Funding concentration · RiskAtoms Academy

By the end you will be able to

1Describe funding concentration by counterparty, product, currency and maturity, and why each can turn into a run.
2Calculate the HHI, the top-k shares and the effective number of providers with summation notation.
3Apply the Basel significance thresholds: 1% of the balance sheet for a counterparty or product, 5% of liabilities for a currency.
4Spot concentration the measures miss: providers that behave alike, unknown holders of securities, maturity cliffs.

Why it matters

A deposit of £850m is nothing to a £67bn bank, until it is one phone call away from leaving. Corriemoor Bank AG lends RiskAtoms Bank that much, more than any other wholesale provider. If its credit officer cuts the line, treasury must replace it the same week, probably at a worse price, while other lenders ask why Corriemoor left. Concentration turns one lender's decision into a signal to everyone else. This lesson measures it in four directions.

Core explanation

Four ways to depend on too few

Illustrative dataRiskAtoms Bank plc's liquidity book

A £67bn balance sheet on one made-up reporting date, in pounds: every line's contractual maturity, its HQLA level, LCR rate and NSFR factors, the undrawn facilities and collateral triggers, and a daily 90-day stress test in three scenarios. The numbers are round illustrative values, not any bank's data, and the cash flows are principal only (no interest). The same book runs through every lesson in Module 3.5, so the figures agree.

Extra for this lesson: the book's £6.5bn of deposits from financial institutions, repo, and CP and CDs is split across 25 providers, the ten largest named, and some funding lines carry a currency split. Both are illustrative and add up exactly to the book's lines. The named firms are invented; any resemblance to a real firm is unintended.

L3.5.02: How banks fund themselves sorted the book's funding into retail, corporate, wholesale and secured. Funding concentration asks a different question: if one source goes, how big is the hole? The Basel liquidity monitoring metrics ask banks to report it in four directions (SRP50.14 to 50.26).

1. By counterparty

Who lends the wholesale money? A counterparty, or a group of connected ones, is significant if it provides more than 1% of the balance sheet: £670m here. Three of the book's providers are.

Provider	Type	Amount	Share	Cumulative	Of balance sheet
Corriemoor Bank AG	Bank	£850m	13.1%	13.1%	1.27%
Varrowmere Sterling Liquidity Fund	Money market fund	£750m	11.5%	24.6%	1.12%
Pellbridge Bank plc	Bank	£700m	10.8%	35.4%	1.04%
Kestermoor Securities LLC	Broker-dealer	£550m	8.5%	43.8%	0.82%
Ravensholt Bank SA	Bank	£450m	6.9%	50.8%	0.67%
Sorrelwick Treasury Reserve Fund	Money market fund	£400m	6.2%	56.9%	0.60%
Ebbsworth Pension Trustees Ltd	Pension scheme	£350m	5.4%	62.3%	0.52%
Bramwick Stores plc	Company	£300m	4.6%	66.9%	0.45%
Tolvenna Life Assurance plc	Insurer	£250m	3.8%	70.8%	0.37%
Halvergate Manufacturing plc	Company	£250m	3.8%	74.6%	0.37%
15 other providers		£1,650m	25.4%	100.0%

Two summary numbers condense the table. The top-10 share is 74.6%. The Herfindahl–Hirschman index, the sum of the squared shares, is 0.0709, or 709 on the 0 to 10,000 scale. Its inverse, the effective number of providers, is 14.1: the 25 providers are about as concentrated as 14 equal ones.

Look at the types, too. Different firms can still behave as one. 5 money market funds supply 22% of the wholesale funding; in a market-wide stress they can all face redemptions at once and stop buying bank CDs together, as money market funds did in March 2020.

Provider type	Providers	Amount	Share
Bank	8	£2,810m	43.2%
Money market fund	5	£1,460m	22.5%
Company	7	£850m	13.1%
Broker-dealer	2	£630m	9.7%
Insurer	2	£400m	6.2%
Pension scheme	1	£350m	5.4%

2. By product

The same 1% test applies to products: 11 of the book's 12 liability lines are significant. By product the HHI is 1,799, driven by insured current accounts at 34.9% of liabilities. That is concentration in the stickiest product a bank has, spread across a very large number of insured depositors. The worrying kind is a product that a whole market can withdraw at once: CP and CDs, or unsecured interbank deposits.

