Analysing a household's credit · RiskAtoms Academy

By the end you will be able to

1Explain what a credit bureau file shows and how lenders use scores.
2Calculate loan to value, loan to income and debt to income, and say what each protects against.
3Run a stressed-rate affordability test and find the most a household can borrow.
4Link a mortgage application to the bank's retail book: its segment, PD, LGD and expected loss.

Why it matters

Sam and Alex Morley want to borrow £340,000 to buy a £400,000 home. At today's 4.6% fixed rate the payment is £1,909 a month, and they can afford it with room to spare. But in two years the rate resets. At 7.5% the payment would be £2,513, 32% more. The bank's job is to lend only what they could still repay then. It decides this for tens of thousands of households a year, mostly by rule.

Core explanation

Lending to people, not companies

A company has accounts, covenants and a relationship manager (L3.3.02: Analysing a company's credit). A household has a payslip, a bank statement and a credit history. Retail lending runs the same lifecycle (L3.3.01: The credit lifecycle) at industrial scale: thousands of small, similar loans, judged by consistent rules and scores rather than case by case. Two questions dominate: will they pay (the credit file), and can they pay (affordability)? For mortgages a third matters: how much is the home worth against the loan?

Illustrative dataRiskAtoms Bank plc's credit book

One made-up lending book, in pounds, at one made-up year end: twelve invented corporate borrowers (exposure at default £587m, expected loss £2.81m a year), 152,100 retail accounts in mortgages, personal loans and cards (exposure £4.485bn), a ten-grade master scale and an illustrative rating transition matrix. No firm or person in it is real. The same book runs through every lesson in Module 3.3, so the figures agree from lesson to lesson.

This lesson adds one invented application, from Sam and Alex Morley, and the bank's illustrative lending policy. The loan would join the book's mortgages.

Will they pay? The credit file

Credit bureaus collect what lenders report about every account: balances, limits, missed payments, defaults, plus public records such as county court judgments and the electoral roll. In the UK the three large ones are Experian, Equifax and TransUnion, the same trio as in the US; in many countries a public credit register, usually run by the central bank, does the job instead or as well. Each turns the file into a credit score. The lender adds its own data (does the applicant bank with it already?) and its own scorecard, built in L3.3.14: Retail credit portfolios. In RiskAtoms Bank's personal loans the PD by score band runs from 1.2% (band A) to 9.0% (band C): a score is a way of sorting borrowers by PD.

Bureau file: Sam and Alex Morley	Shows	Reads as
Score	812 out of 999	strong
Missed payments, last 6 years	0	clean
Credit searches, last 12 months	2	normal (a car loan and this mortgage)
Credit card	£3,200 of £8,000	40% used: fine
Car finance	£290 a month	up to date
County court judgments	0	none
Electoral roll	yes, 4 years	identity confirmed

Can they pay? Three ratios and a stress test

Loan to value (LTV) measures the cushion if the home must be sold: it drives the LGD. Loan to income (LTI) is a blunt cap on how much debt an income can carry. Debt to income (DTI), the US favourite, compares all monthly debt payments with gross monthly income. All three are percentages or multiples (M-A01: Percentages).

The decisive test is affordability: take-home pay, minus essential spending, minus other debt payments, must cover the mortgage payment, and must still cover it at a higher, stressed rate. RiskAtoms Bank stresses at the reversion rate plus 1% point, and never below 7%, and wants at least £300 a month left over. The stress matters because most new UK mortgages are fixed for only two or five years.

Sort itWhat does each check protect against?

Each check guards mainly against one thing. Sort them.

Six years of repayment history across every lender the applicant has used.
The payment at the reversion rate plus one point, against take-home pay after essentials.
A loan no larger than 85% of an independent valuation of the home.
Debt payments no more than about a third of gross income.
No county court judgments and a confirmed address on the electoral roll.

