Lab Test · Module 4.2

Credit risk capital

50 min8 problems33 answers

How it works

Eight problems from the teams that turn a bank's loans into credit risk capital: standardised weights, real estate, IRB modelling for corporates and mortgages, provisions, collateral, capital planning and structured finance. They follow one new bank, Harrowmere Bank plc; later problems reuse earlier answers, restated in each scenario. Answer each part (the unit is shown beside the box; £, %, commas, a minus sign and an x after a multiple are fine), press Check, then step through the worked solution. Numeric answers are marked right within a small tolerance, so round sensibly as you go; risk weights read from a table and the floor factor must be exact. Keep a calculator handy.

Illustrative dataHarrowmere Bank plc, a new bank for the Lab Test

The lessons use RiskAtoms Bank plc's credit book. These problems apply the same rules to a new, smaller UK bank: Harrowmere Bank plc, invented, with £14,000m of assets at 31 December 2025. Its loans, collateral, provisions, RWA and securitisation are all made up and kept hand-sized; amounts in £ millions. Like the module's book it applies Basel 3.1 pro forma: on that date UK banks still reported under the old UK CRR, and the UK applies Basel 3.1 from 1 January 2027 (PRA PS1/26). Rules are the Basel Framework's (CRE20 to CRE44, RBC20), with the UK floor of Problem 7 as the one UK rule.

Problem 1Standardised weights for the floor

L4.2.01 · L4.2.03

Credit risk, standardised approach team

Harrowmere Bank plc (invented) is a UK bank with £14,000m of assets. It uses retail IRB for its mortgages and A-IRB for its mid-sized corporate loans, and the standardised approach (SA) for everything else. The output floor needs a standardised figure for every exposure, so the team starts with a slice of the book at 31 December 2025, in £ millions:

ExposureDrawnOff-balance sheet
Listed retailer, rated A−: term loan, plus a committed undrawn revolving facility12080
Manufacturer, rated BBB; due diligence finds it riskier than the rating90–
Unrated family business, group sales €30m40–
Unrated bank, SCRA grade B: two-year loan60–
Bonds of an overseas central government, rated A150–
Performance bonds issued for an unrated construction firm (group sales €400m)–20
Credit card limits of customers who revolve, cancellable at any time without notice–400

The retailer's undrawn amount is a committed facility. The card customers meet the regulatory retail criteria and are not transactors. The government is not the UK's, so no national discretion applies.

Lessons: L4.2.01: The standardised approach: corporates, banks and sovereigns · L4.2.03: Off-balance sheet items and other exposures

  1. (a)What risk weight does the manufacturer's loan take? Answer in %.

    %

  2. (b)What risk weight does the loan to the unrated bank take? Answer in %.

    %

  3. (c)What is the exposure (EAD) of the three off-balance sheet items together? Answer in £m.

    £m

  4. (d)What are the slice's standardised RWA? Answer in £m.

    £m

Problem 2Mortgages and an office block

L4.2.02

Mortgage and property risk

Harrowmere's standardised figures also need its owner-occupier mortgages, which are not dependent on the property's cash flows. In £ millions, with every loan in a segment at that segment's loan-to-value ratio (as CRE20.74 defines it):

SegmentBalanceLTV
Segment 150055%
Segment 230078%

The borrowers are individuals, whose own weight is 75%. Separately, Harrowmere lends £120m on an office block valued at £180m; the loan is repaid from the tenants' rents.

Lessons: L4.2.02: The standardised approach: retail and real estate

  1. (a)Under the whole-loan approach, what is the risk weight on Segment 2? Answer in %.

    %

  2. (b)Under loan-splitting, what is the risk weight on Segment 2? Answer in %.

    %

  3. (c)By how much do the two segments' RWA change if the bank uses loan-splitting instead of the whole loan? Answer in £m (negative if they fall).

    £m

  4. (d)What are the office loan's RWA under the standardised approach? Answer in £m.

    £m

Problem 3One corporate loan on A-IRB

L4.2.04 · L4.2.05

Wholesale credit modelling

Harrowmere lends to an engineering group with €300m of consolidated sales, so A-IRB is allowed and no SME adjustment applies. The loan is senior and unsecured: £80m drawn and £40m undrawn on a committed revolving facility. The bank's own estimates: PD 2%, downturn LGD 22%, CCF 30% on the undrawn amount, and effective maturity 4 years.

You may need G(0.02)=−2.0537G(0.02) = -2.0537 and G(0.999)=3.0902G(0.999) = 3.0902, where GG is the inverse of the standard normal distribution NN. The site calculator's normcdf, irbcorr and vasicek do the normal arithmetic too.

Lessons: L4.2.04: The IRB approach · L4.2.05: The IRB risk-weight formula

  1. (a)Which Basel 3.1 input floor binds on this loan?

  2. (b)What is the asset correlation R? Answer in %.

    %

  3. (c)What is the maturity adjustment (1 + (M − 2.5)b) / (1 − 1.5b)?

    ×

  4. (d)What is the risk weight? Answer in %.

    %

  5. (e)What are the loan's RWA? Answer in £m.

    £m

Problem 4A mortgage segment at the floor

L4.2.06

Retail credit modelling

A segment of Harrowmere's low-LTV owner-occupier mortgages: EAD £2,500m, the bank's own PD 0.6% and own downturn LGD 4%, both on retail IRB. You may need G(0.006)=−2.5121G(0.006) = -2.5121 and G(0.999)=3.0902G(0.999) = 3.0902.

