Lab Test: Credit risk · RiskAtoms Academy

How it works

Eight problems from the people who lend and watch the loans: a credit analyst, a mortgage underwriter, the rating desk, portfolio analysts, pricing and the provisioning team. Most follow one new borrower, Wrenstow Foods Ltd, from its accounts to its provision, and need more than one lesson. Answer each part (the unit is shown beside the box; £, %, commas and a minus sign are fine; multiples may be typed as 2.5 or 2.5×), press Check, then step through the worked solution. Numeric answers are marked right within a small tolerance, so round sensibly as you go. Keep a calculator handy.

Illustrative dataRiskAtoms Bank plc's credit book

One made-up lending book on one made-up date (31 December, year 0), in pounds: a ten-grade master scale, a one-year rating transition matrix, twelve invented corporate borrowers (£587m of exposure, expected loss £2.81m), retail portfolios and twenty past workout cases. The firms are invented and the numbers are round illustrative values, not anyone's data. The same book runs through every lesson in Module 3.3.

The problems use new inputs on the module's book and its rules: a new borrower (Wrenstow Foods Ltd, invented), a new household, a small-business migration matrix, a past workout, a guarantee and a merger between two of the book's borrowers. All are made up.

Problem 1A new borrower's accounts

L3.3.01 · L3.3.02

Credit analyst, corporate banking

Wrenstow Foods Ltd, a UK maker of chilled ready meals, asks RiskAtoms Bank to renew its £30m revolving facility. Before the credit committee meets, you analyse its last financial year (£m). Its debt includes the £18m it has drawn from the bank; 60% of the debt pays a floating rate, the rest is fixed.

Revenue	EBITDA	Interest	Total debt	Cash	Tax	Capex	Working capital rise
£180m	£27m	£4.2m	£78m	£6m	£3.1m	£9m	£1.4m

The covenants in the facility: net debt at most 3.5 times EBITDA, and EBITDA at least 4 times interest. The bank's debt-capacity test uses the same two limits, with interest at today's average rate on the debt plus 2 percentage points.

Lessons: L3.3.01: The credit lifecycle · L3.3.02: Analysing a company's credit

(a)What is Wrenstow's net leverage (net debt / EBITDA) today?
×
(b)Stress it: EBITDA 25% lower and rates 1.5 points higher on the floating-rate debt. What is the interest cover (EBITDA / interest) then?
×
(c)Under that stress, which covenant breaks?
ANeither: both still holdBThe leverage covenant onlyCThe interest cover covenant onlyDBoth covenants
(d)Back to today's figures. How much more net debt could Wrenstow take on before it reaches the bank's debt capacity? Answer in £m.
£m

Problem 2A mortgage under a stress rate

L3.3.03

Mortgage underwriter, retail banking

Dana and Chris Ellery (invented) want to buy a home for £320,000 with a £40,000 deposit, borrowing £280,000 over 30 years at a two-year fixed rate of 4.3%; after the fix the loan reverts to 5.8%. Together they earn £70,000 a year, £4,450 a month after tax. The bank estimates their essential spending at £1,750 a month. They pay £240 a month on a car loan and have £2,500 on a credit card.

RiskAtoms Bank's policy (as in L3.3.03: Analysing a household's credit): test the repayment at the reversion rate plus 1 point, but never below 7%; count 3% of card balances as a monthly commitment; after essentials, commitments and the stressed repayment at least £300 a month must be left. Repayments are monthly, on a level (annuity) basis. Loan-to-value at most 95%.

Lessons: L3.3.03: Analysing a household's credit

(a)At what rate does the bank test the Ellerys' affordability?
A6.8%: the reversion rate plus 1 pointB7.0%: the policy floor, because the reversion rate plus 1 point is lowerC7.3%: the fixed rate plus 3 pointsD4.3%: the rate they will actually pay for two years
(b)What is the monthly repayment at that stress rate? Answer in £.
£
(c)How much is left each month after essentials, commitments and the stressed repayment? (The test needs at least £300.) Answer in £.
£
(d)What is the largest loan the affordability test allows (leaving exactly £300 a month at the stress rate)? Answer in £.
£

Problem 3Rating the borrower, then a warning signal

L3.3.04 · L3.3.05 · L3.3.06

Credit risk officer, rating desk

The bank rates Wrenstow Foods Ltd with its corporate rating model (as in L3.3.04: Internal ratings and master scales). The score is the log-odds of default:

s = -4.90 + 0.55\,\ell -0.60\ln\kappa -0.25\ln\frac{S}{100} -0.35\,(q - 3), \qquad \text{PD} = \frac{1}{1 + e^{-s}}

with net leverage $\ell = 2.67$ , interest cover $\kappa = 6.43$ , revenue $S$ = £180m and the analyst's qualitative score $q$ = 4. The master scale is in the table below.

