Credit and counterparty risk · RiskAtoms Academy

By the end you will be able to

1Explain default, migration and counterparty risk, and tell them apart.
2Calculate expected loss as PD × LGD × EAD, including undrawn limits.
3Explain how a derivative's exposure changes with markets, and how collateral reduces it.
4Explain why expected loss is a cost of lending and capital covers the unexpected.

Why it matters

Loans are 60% of Example Bank plc's assets. If one borrower in 5 defaulted and the bank lost 50% of what each owed, the loss of £30bn would wipe out its equity. Credit risk is the risk banks exist to take, and the one most likely to sink them.

Core explanation

When someone does not pay

Credit risk is the risk of losing money because someone who owes you money does not pay, or becomes less likely to. You met its market signals in L1.4.07: Credit ratings and credit spreads: ratings and spreads. Here we split it into its parts and put a number on it.

Default risk. The borrower stops paying. A default means a missed payment of interest or principal, or a bankruptcy. The lender then recovers what it can, from collateral such as a house or from the bankruptcy process, and loses the rest.

Migration risk. The borrower keeps paying, but gets weaker. A rating agency downgrades it, or the bank's own rating of it falls. Its debt is worth less, because investors now want a wider spread to hold it. A bond worth £100m with a duration of 5 whose spread widens from 1.5% to 3.0% after a downgrade from BBB to BB loses about 5 × 1.5% × £100m = £7.5m, with no default at all. Market-wide spread moves are market risk (L2.2.02: Market risk); a move caused by this borrower's own downgrade is migration risk, part of credit risk.

Counterparty risk. A loan's exposure is known: the amount lent. A derivative's is not. An interest rate swap starts with a value of zero; as rates move, it becomes an asset for one side and a debt for the other. If the side that owes defaults, the other must replace the trade at today's prices, and loses its positive value. That is counterparty credit risk. Its exposure goes up and down with markets, and it can run both ways. Collateral, netting and central counterparties (L1.7.11: Clearing, margin and collateral) are there to shrink it.

Step throughA swap with a hedge fund, day by day

Day 3

Value of the swap to the bank£45m

Collateral held£30m

Exposure with no collateral£45m

Exposure after collateral£15m

Solid line: value to the bank (£m). Dashed: collateral, posted a day late. Red: what is at risk if the fund fails today.

The fund owes the bank £45m on the swap but has only posted £30m. If it failed today, £15m would be at risk.

Without collateral, the exposure peaks at £45m. With daily collateral it never exceeds £20m: only the move since the last margin call is at risk. Worse is wrong-way risk, when the exposure grows just as the counterparty weakens, for example buying protection against a bank's default from a firm that would fail alongside it.

Settlement risk is the short-lived cousin: in an exchange of payments, you pay your side and the other party fails before paying theirs. It is why currency trades now mostly settle both sides at once (see the Sparks).

Sort itDefault, migration, counterparty or settlement?

A retailer that borrowed from the bank goes into administration and stops paying.
An insurer's corporate bond is cut from investment grade to high yield. Coupons are still paid.
A hedge fund defaults while its currency forwards with the bank are worth £40m to the bank.
The bank pays €100m in Frankfurt for dollars that are due later that day in New York. The other bank fails in between.
A reinsurer fails before paying Example Insurance SE its share of storm claims.

Credit risk is the largest risk on Example Group's balance sheets. Pick “Credit risk” to see where it sits.

ExploreExample Group: where the risks sit

Pick a risk type to light up the lines that carry it. Pick a line to see why.

Example Bank plc

£ billions · assets carrying credit risk: £430bn (86%)

Assets

Liabilities

Example Insurance SE

€ millions · assets carrying credit risk: €60,500m (86%)

Assets

Liabilities

Credit risk

The risk of loss because a borrower or counterparty fails to pay what it owes, or becomes less likely to pay.

Where this goes next

M3.2: Credit risk covers the credit process, ratings, PD, LGD and EAD in depth, and M3.3: Counterparty credit risk counterparty exposure, netting and collateral. The capital rules are in M4.2: Credit risk capital and M4.4: Counterparty, operational and large exposures, and loan loss provisions under IFRS 9 in M4.7: Accounting for risk.

