Exposure at default · RiskAtoms Academy

By the end you will be able to

1Compute EAD as drawn plus CCF × undrawn, for a facility and for the bank's book.
2Estimate a CCF from past defaulted facilities, with the usual choices (reference date, floor, weighting).
3Explain why borrowers draw down their lines before they default, and what that means for CCFs.
4Show how limits, cancellable lines and covenants let a bank manage its EAD.

Why it matters

RiskAtoms Bank has promised its twelve corporate borrowers £692m. They have drawn £474.5m. If one of them defaults next year, how much will it owe? Not the £474.5m, because a company sliding towards default reaches for every pound it has been promised. Not the full £692m either. The bank's answer, £587m, rests on one estimated number per facility: the credit conversion factor.

Core explanation

The exposure that grows as the borrower weakens

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.

Exposure at default (EAD) is the third input to expected loss (L2.2.03: Credit and counterparty risk). For a term loan it is simple: the outstanding balance, plus interest and fees due, at the expected default date. For a revolving facility, an overdraft or a credit card, the borrower decides how much to use, and the undrawn part can turn into a loan at any moment. The bank turns it into an exposure with a credit conversion factor:

\text{EAD} = \text{drawn} + \text{CCF} \times (\text{limit} - \text{drawn})

Across the corporate book, £217.5m is undrawn and the CCFs add £112.5m, an average CCF of 51.7% on the undrawn amount. The largest unused lines:

Borrower	Grade	Limit	Drawn	Undrawn	CCF	EAD
Ostreth Energie GmbH	3	£100.0m	£40.0m	£60.0m	50%	£70.00m
Cindral Pharma Inc	2	£75.0m	£15.0m	£60.0m	50%	£45.00m
Quorrel Systems BV	5	£50.0m	£10.0m	£40.0m	50%	£30.00m
Sallowmere Logistics GmbH	4	£55.0m	£35.0m	£20.0m	50%	£45.00m
Thornvale Engineering Ltd	4	£60.0m	£45.0m	£15.0m	50%	£52.50m
Bramwick Stores plc	6	£80.0m	£70.0m	£10.0m	60%	£76.00m
Larkhollow Freight Ltd	7	£30.0m	£26.0m	£4.0m	75%	£29.00m
Mirefield Care Homes Ltd	6	£45.0m	£42.0m	£3.0m	75%	£44.25m
Hastemoor Construction Ltd	8	£25.0m	£22.0m	£3.0m	75%	£24.25m
Vellacourt Hôtels SAS	7	£40.0m	£38.0m	£2.0m	50%	£39.00m
Graybeck Plastics Ltd	9	£12.0m	£11.5m	£0.5m	100%	£12.00m
Pellcourt Properties Ltd	5	£120.0m	£120.0m	£0.0m	0%	£120.00m
Book		£692m	£474.5m	£217.5m	51.7%	£587m

The CCFs differ for a reason. Pellcourt Properties' term loan is fully drawn (CCF irrelevant). Graybeck Plastics, on the watchlist at grade 9, is given 100%: whatever is left will be used. Strong borrowers like Cindral Pharma and Ostreth Energie carry 50%, but they also hold most of the unused limits,£60m each. Retail works the same way: card transactors, who repay in full each month, get a CCF of 10% on £310m of unused limits, while revolvers, who carry balances, get 45%, adding £54m to their EAD.

Why borrowers draw before they default

Utilisation is not stable. It rises as a borrower weakens, and the bank sits on the wrong side of that. Open each card:

Estimating a CCF from past defaults

A bank estimates CCFs from its own defaulted facilities. Fix a reference date (often twelve months before default), then measure how much of the then-undrawn amount was drawn by default: the realised CCF. Six past defaults on revolving facilities:

Illustrative data An extra for this lesson: six invented past defaults, not part of the current book.

Facility	Sector	Limit	Drawn 12 months before	Drawn at default	Realised CCF
F1	Retail trade	£20m	£10.0m	£18.0m	80%
F2	Manufacturing	£15m	£12.0m	£15.0m	100%
F3	Transport	£40m	£25.0m	£31.0m	40%
F4	Construction	£10m	£4.0m	£8.5m	75%
F5	Real estate	£30m	£28.0m	£27.0m	−50%
F6	Technology	£25m	£5.0m	£20.0m	75%

F1F2F3F4F5F6

Average utilisation rose from 58% a year before default to 87% at default, and most of the rise came in the last months (the monthly paths are smoothed for illustration). Three choices turn the six numbers into one CCF:

Negative values. F5 repaid some of its line: −50%. The simple average is 53.3%; floored at zero it is 61.7%.
Weighting. Weighting each facility by its undrawn amount (total extra drawing over total undrawn) gives 65.2%, because the big undrawn line F6 was drawn heavily.
Segments. With more data, CCFs are set by product, by utilisation band (a line that is already 95% drawn has little left to convert) and by grade.

Managing EAD

EAD is partly in the bank's hands. Cancelling or reducing unused commitments cuts it: if Quorrel Systems BV agreed to a £20m smaller limit, its EAD would fall from £30m to £20m. Covenants let the bank stop drawing early. Unconditionally cancellable lines (most card limits) can be cut, but banks rarely act fast enough to cut them all, so their CCF is not zero. Off-balance-sheet items such as letters of credit and guarantees issued get CCFs too.

Sort itWhat drives the EAD of each facility?

