Show why exposure and concentration limits matter and what makes them hard to set.
The idea
Exposure limits cap what the bank can lose to a single obligor, group, industry, country or product. Concentration limits cap the share of the portfolio or of capital in one such bucket. They matter because borrowers sharing a driver default together, so diversification fails and the loss tail fattens even if every name is highly rated. Limits are hard to set for several reasons. Correlations are unobserved and unstable. Derivative and undrawn exposure changes with markets and so needs a potential future exposure measure. Links between names such as a parent and its subsidiary are easy to miss. Limits expressed relative to capital move when capital moves. Too tight a limit costs business, and too loose a limit threatens capital. Exposure should include committed lines, not only drawn balances.
Formulas
Unexpected loss of N identical loans with a common default correlation
ULP = UL × √(N × (1 + (N − 1) × ρ))
- UL
- the unexpected loss of one loan
- N
- the number of loans
- ρ
- the pairwise default correlation
Fixed LGD and exposure. With ρ of zero, UL grows only with √N; with ρ of one it equals N × UL, the sum of single-loan ULs.
A practice question
Which statement best describes a concentration limit?
- A cap on the loss given default the bank will accept on any single loan or facility it books.Why not: Confuses a concentration limit with an LGD constraint; limits cap exposure, not recovery outcomes.
- A cap on how many officers may approve exposures to the same borrower.Why not: Confuses limits with approval authority and segregation of duties.
- A cap on the share of the portfolio or capital exposed to one obligor group or sector. - correct
- A requirement that capital equal the largest single exposure.Why not: Confuses a limit with a capital requirement; limits restrict exposure rather than set capital.
Concentration limits control how much of the book or of capital depends on a single risk driver. They differ from approval authorities and from the capital requirement itself.
A harder one
A bank has Tier 1 capital of USD 2.0 billion and a single-name limit of 15 percent of Tier 1. Its exposure to one corporate group is USD 180 million drawn, USD 90 million of undrawn committed facilities and a derivatives potential future exposure (PFE) of USD 60 million. The limit is measured on the sum of all three. Compared with the limit, the exposure:
- Is within it, with headroom of USD 120 million.Why not: Counts only the drawn balance and ignores undrawn commitments and PFE.
- Is within it, with headroom of USD 30 million.Why not: Adds drawn and undrawn amounts but ignores the derivative PFE.
- Is within it, with headroom of USD 210 million.Why not: Counts only the undrawn commitments and forgets the drawn balance and PFE.
- Exceeds it by USD 30 million. - correct
Limit = 15% x 2,000 = 300. Exposure = 180 + 90 + 60 = 330. The exposure exceeds the limit by 30. Limits should capture committed lines and derivative exposure, not only drawn balances.
The hardest tier
A portfolio holds 20 equal loans of USD 10 million, each with PD 2 percent and LGD 50 percent, and a pairwise default correlation of 0.10. Using unexpected loss as the standard deviation of loss, with fixed LGD and exposure, the portfolio's unexpected loss is closest to:
- USD 5.33 million - correct
- USD 3.13 millionWhy not: Assumes independent defaults (correlation zero), so it ignores the common-factor dependence that makes concentration matter.
- USD 14.00 millionWhy not: Sums the 20 individual ULs, which assumes a default correlation of 1.
- USD 28.42 millionWhy not: Reports the portfolio variance without taking the square root.
Single-loan sigma = 0.5 x 10 x sqrt(0.02 x 0.98) = 0.70. Portfolio variance = 20 x 0.70² x (1 + 19 x 0.10) = 28.4, so UL = 5.33. Ignoring correlation understates it; adding single-loan ULs assumes perfect correlation.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Credit Risk Management
- Outline the main building blocks of a sound lending or financing policy.
- Outline how the scope and allocation of a bank's credit facility are handled, and the bank-level policies and steps used to cut credit risk.
- Review the considerations that feed into classifying credit assets.
- Set out what loan loss provisions and loan loss reserves are and how they work.
- Break expected loss into its components, then show how it differs from unexpected loss.
- Account for what IFRS 9 requires when expected loss is estimated.
- Outline a workout procedure for loss assets, and weigh the approach of keeping loss assets on the books against that of writing them off.
- Account for the elements that make up credit risk analysis.
- Lay out what makes up a bank's capacity to manage credit risk, and list the questions its board of directors should be asking.