Grade	PD band	Central PD
3	0.1% to 0.2%	0.14%
4	0.2% to 0.4%	0.28%
5	0.4% to 0.8%	0.57%
6	0.8% to 1.6%	1.13%
7	1.6% to 3.2%	2.26%
8	3.2% to 6.4%	4.53%
9	6.4% to 20.0%	11.31%

The validation team also pulls five years of the bank's own food-and-drink borrowers rated in the same grade:

Year	−4	−3	−2	−1	0
Borrowers at the start	140	150	160	170	180
Defaults in the year	0	1	3	2	1

Six months later Wrenstow's suppliers report payments stretched beyond 60 days. Past data: the signal shows up in 40% of borrowers who go on to default within a year, and in 8% of those who do not.

Lessons: L3.3.04: Internal ratings and master scales · L3.3.05: External ratings in practice · L3.3.06: Probability of default

(a)What PD does the model give Wrenstow? Answer in %.
%
(b)Which master-scale grade is that?
(c)What long-run default rate does the five-year history give for the grade? Answer in %.
%
(d)Starting from the grade's central PD, what is Wrenstow's PD after the supplier signal (Bayes' rule)? Answer in %.
%
(e)Which grade does that updated PD fall in?

Problem 4Where small businesses are in three years

L3.3.07

Portfolio analyst, business banking

For its small-business loans the bank tracks just two performing states, Strong (grades 1 to 5) and Weak (grades 6 to 10), plus Default. Its one-year transition matrix (illustrative), rows from and columns to Strong, Weak, Default:

P = \begin{pmatrix} 0.92 & 0.07 & 0.01 \\ 0.10 & 0.84 & 0.06 \\ 0.00 & 0.00 & 1.00 \end{pmatrix}

Assume the chain is Markov and the matrix stays the same each year.

Lessons: L3.3.07: Rating migration

(a)A loan starts Strong. What is the probability it has defaulted within two years? Answer in %.
%
(b)What is the probability it is Weak (and not in default) after two years? Answer in %.
%
(c)What is the probability it has defaulted within three years? Answer in %.
%
(d)The three-year figure is above 1 − 0.99³ = 2.97%, what you would get if the one-year PD stayed at 1%. Why?
AThe matrix counts some defaults twice, once in each yearBSome Strong loans move to Weak, where the one-year PD is 6%, so later years carry more default riskCDefault is absorbing, so the default probability grows faster than it shouldDThe Markov assumption builds in momentum: downgraded loans are more likely to be downgraded again

Problem 5What a default costs, and what this loan is expected to lose

L3.3.08 · L3.3.09 · L3.3.10

Credit risk analyst, loss modelling

A food wholesaler that defaulted three years ago has just closed its workout. At default the bank was owed £6.4m. It recovered £2.5m, £1.8m, £0.9m at the end of years 1, 2 and 3, and spent £0.3m on lawyers and administrators, paid evenly over the three years. The bank discounts workout cash flows at 8% a year.

Wrenstow Foods Ltd's facility: limit £30m, drawn £18m, the bank's credit conversion factor 60%. It is secured on a cold store valued at £14m, with a 30% haircut. As in the bank's book, the part covered by collateral after its haircut loses 10% if the borrower defaults and the rest loses 45%. Wrenstow is grade 5 (PD 0.57%).

Lessons: L3.3.08: Loss given default and recovery · L3.3.09: Exposure at default · L3.3.10: Expected loss

(a)What was the workout LGD on the wholesaler's loan? Answer in %.
%
(b)What is the exposure at default on Wrenstow's facility? Answer in £m.
£m
(c)What LGD does the bank's rule give Wrenstow's facility? Answer in %.
%
(d)What is the facility's expected loss over one year? Answer in £.
£

Problem 6Capital for a bad year, and the price

L3.3.10 · L3.3.11

Relationship manager and credit pricing

Wrenstow's facility: PD 0.57%, LGD 31.4% (rounded from Problem 5), EAD £25.2m. The bank sets capital per £ of EAD as the one-factor (Vasicek) unexpected loss at 99.9%, with asset correlation 0.20, as in L3.3.10: Expected loss. Its pricing assumptions: cost of funds 4.5%, operating cost 0.4% of EAD a year, and a required return on capital of 15%.