The formal version

Expected loss is an expectation

Three numbers describe a credit exposure: the probability of default (PD), the loss given default (LGD) and the exposure at default (EAD). L1.4.07: Credit ratings and credit spreads used PD × LGD as a percentage loss; multiplying by EAD turns it into money.

Over a year, a loan has two outcomes. With probability PD it defaults and the bank loses LGD × EAD; with probability 1 − PD it does not and the bank loses nothing. The expected loss is the probability-weighted average of the outcomes (M-C02: Expectation):

\text{EL} = E[\text{loss}] = \text{PD} \times (\text{LGD} \times \text{EAD}) + (1 - \text{PD}) \times 0

\text{EL} = \text{PD} \times \text{LGD} \times \text{EAD}

For a credit line, the borrower may draw more before it defaults: firms in trouble use every limit they have. So EAD adds a share of the unused limit, the credit conversion factor (CCF):

\text{EAD} = \text{drawn} + \text{CCF} \times \text{undrawn}

For a derivative, EAD is built from its replacement cost after collateral, plus an add-on for how much it could grow:

\text{exposure today} = \max(\text{value} - \text{collateral},\ 0)

Conventions

PD over one year unless stated; LGD and PD as decimals or percentages; EAD in money. Expected loss assumes PD, LGD and EAD are independent, which fails in a recession: defaults rise and recoveries fall together.

Try it

A business loan of £8m with a further £4m of unused overdraft. At the starting settings, EAD is £10m and expected loss £0.08m. Raise the share of the limit drawn before default and watch EAD grow, then move PD and see that the loss if default does not change at all.

Try itExpected loss calculator

Probability of default (PD), one year2.0%

Loss given default (LGD)40%

Drawn amount£8.0m

Unused limit£4.0m

Share of the unused limit drawn before default (CCF)50%

Exposure at default (EAD)£10.00m

Loss if it defaults (LGD × EAD)£4.00m

Expected loss (PD × LGD × EAD)£0.080m

Expected loss as a share of EAD0.80%

The bank never loses the expected loss on one loan: it loses nothing, or the full loss if default. The expected loss is what it loses on average across many such loans.

Worked example

Expected loss on Example Bank plc's loan book

Example Bank plc's £300bn of loans, split into four made-up portfolios with typical PDs and LGDs. Mortgages have low LGDs because the house is collateral; credit cards have no collateral at all.

From PD, LGD and EAD to the year's expected loss

Step 1 of 6

1
Residential mortgages
EAD = £180bn drawn. EL = 0.5% × 15% × £180bn = £0.135bn.

Portfolio	EAD £bn	PD	LGD	EL £bn
Residential mortgages	180	0.5%	15%	0.135
Loans to small businesses	60	2.0%	40%	0.480
Loans to large companies	40	0.8%	45%	0.144
Credit cards and personal loans	30	3.0%	80%	0.720
Total	310			1.479

Regulatory lens

Capital: under Basel, banks hold capital against credit risk either with standard risk weights or, with approval, with their own estimates of PD (and for some, LGD and EAD) in the internal ratings-based approach. Capital is sized for unexpected loss; expected loss is meant to be covered by provisions.
Provisions: IFRS 9 makes banks set aside expected credit losses: 12 months' worth for healthy loans, lifetime losses once credit risk has risen significantly. The US uses lifetime losses from the start (CECL).
Counterparty and concentration: Basel sets the exposure measure for derivatives (SA-CCR), capital for losses from a counterparty's worsening credit (CVA), and a large exposures limit of 25% of Tier 1 capital to any one counterparty or connected group.
Insurers: Solvency II charges capital for spread and counterparty default risk, including on reinsurers.

The calculations are in M4.2: Credit risk capital, M4.3: Market risk capital (FRTB) and CVA, M4.4: Counterparty, operational and large exposures and M4.7: Accounting for risk.

Sparks

SparkThe bank that closed mid-trade

On 26 June 1974 German regulators shut Bankhaus Herstatt at the end of the German business day. Banks that had paid it Deutsche marks that morning were still waiting for the dollars due to them in New York, and never got them. The shock helped lead to the creation of the Basel Committee that year, and “Herstatt risk” is still the nickname for settlement risk. CLS, a system that settles both sides of currency trades at once, began operating in 2002.

