World GDP 2026F3.0%World CPI 2026F4.7%Brent$88/bblFed funds3.50-3.75%ECB deposit2.25%Data centre load485 TWhReadings as at 1 Aug 2026
QuantiaQuantitative economics
Data model QM-02 · Housing

Housing Affordability and Capacity Model

Borrowing capacity, payment burden and the gap between price and what income supports

Reference QM-02Inputs 7 assumptionsOutputs 4 metrics, 2 exhibitsRuns In your browser
Working session over reported figures

Convert a price, an income and a mortgage rate into a payment burden, an affordability-implied price and the gap between them. The rate sensitivity curve prices what each 100 basis point move does to buying power, which is the single largest lever in the model.

The model executes entirely in the browser. No assumption entered here is transmitted or retained. Use Copy results to export the full assumption set and output for use in a note or spreadsheet.

What the model does

It answers one question in two directions. Given a price, what does the household pay and can it afford that. And given an income and a constraint, what price can the household actually support. The gap between the second answer and the market price is the useful number, because it is denominated in percent rather than in ratio units that mean nothing outside their own context.

Monthly cost is a conventional annuity plus a carrying charge.

m = P × (1 − δ) × i / (1 − (1 + i)-n) + P × c / 12 P is price, δ the deposit share, i the monthly rate, n the number of payments, and c the annual carrying cost rate covering tax, insurance and maintenance.

Because both terms are linear in price, the whole thing collapses to a single cost coefficient per unit of price, which is what makes the inversion clean.

k = (1 − δ) × i / (1 − (1 + i)-n) + c / 12
Pmax = (Y × τ / 12) / k Y is annual household income and τ the maximum share of income the constraint allows to go to housing. Pmax is the affordability-implied price.

Rate sensitivity

The capacity curve is the exhibit worth spending time on. Borrowing capacity is a convex function of the mortgage rate, so the effect of a 100 basis point move is not constant: it is much larger at low rates than at high ones. A move from 3 to 4 percent destroys considerably more buying power than a move from 9 to 10.

This has a consequence that is routinely missed in forecasting. When supply is fixed or slow to respond, a fall in the mortgage rate raises what every buyer can bid without changing what exists to be bought. The predictable result is that price rises to absorb the capacity, and the payment-to-income ratio ends up roughly where it started. That is the mechanism behind the finding in QR-02 and QR-09 that affordability deteriorated fastest during the cheapest decade of credit on record.

The affordability constraint

The thirty percent payment-to-income threshold is a convention, not a law. It is defensible as a shorthand and indefensible as a universal: it takes no account of household size, of the share of income that is discretionary at different income levels, or of whether the figure is gross or net. Lenders in practice use a debt service ratio on net income with a stress rate applied on top.

The constraint is exposed as a slider for exactly this reason. Set it to your own underwriting standard rather than accepting ours.

Applications

  • Real estate developers and investors. Size the addressable buyer pool at a given price point, and test how far a price has to fall, or an income rise, before the constraint clears. The capacity curve is the fastest way to price rate risk in a pipeline.
  • Housing and urban researchers. A transparent alternative to the price-to-income ratio, which conflates the price level with financing conditions. Running the same price and income across rate environments separates the two.
  • Mortgage, homebuilder and REIT analysts. The buying power sensitivity per 100 basis points is a direct input to volume forecasts, and it is convex, so it should not be applied as a constant.
  • Policy and planning teams. Compare a demand-side intervention, which moves the constraint or the deposit, against a supply-side one, which moves the price. The model makes the difference in outcome explicit.

Limitations

Every model is a simplification and this one is explicit about which simplifications it makes.

  • It is a single representative household. Real markets clear against a distribution of incomes and deposits, and the marginal buyer is rarely the median one.
  • It uses gross income. Lenders underwrite on net income after other commitments, so a real credit decision applies a tighter effective constraint than this.
  • The mortgage rate is fixed for the full term. Where variable or short-fix products dominate, capacity should be computed at the stress rate rather than the offer rate.
  • Carrying cost is a flat percentage of price. In practice tax assessment lags the market and insurance is increasingly climate-differentiated, so both drift from a fixed share.
  • There is no transaction cost, no rental alternative and no expectation of capital gain, all of which affect the decision to buy at the margin.

Use in client and published work

The model is free to use and the specification above is published so that results can be reproduced independently. Figures generated here should be cited with the model reference and assumption set, as with any other calculation. Extension, recalibration to a specific market, or integration with proprietary data are all within scope of a standard engagement: contact@quantiaconsulting.online.