The formal version

Ratios and the largest affordable loan

For a loan $B$ on a home worth $V$ , gross annual income $Y$ , other monthly debt payments $C$ , and a monthly mortgage payment $P$ :

\mathrm{LTV} = \frac{B}{V}, \qquad \mathrm{LTI} = \frac{B}{Y}, \qquad \mathrm{DTI} = \frac{P + C}{Y/12}

The payment is the level annuity of L1.3.04: Annuities and perpetuities, with monthly rate $i = r/12$ and $n = 12T$ payments. Its inverse, the annuity factor $a(r)$ , is the loan one pound a month supports:

\begin{aligned} P(r) &= \frac{B\,i}{1 - (1+i)^{-n}} = \frac{B}{a(r)}, \qquad a(r) = \frac{1 - (1+i)^{-n}}{i} \\ a(4.6\%) &= 178.09, \qquad a(7.5\%) = 135.32 \end{aligned}

The affordability test requires that take-home pay $N$ , less essentials $E$ , other debts $C$ and a buffer $b$ , cover the payment at the stress rate $r_s$ . Solving for the loan gives the most the test allows:

\begin{aligned} N - E - C - P(r_s) &\ge b \\ \frac{B}{a(r_s)} &\le N - E - C - b \\ B^{\max} &= (N - E - C - b)\; a(r_s) \\ &= (5{,}350 - 1{,}950 - 386 - 300) \times 135.32 = \text{£}367{,}257 \end{aligned}

The loan granted is the smallest of this, the LTV cap $\mathrm{LTV}^{\max}\,V$ , and any LTI limit. Because $B^{\max}$ is proportional to $a(r_s)$ , the percentage effect of a tougher stress is just the change in the annuity factor: one more point on the stress rate cuts the largest loan by

\frac{a(8.5\%)}{a(7.5\%)} - 1 = -8.2\%, \qquad \text{£}367{,}257 \to \text{£}337{,}048

Try it

Start from the Morleys' application. Cut the deposit until the decision changes: which test bites first? Then raise the reversion rate and watch the largest affordable loan fall.

Try itUnderwrite the Morleys' mortgage

Gross household income£85k a year

Deposit (home £400,000)£60k

Two-year fixed rate4.6%

Reversion rate (stress = this + 1 point, at least 7%)6.50%

Essential spending£1,950 a month

Decisionapprove

Loan£340,000

Loan to value85.0%

Loan to income4.00×

Debt to income (gross)32.4%

Book segment: LTV 80–95%PD 1.5%, LGD 20%

Expected loss a year£1,020

Monthly payment£1,909

Payment at the 7.50% stress rate£2,513

Left each month under stress£501

Most the stress test allows£367,257

95% LTV cap£380,000

4.5× income (above: high-LTI allowance)£382,500

Committed credit: car finance £290 and 3% of the £3,200 card balance. The bank wants at least £300 left each month after the stressed payment. Take-home pay moves in proportion to gross income, a simplification.

Worked example

Underwriting Sam and Alex Morley

£340,000 over 25 years on a £400,000 home

Step 1 of 7

1
Credit file
Score 812, no missed payments or judgments, card 40% used, two recent searches. Nothing to explain: the application goes on to affordability.

The same household at 95% LTV

With a £20,000 deposit the loan is £380,000 (LTV 95%, LTI 4.47×). The stressed payment is £2,808, leaving £206 a month, below the £300 buffer: decline, even though LTV and LTI pass. The most they could borrow is £367,257, so they need a deposit of at least £32,743.

Regulatory lens

In the UK, the FCA's mortgage rules (MCOB 11.6.18R) require lenders to consider the effect of likely rate rises on affordability over at least five years, unless the rate is fixed for five years or more; the rule does not set the stress rate, and many lenders add a margin to their reversion rate, as RiskAtoms Bank does. The Bank of England's Financial Policy Committee withdrew its own 3-point affordability test in August 2022. Its loan-to-income flow limit remains: no more than 15% of new mortgages at 4.5 times income or more. Since 2014 that cap applied to each lender; under guidance finalised in October 2026 a lender may exceed 15% as long as the market as a whole stays within it. In the US, the CFPB's ability-to-repay rule requires lenders to consider and verify debt to income or residual income. How retail loans are capitalised is in M4.2: Credit risk capital.