Wrenstow's finance director asks for a rate of 5.20%.

Lessons: L3.3.10: Expected loss · L3.3.11: Unexpected loss and default correlation

(a)In the one-factor model, what default rate is reached in a 1-in-1,000 year for loans like this? Answer in %.
%
(b)What capital per £ of EAD does that imply: LGD × (that rate − PD)? Answer in %.
%
(c)What loan rate does the bank need to earn its required return? Answer in %.
%
(d)What return on capital would the bank earn at the 5.20% Wrenstow asks for? Answer in %.
%

Problem 7A guarantee, a new name and a merger

L3.3.12 · L3.3.13

Portfolio manager, credit risk

Three changes reach the corporate book (the twelve borrowers in the module's book) in one week.

Hastemoor Construction Ltd (grade 8, PD 4.53%, unsecured LGD 55%; limit £25m, drawn £22m, CCF 75%) gets a guarantee from a grade-2 bank (PD 0.07%) for £10m of the facility. The bank treats the guaranteed part by substitution, with the guarantor's LGD of 45%.
Wrenstow Foods Ltd joins the book with an EAD of £25.2m. Today the book's EAD is £587m and its HHI by name is 0.1098.
Sallowmere Logistics GmbH (limit £55m, drawn £35m, CCF 50%) agrees to buy Larkhollow Freight Ltd (limit £30m, drawn £26m, CCF 75%). From completion the two are one connected group. The bank's Tier 1 capital is £560m; a large exposure is one of at least 10% of Tier 1, and the limit is 25%. Exposures are EADs.

Lessons: L3.3.12: Collateral, guarantees and credit risk mitigation · L3.3.13: Concentration risk

(a)What is the expected loss on Hastemoor Construction Ltd's facility with the guarantee? Answer in £.
£
(b)What is the book's HHI by name once Wrenstow joins? (Hint: the sum of squared EADs is HHI × total².)
(c)What is the merged group's exposure as a share of Tier 1? Answer in %.
%
(d)How do the large-exposure rules treat the group after completion?
AAs two separate exposures, each below 10% of Tier 1: nothing to reportBAs one large exposure: report it; it is within the 25% limit, with room to spareCAs a breach of the 25% limit: the bank must cut the exposureDOnly the target counts, because it is the weaker borrower

Problem 8A year later: the market's view and the provision

L3.3.16 · L3.3.17 · L3.3.18

Credit risk and finance, IFRS 9 provisioning

A year after the loan was written, the review confirms Wrenstow Foods Ltd at grade 7 (PD 2.26%); it was grade 5 (PD 0.57%) when the loan was made. It is up to date on its payments and not on the watchlist. Its listed notes now trade at a credit spread of 330bp; assume a recovery rate of 40%.

The facility: EAD £25.2m, LGD 31.4%, 4 years left, effective interest rate 5.4%. The bank's staging rule (as in L3.3.18: Provisioning basics): stage 2 if the 12-month PD is at least 3 times the PD at origination, the loan is more than 30 days past due, or it is on the watchlist; stage 3 if it is in default or 90 days past due. ECL uses a constant annual PD from the grade, losses in the middle of the year, discounted at the effective interest rate.

Lessons: L3.3.16: Market-implied default risk · L3.3.17: Early warning, watchlists and workout · L3.3.18: Provisioning basics

(a)What hazard rate does the credit triangle give from the spread? Answer in % a year.
%
(b)At that constant hazard rate, what is the probability of default within five years? Answer in %.
%
(c)Which IFRS 9 stage is the loan in now?
AStage 1: it is not past due and not on the watchlistBStage 2: its 12-month PD is at least 3 times what it was at originationCStage 2: the market-implied five-year PD is above 20%DStage 3: a grade this weak counts as credit-impaired
(d)What would the 12-month ECL be? Answer in £.
£
(e)What is the lifetime ECL over the 4 remaining years? Answer in £.
£

Score 0 / 340 of 8 problems checked

Back · L3.3.18

Provisioning basics

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What counterparty credit risk is