Lessons: L4.2.06: IRB for retail and specialised lending

  1. (a)What is the segment's conditional PD at the 99.9th percentile? Answer in %.

    %

  2. (b)What risk weight applies, after any input floors? Answer in %.

    %

  3. (c)What are the segment's RWA? Answer in £m.

    £m

Problem 5Provisions on both approaches

L4.2.03 · L4.2.07

Finance, provisions and capital

On the standardised book, an unrated corporate borrower has defaulted: £40m outstanding, with specific provisions of £6m. Next quarter the provisions are raised to £10m.

On the IRB book (no exposure in default), in £ millions, with IFRS 9 provisions of £16.4m on the corporates and £3.0m on the mortgages:

PortfolioEADPDLGD
Corporates, grades 1–41,0000.4%30%
Corporates, grades 5–75002.5%32%
Mortgages8,0000.5%9%

IRB credit RWA are £1,500m.

Lessons: L4.2.03: Off-balance sheet items and other exposures · L4.2.07: Expected loss, provisions and the shortfall

  1. (a)What are the defaulted loan's RWA now? Answer in £m.

    £m

  2. (b)And after the provisions are raised? Answer in £m.

    £m

  3. (c)What is the IRB book's regulatory expected loss? Answer in £m.

    £m

  4. (d)How much of the provisions counts in Tier 2? Answer in £m.

    £m

  5. (e)The mortgages' provisions are below their expected loss. What does that do to capital?

Problem 6Collateral, a guarantee and a short CDS

L4.2.08

Collateral management

Three sterling loans on Harrowmere's standardised book, in £ millions:

  • Loan 1: £120m to a BBB-rated company. It is secured lending, revalued daily, against £50m of German government bonds (AAA, two years to run, in euros) and £30m of FTSE 100 shares. The bank uses the comprehensive approach with supervisory haircuts.
  • Loan 2: £80m to a BB-rated company, of which £50m is guaranteed by an A-rated bank. The guarantee meets the CRM conditions.
  • Loan 3: £60m to a BBB-rated company with 4.5 years to run, hedged with a £60m CDS bought from an AA-rated bank. The CDS was written for five years, covers restructuring, and has 2 years left.

Lessons: L4.2.08: Credit risk mitigation

  1. (a)What total haircut (Hc + Hfx) applies to the German bonds at the holding period that fits? Answer in %.

    %

  2. (b)What is Loan 1's exposure after mitigation, E*? Answer in £m.

    £m

  3. (c)What are Loan 2's RWA? Answer in £m.

    £m

  4. (d)How much of Loan 3's protection is recognised after the maturity mismatch? Answer in £m.

    £m

  5. (e)What are Loan 3's RWA? Answer in £m.

    £m

Problem 7The output floor

L4.2.09 · L4.2.11

Capital planning

Harrowmere's RWA at 31 December 2025, Basel 3.1 applied pro forma, in £ millions:

PortfolioAs used (U-TREA)Standardised (S-TREA)
Mortgages (retail IRB)6402,240
Mid-sized corporates (A-IRB)8601,200
Other credit (SA)1,6001,600
Counterparty, CVA, market and operational700700
Total3,8005,740

For the UK, the floor adds OF-ADJ = 12.5 × (IRB T2 − IRB CET1 − GCRA + SA T2). IRB T2 is the excess provisions counted in Tier 2 in Problem 5 (£9.0m); there is no shortfall, and all provisions are specific, so GCRA and SA T2 are 0. Hold the balance sheet fixed.

Lessons: L4.2.09: The output floor · L4.2.11: Credit risk capital: what changes from 2027

  1. (a)Under the Basel floor of 72.5%, how much does the floor add to RWA? Answer in £m.

    £m

  2. (b)Which portfolio contributes most to the floor add-on?

  3. (c)What floor factor applies in the UK in 2028? Answer in %.

    %

  4. (d)What are Harrowmere's total RWA in the UK in 2028, with OF-ADJ? Answer in £m.

    £m

Problem 8Securitising the corporate book

L4.2.10

Structured finance

Harrowmere securitises £1,000m of its mid-sized corporate loans in a traditional STS deal. KIRB, the pool's IRB capital including expected loss, is 4%. The tranches are a first loss of 0%–3%, a mezzanine of 3%–10% and a senior tranche of 10%–100%. The bank sells the mezzanine and keeps all of the first loss and the senior tranche; the deal achieves significant risk transfer.

It uses SEC-IRBA. For the senior tranche, with N = 100, LGD 40% and MT = 3 years, the STS formula gives p = max(0.3, 0.5 × 0.3916) = 0.3.

Lessons: L4.2.10: The securitisation framework

  1. (a)What are the RWA on the first-loss tranche? Answer in £m.

    £m

  2. (b)What are the RWA on the senior tranche? Answer in £m.

    £m

  3. (c)By how much are the bank's RWA lower than if it had kept the pool (12.5 × KIRB × pool)? Answer in £m.

    £m
Score 0 / 330 of 8 problems checked

Back · L4.2.11

Credit risk capital: what changes from 2027

Next module · L4.3.01 · coming soon

The trading book boundary