Spark Atoms

Spark AtomThe end of self-certified mortgages

Before the 2008 crisis, UK lenders offered “self-certified” mortgages on the borrower's own word about their income. The FCA's Mortgage Market Review rules, in force from 26 April 2014, ended them: lenders must always check a borrower's income.

Spark AtomThe 43% line

From January 2014, the general definition of a US “qualified mortgage” capped the debt-to-income ratio at 43% (loans eligible for sale to Fannie Mae or Freddie Mac were temporarily exempt). The CFPB replaced that cap with a price-based test in rules effective 1 March 2021, but lenders must still consider and verify DTI or residual income.

Key takeaways

Household credit asks: will they pay (the bureau file and scores) and can they pay (affordability).
LTV = loan ÷ value sets the cushion and drives LGD; LTI = loan ÷ income caps debt; DTI = payments ÷ gross income.
Affordability is tested at a stressed rate: take-home pay less essentials and other debts must cover it with a buffer.
The largest loan is (N − E − C − b) × a(r_s): one point on the stress rate cuts it by 8.2% on a 25-year loan.
The Morleys: £340,000 at 85% LTV, 4.0× income, £501 a month left under stress; EL £1,020 a year.

Reaction

Check what stuck

Question 1 · objective 2

A couple borrow £270,000 to buy a £300,000 flat. What is the loan to value, in %?

%

Question 2 · objective 2

The same couple earn £60,000 a year between them. What is the loan to income multiple?

×

Question 3 · objective 3

What is the monthly payment on a £200,000 repayment mortgage at 5% a year over 25 years (to the nearest £)?

£

Question 4 · objective 2

A household earns £6,000 a month before tax, will pay £1,500 a month on its mortgage and £300 on a car loan. What is its debt-to-income ratio, in %?

%

Question 5 · objective 1

Which of these would a lender get from a credit bureau rather than from the applicant?

AThe price of the homeBWhether the applicant has missed payments on other loans in the last six yearsCHow much the applicant spends on childcareDThe interest rate the applicant wants

Glossary

Affordability: Whether a household can meet the loan payments from its income after tax, essential spending and other debts, now and if rates rise.
Credit bureau: A credit reference agency: a firm that collects people's borrowing and repayment records from lenders and public sources and sells them, with scores, to lenders.
Credit score: A number summarising a credit file, built so that higher scores go with fewer defaults.
Loan to value (LTV): Loan to value: the loan as a percentage of the property's value. The deposit is the rest.
Loan to income (LTI): Loan to income: the loan as a multiple of gross annual income.
Debt to income (DTI): Debt to income: monthly debt payments as a percentage of gross monthly income.
Stressed rate: Testing affordability at an interest rate higher than the one the borrower will pay at first.
Reversion rate: The rate a mortgage moves to when its fixed or discounted period ends, often the lender's standard variable rate.
Essential spending: Spending a household cannot easily cut: food, utilities, council tax, transport, childcare.
County court judgment: County court judgment: a court order to repay a debt in England and Wales, recorded on the credit file.

Deep Dives & Origins

Deep Dives

L. C. Thomas, J. N. Crook and D. B. Edelman, Credit Scoring and Its Applications, 2nd ed., SIAM, 2017. Intermediate.
Financial Conduct Authority, Interest rate ‘stress test’ rule: application of MCOB 11.6.18R, web page, last updated 15 December 2025. Introductory.

Origins

Financial Conduct Authority, Interest rate ‘stress test’ rule: application of MCOB 11.6.18R, 2025.
Financial Conduct Authority, FG26/11: The Financial Policy Committee's recommendation on loan to income ratios in mortgage lending: general guidance, 14 October 2026.
Financial Conduct Authority, “New mortgage rules come into force”, press release, 26 April 2014.
Consumer Financial Protection Bureau, Qualified Mortgage Definition under the Truth in Lending Act (Regulation Z): General QM Loan Definition, final rule, Federal Register 85, 86308, 29 December 2020.

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