Concentration risk · RiskAtoms Academy

By the end you will be able to

1Measure single-name, sector and country concentration in a loan book, and explain why each matters.
2Calculate the HHI and the effective number of names for a book, and read what they say.
3Check exposures against large-exposure limits, adding up connected borrowers.
4Show from the loss variance why a concentrated book has more uncertain losses at the same expected loss.

Why it matters

RiskAtoms Bank's corporate book is twelve loans and £587m of exposure. One of them, Pellcourt Properties Ltd, is 20% of it on its own, and property companies make up 27%. Expected loss is only £2.81m a year. But if a few of those names fail in the same year, the loss is many times that. Concentration is how a bank with sound loans can still have a very bad year.

Core explanation

Too many eggs in too few baskets

Illustrative dataRiskAtoms Bank plc's credit book

The module's lending book: twelve invented corporate borrowers (exposure at default £587m, expected loss £2.81m), retail mortgages, personal loans and cards, a ten-grade master scale, personal-loan vintages and twenty past workouts. Every firm and figure is made up for teaching, in pounds, at one date; none is real data.

This lesson adds two extras to the book, both illustrative assumptions: the bank's Tier 1 capital of £560m, and an ownership link: Thornvale Engineering Ltd owns 80% of Graybeck Plastics Ltd. Exposures are the book's EADs.

L2.6.05: Diversification and its limits showed that diversification shrinks risk only when the pieces do not all move together. In a loan book, concentration risk is what is left when they do. It comes in three forms:

Single-name concentration: a few large loans. Their defaults are rare, but each one hurts.
Sector concentration: many loans to one industry. A property crash or an energy price shock hits them all at once.
Country (geographic) concentration: the same, for one economy or one region, plus the risk that a government stops money leaving the country.

Single-name concentration is about size. Sector and country concentration are about correlation: they make defaults cluster, which is what L3.3.11: Unexpected loss and default correlation showed fattens the tail of the loss distribution.

The book by name, sector and country

By sector

Real estate

27.1%

Healthcare

15.2%

Retail trade

12.9%

Transport

12.6%

Energy

11.9%

Manufacturing

11.0%

Technology

5.1%

Construction

4.1%

By country

UK

61.0%

Germany

19.6%

US

7.7%

France

6.6%

Netherlands

5.1%

The three largest names hold 45% of the book. Real estate (Pellcourt Properties Ltd and Vellacourt Hôtels) is 27.1%, and the UK 61.0%. Shares like these are the first thing a credit portfolio report shows.

One number for concentration: the HHI

To compare books, or the same book over time, risk teams squeeze the shares into one number. The Herfindahl-Hirschman index squares each share and adds them up (M-A08: Summation notation). Squaring makes big shares count far more than small ones. Twelve equal loans would give 1/12 = 0.083; the book gives 0.110. Its effective number of names, 1/HHI, is 9.1: twelve borrowers, but as concentrated as about nine equal ones.

Name HHI

0.110

≈ 9.1 equal names

Sector HHI

0.160

≈ 6.3 equal sectors

Country HHI

0.423

≈ 2.4 equal countries

The country HHI is the worst of the three: a UK recession is the scenario this book fears most. The HHI has a blind spot, though. It sees sizes, not how strong each borrower is or how their fortunes are linked. A risk team reads it alongside the shares, the grades and stress tests.

Large exposures and connected borrowers

The hard limit is on single names. A large exposure is one of at least 10% of Tier 1 capital; no exposure may exceed 25%. With the assumed £560m of Tier 1, that is £56m and £140m. The limit applies to connected counterparties as a group. Alone, Thornvale Engineering Ltd (£52.5m) is below 10%; with Graybeck Plastics Ltd it is £64.5m, 11.5% of Tier 1, a large exposure.

Counterparty or group	Exposure	% of Tier 1	Status
Pellcourt Properties Ltd	£120.0m	21.4%	large
Bramwick Stores plc	£76.0m	13.6%	large
Ostreth Energie GmbH	£70.0m	12.5%	large
Thornvale group	£64.5m	11.5%	large
Cindral Pharma Inc	£45.0m	8.0%	below 10%
Sallowmere Logistics GmbH	£45.0m	8.0%	below 10%

4 large exposures, none above 25%. Pellcourt Properties Ltd uses 21.4% of Tier 1, so only £20m of headroom is left. Its property collateral does not reduce the figure: the large-exposure rules recognise only some kinds of mitigation (financial collateral, guarantees and credit derivatives).

Sort itWhich kind of concentration?

Sort each finding from a credit portfolio review.

One borrower is 20% of the corporate book.
A third of new lending this year went to commercial property firms.
Most of the book's borrowers sell mainly into one economy.
Two borrowers with different names share a parent that guarantees both.
A supplier sells 80% of its output to another of the bank's borrowers.