3. By currency

A currency is significant when liabilities in it reach 5% of total liabilities (£3.15bn here). The book raises some of its senior bonds, CP and deposits in dollars and euros:

Currency	Liabilities (£ equivalent)	Share	Significant?
GBP	£56.9bn	90.3%	Yes
USD	£3.6bn	5.7%	Yes
EUR	£2.5bn	4.0%	No

The dollar is significant at 5.7%; the euro, at 4.0%, is not. For a significant currency the bank also monitors its LCR in that currency (SRP50.35). A bank that funds dollar assets with pounds swapped into dollars depends on the FX swap market rolling over, which can seize up or close in a stress even when sterling funding is fine, as the Basel liquidity principles warn.

4. By maturity

The metric splits each source by time band. Of the book's £14.5bn of wholesale funding, 32% falls due within a month.

Long-dated funding can bunch too. The £1.0bn of central bank term funding all falls due in the same bucket, one to two years out: a cliff the bank must plan to refinance well in advance.

Sort itWhich kind of concentration?

Half of the bank's CDs are bought by two money market funds.
40% of the bank's wholesale funding is commercial paper.
The bank funds $3bn of dollar loans with pounds swapped into dollars, rolled every week.
£2bn of senior bonds issued in one programme all mature in the same month.

The formal version

Concentration measures are sums over shares, written with summation notation (M-A08: Summation notation).

Why the HHI lies between 1/n and 1. The upper bound: each share is between 0 and 1, so $s_i^2 \le s_i$ and $\sum s_i^2 \le \sum s_i = 1$ . The lower bound comes from a sum of squares that cannot be negative:

\begin{aligned} 0 \le \sum_{i=1}^{n} \left(s_i - \tfrac{1}{n}\right)^2 &= \sum_{i=1}^{n} s_i^2 - \tfrac{2}{n}\sum_{i=1}^{n} s_i + \sum_{i=1}^{n} \tfrac{1}{n^2} \\ &= \text{HHI} - \tfrac{2}{n} + \tfrac{1}{n} \\ \Rightarrow\ \text{HHI} &\ge \tfrac{1}{n}, \quad \text{with equality only when every } s_i = \tfrac{1}{n} \end{aligned}

Splitting the sum. A sum can be split into parts, which is how the worked example adds the top ten and the rest:

\text{HHI} = \sum_{i=1}^{10} s_{(i)}^2 + \sum_{i=11}^{25} s_{(i)}^2, \qquad \text{CR}_{10} = \sum_{i=1}^{10} s_{(i)}

The HHI weights each provider by its own share, so it reacts most to the largest. The top-k share ignores how the top k are split, and ignores the tail. Banks report both.

Try it

Switch between the four views. Then, in the counterparty view, raise new overnight funding: first from the largest provider, then from new £100m providers. The amount is the same; watch what happens to the HHI and the effective number.

Try itMeasure the concentration

View the funding by

New overnight wholesale funding£0m

Raised from

Corriemoor Bank AG13.1%
Varrowmere Sterling Liquidity Fund11.5%
Pellbridge Bank plc10.8%
Kestermoor Securities LLC8.5%
Ravensholt Bank SA6.9%
Sorrelwick Treasury Reserve Fund6.2%
Ebbsworth Pension Trustees Ltd5.4%
Bramwick Stores plc4.6%
Tolvenna Life Assurance plc3.8%
Halvergate Manufacturing plc3.8%

HHI (0 to 10,000)709

Effective number14.1

Largest share13.1%

Top 3 share35.4%

Top 10 share74.6%

Total in this view£6.5bn

Significant (> 1% of balance sheet)3 of 25

Highlighted bars are significant under the Basel monitoring metric. Counterparty: wholesale funding from banks, funds and companies (£6.5bn plus any new funding). Product: every liability line. Maturity: all wholesale funding by time band. Illustrative extra on the book.

Worked example

The HHI of the wholesale book

From amounts to concentration

Step 1 of 6

1
Shares
$\begin{aligned} \sum_{j=1}^{25} x_j &= \text{£}6{,}500\text{m} \\ s_1 &= 850 / 6{,}500 = 0.1308 \quad \text{(Corriemoor)} \\ s_2 &= 750 / 6{,}500 = 0.1154 \quad \text{(Varrowmere)} \end{aligned}$

Shares of £6.5bn of wholesale funding: 25 providers. Total liabilities £63bn, balance sheet £67bn.

