Risk Foundationsbeginner

Credit Risk

Credit risk is the risk of loss when a borrower or counterparty fails to meet its obligations. Its expected size is built from three components: the probability of default (PD), the loss given default (LGD, the fraction not recovered), and the exposure at default (EAD, the amount owed when default occurs). Important sub-types include settlement risk (a counterparty fails after you have delivered but before you are paid) and sovereign risk (a government defaults or imposes capital controls). For most banks, credit risk is the single largest exposure on the balance sheet.

Why it matters

Credit risk is the chance someone you lent to does not pay you back. Three things set the expected damage: how likely they are to default (PD), how much you fail to recover when they do (LGD), and how big the debt is at that moment (EAD). Multiply them and you have the expected loss. Two flavours deserve names: settlement risk, where you hand over your side of a trade and the other side vanishes, and sovereign risk, where the borrower is a whole country.

Formulas

Expected credit loss

EL = PD \times LGD \times EAD

Expected loss is the product of the probability of default, the loss given default (one minus the recovery rate), and the exposure at default. Each can be estimated separately.

Loss given default and recovery

LGD = 1 - \text{Recovery Rate}

If 40% of the exposure is recovered after default, LGD is 60%. Higher recovery (better collateral or seniority) means a lower LGD and a smaller expected loss.

Worked examples

Scenario

A bank lends US$1M to a firm with a 2% one-year default probability and an expected 40% recovery. Find the expected credit loss.

Solution

LGD is one minus the recovery rate, so $\text{LGD} = 1 - 0.40 = 0.60$ . With EAD of US$1M and PD of 2%, expected loss is $\text{PD} \times \text{LGD} \times \text{EAD} = 0.02 \times 0.60 \times 1{,}000{,}000 = 12{,}000$ , that is US$12,000. This is only the expected loss; the bank also holds capital against the much larger unexpected loss in the tail of the default distribution.

Common mistakes

✗Credit risk only exists for loans. It arises in any contract where a counterparty owes future performance, including derivatives, bonds, trade receivables, and unsettled trades.
✗Expected loss is the amount a bank should hold capital for. Capital is held against unexpected loss in the tail; expected loss is meant to be covered by pricing and provisions, not capital.
✗A high recovery rate means credit risk is negligible. Recovery lowers LGD but says nothing about default probability or exposure, so significant credit risk can remain.
✗Sovereign debt is free of credit risk. Governments can and do default or impose controls; a government bond is default-risk-free only in a narrow, currency-specific sense, not absolutely.

Revision bullets

•Credit risk = loss when a counterparty fails to pay
•Expected loss = PD x LGD x EAD
•LGD = 1 minus the recovery rate
•Sub-types: settlement risk, sovereign risk
•Usually the largest single exposure for a bank; capital covers unexpected (tail) loss

Quick check

The expected credit loss on an exposure is given by

If the recovery rate on a defaulted loan is 35%, the loss given default (LGD) is

Connected topics

Risk Taxonomy Operational Risk Distress Models Sovereign Risk

Sources

Jorion (2007), Ch. 18-19
Jorion, P. Value at Risk: The New Benchmark for Managing Financial Risk. 3rd ed. McGraw-Hill, 2007.
Develops credit risk through default probability, recovery (LGD), and exposure, plus settlement risk.
Hull (2018), Ch. 16-17
Hull, J. C. Risk Management and Financial Institutions. 5th ed. Wiley, 2018.
Presents the EL = PD x LGD x EAD decomposition and the expected-versus-unexpected-loss distinction.

How to cite this page

Dr. Phil's Quant Lab. (2026). Credit Risk. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-credit-risk

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