Banks manage concentration with limits by name, group, sector and country, set from the risk appetite (L2.3.06: Limits and escalation), and with tools that move risk off the book: syndication and loan sales, credit derivatives (L3.3.12: Collateral, guarantees and credit risk mitigation), and simply saying no to a good borrower who has had enough.

The formal version

For a book of $n$ exposures with total $E = \sum_i \text{EAD}_i$ and shares $s_i = \text{EAD}_i / E$ :

\begin{aligned} \text{HHI} &= \sum_{i=1}^{n} s_i^2, \qquad \frac{1}{n} \le \text{HHI} \le 1, \qquad N_{\text{eff}} = \frac{1}{\text{HHI}} \\ \text{HHI}_{\text{book}} &= 0.2044^2 + 0.1295^2 + \dots + 0.0204^2 = 0.1098, \qquad N_{\text{eff}} = 9.11 \end{aligned}

Why the HHI is the right summary for single-name risk follows from the variance of the loss:

\begin{aligned} L &= \sum_{i=1}^{n} D_i\,\text{LGD}_i\,\text{EAD}_i, \qquad D_i \sim \text{Bernoulli}(\text{PD}_i) \\ \mathbb{E}[L] &= \sum_{i=1}^{n} \text{PD}_i\,\text{LGD}_i\,\text{EAD}_i \\ \operatorname{Var}(L) &= \sum_{i=1}^{n} \text{PD}_i(1-\text{PD}_i)\,\text{LGD}_i^2\,\text{EAD}_i^2 \qquad \text{(independent defaults)} \\ &= \text{PD}(1-\text{PD})\,\text{LGD}^2 \sum_{i=1}^{n} \text{EAD}_i^2 \qquad \text{(equal PD and LGD)} \\ &= \text{PD}(1-\text{PD})\,\text{LGD}^2\,E^2 \sum_{i=1}^{n} s_i^2 = \text{PD}(1-\text{PD})\,\text{LGD}^2\,E^2\,\text{HHI} \\ \operatorname{sd}(L) &= \text{LGD}\,\sqrt{\text{PD}(1-\text{PD})}\;E\,\sqrt{\text{HHI}} \end{aligned}

The expected loss does not depend on the HHI at all. The spread of the loss grows with its square root. With the book's EAD-weighted PD of 1.126% and LGD of 31.8%:

\begin{aligned} \operatorname{sd}(L) &= 0.3176 \times \sqrt{0.01126 \times 0.98874} \times \text{£}587\text{m} \times \sqrt{0.1098} = \text{£}6.52\text{m} \\ \text{12 equal loans:}\quad &\sqrt{1/12}\ \Rightarrow\ \text{£}5.68\text{m}, \qquad \text{1,000 equal loans:}\quad \sqrt{1/1000}\ \Rightarrow\ \text{£}0.62\text{m} \end{aligned}

Using each loan's own PD and LGD (the third line) gives £6.18m, close to the shortcut. A thousand small loans would cut the spread by a factor of ten: that is what a granular retail book buys. Independence is the generous case. With correlated defaults (L3.3.11: Unexpected loss and default correlation) there is a floor that no amount of splitting removes; sector concentration raises that floor.

Try it

Start with Pellcourt Properties Ltd and add £20m: it reaches the 25% limit. Then try the same £20m for Quorrel Systems BV and compare the HHIs. Finally, cut Pellcourt to half and see how far the country HHI moves: not much, because the UK dominates whatever you do to one name.

Try itChange one exposure

Borrower

Change in EAD+£0m → £120.0m

Book EAD£587.0m

Name HHI (today 0.110)0.110

Effective number of names9.1

Sector HHI (today 0.160)0.160

Country HHI (today 0.423)0.423

Pellcourt Properties Ltd: share of Tier 121.4%large

Headroom to the 25% limit (£140m)£20.0m

Loss sd, independent defaults (today £6.18m)£6.18m

Real estate

27.1%

Healthcare

15.2%

Retail trade

12.9%

Transport

12.6%

Energy

11.9%

Manufacturing

11.0%

Technology

5.1%

Construction

4.1%

Worked example

Pellcourt Properties Ltd asks for £30m more

A concentration check on one request

Step 1 of 5

1
The request
Pellcourt Properties Ltd, grade 5, wants a further £30m to buy a neighbouring site. Its loan would go from £120m to £150m. The credit case is sound: the extra loan would be secured too. The question here is concentration.

What the risk team writes

Request breaches the 25% large-exposure limit (26.8% of Tier 1). Maximum £20m within limit. Real estate would rise to 31% of the corporate book. Recommend a £20m participation in a syndicated facility.