SparkYour overdraft limit is part of your exposure

Studies of defaulted companies find that they tend to draw heavily on their credit lines in the months before default. That is why banks hold capital and provisions against limits customers have not yet used, and why the CCF exists.

Key takeaways

Credit risk has three main forms: default (no payment), migration (weaker credit, lower value) and counterparty risk (the other side of a trade fails).
Expected loss = PD × LGD × EAD: the probability-weighted average of losing LGD × EAD or nothing.
EAD includes the share of unused limits likely to be drawn before default (CCF).
Counterparty exposure moves with markets; collateral, netting and CCPs shrink it, wrong-way risk grows it.
Expected loss is a cost of lending covered by pricing and provisions; capital covers the unexpected.

Reaction

Check what stuck

Question 1 · objective 2

A loan has EAD £5m, PD 2% and LGD 40%. What is its expected loss, in £ thousands?

£k

Question 2 · objective 2

A company has drawn £6m of a £10m credit line. The bank expects 75% of the unused part to be drawn before any default. PD is 1% and LGD 50%. What is the expected loss, in £ thousands?

£k

Question 3 · objective 1

A bond the bank holds is downgraded from A to BBB. The issuer has paid every coupon. The bond's price falls. Which risk is this?

ADefault riskBMigration riskCSettlement riskDThere is no loss until a default

Question 4 · objective 3

A swap is worth £50m to a bank. The counterparty has posted £35m of collateral. If the counterparty defaulted today, how much would be at risk, in £m, before any recovery?

£m

Question 5 · objective 3

Which of these is wrong-way risk?

AA bank buys credit protection on a large bank from that bank's own close affiliateBA bank lends to a supermarket chainCA bank posts collateral to a CCPDA bank holds government bonds

Glossary

Credit risk: The risk of loss because a borrower or counterparty fails to pay what it owes, or becomes less likely to pay.
Default: A failure to pay interest or principal when due, or a bankruptcy.
Migration risk: The risk that a borrower's credit quality worsens, for example a downgrade, so the debt loses value even though it is still being paid.
Counterparty credit risk: The risk that the other side of a derivative or securities financing trade defaults before it has paid what the trade owes.
Settlement risk: The risk of paying out one side of an exchange and not receiving the other.
PD: Probability of default: the chance a borrower defaults within a set period, usually one year.
LGD: Loss given default: the share of the exposure lost if the borrower defaults, after recoveries. One minus the recovery rate.
EAD: Exposure at default: how much the borrower will owe at the moment it defaults, including limits it may draw first.
CCF: Credit conversion factor: the share of an unused credit limit expected to be drawn before a default.
Expected loss: Expected loss: the average loss to expect, PD × LGD × EAD. A cost of lending, priced in and provided for.
Unexpected loss: Unexpected loss: how far losses can exceed the expected loss in a bad year. This is what capital is for.
Replacement cost: What it would cost to replace a defaulted counterparty's trades at today's prices: the positive value of the trades.
Wrong-way risk: Exposure to a counterparty that grows just as that counterparty becomes more likely to default.
Concentration risk: The risk of large losses from too much exposure to one borrower, sector or region.

Deep Dives & Origins

Deep Dives

Saunders and Cornett, Financial Institutions Management: A Risk Management Approach (McGraw-Hill), the chapters on credit risk. Beginner.
Gregory, The xVA Challenge: Counterparty Risk, Funding, Collateral, Capital and Initial Margin, 4th edition (Wiley, 2020), the opening chapters. Advanced.

Origins

BCBS, The Basel Framework, chapters CRE (credit risk) and MAR50 (CVA).
BCBS, The standardised approach for measuring counterparty credit risk exposures, March 2014.
BCBS, Supervisory framework for measuring and controlling large exposures, April 2014.
IASB, IFRS 9 Financial Instruments, 2014.
Hull, Risk Management and Financial Institutions (Wiley), the chapters on credit risk and counterparty credit risk.

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