrete. A straight 3.5% line says prices in year 5 are certainly above today. A model with a persistent cycle says there is nearly a one-in-five chance they are not. For a project that breaks even only above a certain index, the difference between "certainly above" and "82% above" is the difference between an unhedged plan and a financed one.
This is a forward path model — distinct from a point-in-time equilibrium. The log price index evolves year by year:
log P_t = log P_{t-1} + drift + cycle_t + shock_t
with three sources of uncertainty, each doing a different job:
cycle_t = 0.70 × cycle_{t-1} + innovation
The index is modeled in logs, so it stays strictly positive on every path. The autocorrelation is the whole point of the model, so it was verified in the simulated output:
Without that persistence the year-10 cone would collapse toward a thin central-limit band. With it, the fan stays wide and realistically cyclical.
The headline is the forecast cone itself — 40,000 paths summarized as percentile bands against the deterministic plan.
Two features matter. First, the median path (solid) sits slightly below the deterministic plan (dashed) — a structural consequence of compounding lognormal growth, where the mean drifts above the median. The firm's straight-line plan was quietly optimistic about the typical outcome. Second, the P10 band dips below today's level (100) and stays there for years, while the P90 band runs to 207 by 2035. The cone is asymmetric and wide: median 139 at year 10, but a P10–P90 spread of 113 index points around it. A single growth rate reports the centerline of this cone and nothing about its width.
Collapsing the year-5 slice gives the cumulative distribution that the headline number cannot.
Year-5 percentiles run P10 = 94, P50 = 117, P90 = 147. The deterministic year-5 value (119) again sits just above the median. The marked point reads the operationally relevant probability directly off the curve: P(year-5 index below today) = 18%, with a 7% chance of being more than 10% below. That 18% is the number a five-year financing covenant should be stress-tested against — and it does not exist in the deterministic world, where the answer is a flat zero.
The cone's width is not mainly about the average growth rate; it is about how persistent the cycle is. Sweeping the AR(1) parameter makes the lever explicit.
Holding drift fixed and varying only persistence rho, the probability of being below today in year 5 climbs from 8% at rho = 0 (no momentum) to 20% at rho = 0.9 (strong momentum). The same expected growth produces very different downside risk depending on how sticky the cycle is. A forecaster who calibrates only the average and ignores persistence will systematically under-state the chance of a lost half-decade.
rho
Ranking the inputs by their effect on the year-10 index confirms the hierarchy.
Long-run drift is the largest single driver of where the index ends up, but the cycle innovation scale and cycle persistence together dominate the spread — they are what make the cone wide rather than where they center it. The idiosyncratic annual shock is comparatively minor. The message: getting the average growth right fixes the median; getting the cycle right fixes the risk.
The deterministic plan supported an unhedged, "prices only go up" posture. The probabilistic forecast reframed it: the firm now reports projects against the P10 path rather than the central line, sizes interest-rate and pre-sale hedging to keep the venture solvent in the 18%-probability "below today in year 5" scenario, and tracks the cycle state as a leading indicator rather than extrapolating a single growth rate. The median did not move; the decisions did.
Monte Carlo turns a growth rate into a distribution of forecasts, and only that frame distinguishes "prices will rise 3.5% a year" from "prices will probably rise, but there is a real chance they are lower five years from now."