Regulatory lens

The Basel Committee's large exposures standard, issued in April 2014 and in force since 1 January 2019, defines a large exposure as 10% or more of Tier 1 capital, caps any exposure to one counterparty or group of connected counterparties at 25% of Tier 1, and caps a global systemically important bank's exposure to another at 15%. Off-balance sheet items are converted with the standardised approach's conversion factors, so the regulatory figure can differ from a bank's own EAD. Banks report every large exposure and their twenty largest exposures, whatever their size. The EU applies these rules through the Capital Requirements Regulation (Articles 392 and 395), and the UK through the Large Exposures (CRR) Part of the PRA Rulebook. Sector and country concentration have no hard regulatory limit; supervisors review them under Pillar 2 and may ask for more capital. The detail is in M4.4: Counterparty, operational and large exposures, and portfolio models that capture concentration in M6.5: Portfolio credit models.

Spark Atoms

Spark Atom76% of capital in one borrower

Johnson Matthey Bankers, a London bank, grew its loans from £34 million in 1980 to £309 million by March 1984. By June 1984 two borrowers were owed sums equal to 76% and 39% of its capital. The Bank of England bought it in October 1984. The UK's Banking Act 1987 then made banks report any exposure above 10% of their capital, and tell the Bank before going above 25%. In 1991 the Basel Committee noted that “a significant proportion of major bank failures have been due to credit risk concentration of one kind or another”.

Spark AtomAn index borrowed from antitrust

Competition authorities use the same HHI, on market shares in percentage points, so it runs to 10,000. The US merger guidelines of December 2023 presume a merger anticompetitive if it leaves a market with an HHI above 1,800 and raises it by more than 100. On that scale RiskAtoms Bank's corporate book would score 1,098.

Key takeaways

Concentration risk comes from single names (size), and from sectors and countries (correlated defaults).
HHI = Σ sᵢ², from 1/n to 1; 1/HHI is the effective number of equal names. The book's name HHI is 0.110, about 9 equal names.
Expected loss ignores concentration; with independent defaults the loss standard deviation grows with √HHI.
A large exposure is 10% or more of Tier 1; the limit is 25%, applied to groups of connected counterparties.
Banks manage concentration with name, sector and country limits, syndication, loan sales and credit protection.

Reaction

Check what stuck

Question 1 · objective 2

A book has four loans with shares 40%, 30%, 20% and 10%. What is its HHI (two decimals)?

Question 2 · objective 1

Two books have the same name HHI. One lends to twelve firms in twelve industries; the other to twelve UK commercial property companies. Which carries more concentration risk?

AThey are the same: the HHI is the sameBThe property book: its borrowers share one sector and one country, so their defaults are correlatedCThe diversified book: twelve industries are harder to monitorDNeither: concentration only matters for single names

Question 3 · objective 3

A bank has Tier 1 capital of £800m. Under the Basel standard, what is the most it may lend to one counterparty group, in £m?

£m

Question 4 · objective 3

Thornvale Engineering Ltd owns 80% of Graybeck Plastics Ltd. Why does the bank add the two exposures together for its large-exposure limit?

ABecause they are in the same sectorBBecause control links them: if one fails, the other is likely to be in trouble, so they are one riskCBecause both are in the UKDIt should not: each is a separate legal entity

Question 5 · objective 4

With the same PD and LGD on every loan, by what factor does the standard deviation of the loss fall when a book's HHI falls from 0.16 to 0.04 (same total)?

Glossary

Concentration risk: Credit concentration risk: the risk of a large loss because much of a book is lent to one borrower, or to borrowers that tend to fail together.
Single-name concentration: Too much lent to one borrower or one group of connected borrowers.
Sector concentration: Too much lent to one industry, or one country, whose borrowers are hit by the same shock and so default together.
HHI: Herfindahl-Hirschman index: the sum of the squared shares of a book. It runs from 1/n (n equal parts) to 1 (all in one).
Effective number of names: 1 / HHI: the number of equal exposures that would give the same HHI.
Large exposure: Under the Basel standard, an exposure to one counterparty or connected group of at least 10% of the bank's Tier 1 capital.
Tier 1 capital: Tier 1 capital: the bank's highest-quality capital, mostly shareholders' equity, which absorbs losses while the bank keeps trading.
Connected counterparties: Borrowers linked by control (one owns or controls the other) or by economic dependence (one's failure would likely bring down the other), treated as one counterparty for limits.
Granular portfolio: A book of many small, similar exposures, in which no single default matters much.
Syndication: Sharing one large loan among several banks, so each holds only part of it.

Deep Dives & Origins

Deep Dives

D. Chapman, H. Miller, K. Pascarella and L. Withfield, “‘Don't put all your eggs in one basket’: protecting banks from the failure of individual counterparties”, Bank of England Quarterly Bulletin 2020 Q2. Introductory.
Basel Committee on Banking Supervision, Studies on credit risk concentration, Working Paper 15, BIS, November 2006. Advanced.

Origins

Basel Committee on Banking Supervision, Supervisory framework for measuring and controlling large exposures, BIS, April 2014.
Financial Stability Institute, Large exposures standard: executive summary, BIS.
US Department of Justice and Federal Trade Commission, Merger Guidelines, 18 December 2023.

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