A fully drawn five-year term loan to buy a property
A £100m revolving facility, £40m drawn, to a large energy company
A credit card with a £5,000 limit and a £300 balance
A repayment mortgage with no further advance

The formal version

EAD and the realised CCF. With limit $L$ , drawn amount $D_r$ at the reference date $r$ and $D_d$ at default:

\begin{aligned} \text{EAD} &= D_r + \text{CCF}\,(L - D_r) \\ \text{CCF}_{\text{realised}} &= \frac{D_d - D_r}{L - D_r} \\ \overline{\text{CCF}}_{\text{pooled}} &= \frac{\sum_i \max(0,\ D_{d,i} - D_{r,i})}{\sum_i (L_i - D_{r,i})} \end{aligned}

The realised CCF is undefined for a fully drawn line ( $L = D_r$ ) and very noisy when little is undrawn, which is why some banks model the EAD directly, or a loan equivalent of the limit, for nearly full lines. For the six facilities:

\overline{\text{CCF}}_{\text{pooled}} = \frac{8.0 + 3.0 + 6.0 + 4.5 + 0.0 + 15.0}{10 + 3 + 15 + 6 + 2 + 20} = 65.2\%

The link with PD. EAD enters expected loss as $\mathbb{E}[\text{EAD} \times \text{LGD} \times \mathbf{1}_{\text{default}}]$ . Writing it as PD × LGD × EAD uses the EAD given default. That is why the CCF is measured on defaulted facilities: an average over all facilities, most of which never default, would understate it.

Try it

Choose a facility and move the drawn amount and the CCF. Then apply a drawdown stress to the whole book and watch how much, and how little, the expected loss moves.

Try itDrawn, undrawn and EAD

Facility

Drawn today£22.00m

CCF on the undrawn part75%

Drawn£22.00m
Expected further drawing (CCF × undrawn)£2.25m
Undrawn, not expected to be drawn£0.75m
EAD£24.25m

EAD£24.25m

Expected loss£604.2k

Utilisation (drawn / limit)88%

PD (grade)4.53% (8)

LGD55.0%

Book's figures for this facility£24.25m, £604.2k

Drawdown stress on the whole corporate book

Book EAD£587.0m

Change+£0.00m

Book expected loss£2.814m

Change+0.0%

Worked example

Bramwick Stores plc's revolving facility

Drawn, undrawn, EAD and expected loss

Step 1 of 5

1
The facility
Bramwick Stores plc (grade 6, PD 1.13%, senior unsecured, LGD 45%) has a £80m revolving facility, £70m drawn. Undrawn: £10m. The bank's CCF for a grade 6 retailer is 60%.

Regulatory lens · looking ahead

Capital rules set EAD for off-balance-sheet items with CCFs: fixed percentages by product in the standardised approach and the foundation IRB approach, and the bank's own estimates, within limits, for some exposures under advanced IRB. The detail is in M4.2: Credit risk capital. For derivatives, where exposure moves with market prices rather than with the borrower's drawing, EAD needs its own methods (M3.4: Counterparty credit risk and M4.4: Counterparty, operational and large exposures).

Spark Atoms

Spark AtomThe biggest drawdown on record

In March 2020 firms drew on their credit lines so heavily that researchers at the NBER called it the largest increase in liquidity demands banks had ever faced. The demand was concentrated at the largest banks, which serve the largest firms, and the banks met it, helped by inflows of deposits and central bank liquidity.

Spark AtomLines get quieter with age

A study of Spanish corporate credit lines found that usage falls by roughly 10% for each year of a line's life, while a firm's worsening finances push it up. Age and distress pull utilisation in opposite directions.

Key takeaways

EAD = drawn + CCF × undrawn; for term loans it is the balance plus interest due.
The corporate book: £474.5m drawn, £217.5m undrawn, EAD £587m (average CCF 52%).
Borrowers draw their lines as they weaken, so CCFs are estimated on defaulted facilities, from a reference date to default.
Choices matter: the reference date, flooring negative CCFs and weighting change the estimate.
PD and EAD rise together, and limits, covenants and cancellable lines are how a bank manages EAD.

Reaction

Check what stuck

Glossary

Exposure at default (EAD): Exposure at default: what the borrower will owe the bank at the moment it defaults, including any further drawing before then.
Revolving credit facility: A revolving credit facility: a committed line the borrower can draw, repay and draw again up to a limit until it matures.
Undrawn commitment: The part of a committed limit not yet used. The bank has promised to lend it on request.
Credit conversion factor (CCF): Credit conversion factor: the share of today's undrawn amount expected to be drawn by the time of default.
Utilisation: Utilisation: drawn amount divided by the limit.
Realised CCF: A CCF measured on a facility that has defaulted: the extra amount drawn between a reference date and default, divided by what was undrawn on the reference date.
Unconditionally cancellable: A commitment the bank can cancel at any time without notice. It still carries some EAD, because banks rarely cancel fast enough.
Off-balance-sheet exposure: Commitments and guarantees that are not loans on the balance sheet today but can become loans, such as undrawn lines, letters of credit and guarantees issued.

Deep Dives & Origins

Deep Dives

B. Engelmann and R. Rauhmeier (eds), The Basel II Risk Parameters, 2nd ed., Springer, 2011, the chapters on EAD estimation. Advanced.
G. Jiménez, J. A. Lopez and J. Saurina, “Empirical Analysis of Corporate Credit Lines”, Review of Financial Studies 22(12), 2009. Intermediate.

Origins

G. Jiménez, J. A. Lopez and J. Saurina, “Empirical Analysis of Corporate Credit Lines”, Review of Financial Studies 22(12), 2009.
L. Li, P. E. Strahan and S. Zhang, “Banks as Lenders of First Resort: Evidence from the COVID-19 Crisis”, NBER Working Paper 27256, 2020 (published in the Review of Corporate Finance Studies 9(3), 2020).

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