Regulatory lens

Concentration of funding is one of the Basel liquidity monitoring metrics (SRP50.14 to 50.26), reported alongside the contractual maturity mismatch of L3.5.04: Cash flow ladders and maturity gaps, available unencumbered assets and the LCR by significant currency. These are tools for supervisors, not minimum ratios: there is no Basel limit on an HHI. Banks set their own limits, for example on the share of a single provider or on wholesale funding falling due in any one week. National reporting templates and supervisory use are in M4.5: Liquidity and IRRBB regulation; behavioural models of how concentrated providers react in a stress are in M6.7: Liquidity, ALM and behavioural models.

Spark Atoms

Spark AtomWhose index is it?

Albert Hirschman proposed a concentration index in 1945, in National Power and the Structure of Foreign Trade, to measure how concentrated a country's trade was. Orris Herfindahl reinvented it in his 1950 dissertation on the US steel industry. In a 1964 note in the American Economic Review, Hirschman observed that his index was named “either after Gini who did not invent it at all or after Herfindahl who reinvented it.” (Hirschman's original was the square root of today's HHI.)

Spark AtomThe metric undercounts

Debt securities such as CDs and CP can change hands, and the issuer often does not know who holds them. The Basel text admits that, for this reason, true concentration “could likely be higher” than the metric shows (SRP50.23). RiskAtoms Bank knows its CD holders here only because the book says so.

Key takeaways

Funding concentration is reliance on too few sources: by counterparty, product, currency and maturity.
HHI = Σ s²: on the book's wholesale funding 709 out of 10,000, an effective 14.1 providers; the top ten supply 74.6%.
Basel thresholds: a counterparty or product above 1% of the balance sheet (£670m) is significant; a currency at 5% of liabilities. Three providers and the US dollar qualify.
Product concentration in insured retail deposits is not the worry; products a whole market can withdraw are.
Providers of the same type act alike, and holders of securities may be unknown: the measures understate true concentration.
Maturity bunching creates cliffs, even in long-term funding.

Reaction

Check what stuck

Question 1 · objective 2

Three providers supply a bank's wholesale funding: 50%, 30% and 20%. What is the HHI on the 0 to 10,000 scale?

Question 2 · objective 2

For the same three providers, what is the effective number of equal providers?

Question 3 · objective 3

Under the Basel monitoring metric, above what amount (in £m) is a counterparty significant for a bank with a £67bn balance sheet?

£m

Question 4 · objective 1

By product, the book's funding has an HHI of 1,799, with insured current accounts 35% of liabilities. Why is that less worrying than it looks?

AThat one product is spread over a very large number of insured depositors, the stickiest funding a bank hasBProduct concentration never mattersCThe HHI is wrong for productsDCurrent accounts have a fixed maturity

Question 5 · objective 4

RiskAtoms Bank's ten named providers are all different firms, and none supplies more than 13%. What can the counterparty metric still miss?

AProviders of the same kind, such as money market funds, tend to pull back at the same time, so they act like one sourceBNothing: the HHI is low, so the funding is safeCThe currency of the depositsDThe bank's LCR

Glossary

Funding concentration: Reliance on a few sources of funding, so that the loss of one of them, or of one market, would leave a hole the bank cannot fill quickly.
Wholesale funding: Funding from banks, funds, companies and other professional investors, as opposed to retail deposits.
Herfindahl–Hirschman index (HHI): Herfindahl–Hirschman index: the sum of the squared shares of each source. 1 means one source; 1/n means n equal sources. Often quoted on a 0 to 10,000 scale.
Top-k share: The share of the total that comes from the k largest sources, for example the top-10 share.
Effective number of providers: The effective number of sources: 1 / HHI, the number of equal-sized sources that would give the same HHI.
Significant counterparty: Under the Basel monitoring metric, a counterparty or group of connected counterparties that provides more than 1% of the bank's total balance sheet.
Significant currency: A currency in which the bank's liabilities are 5% or more of its total liabilities.
Money market fund: Money market fund: a fund that invests in short-term debt such as CDs, CP and repo, and lets investors withdraw at short notice.

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, Basel Framework, SRP50 Liquidity monitoring metrics, BIS. Intermediate.
T. Taylor, “The Herfindahl-Hirschman Index: Story, Primer, Alternatives”, Conversable Economist, 18 February 2020. Introductory.

Origins

Basel Committee on Banking Supervision, Basel Framework, SRP50 Liquidity monitoring metrics, paragraphs 50.14 to 50.26 and 50.35, BIS, version effective 15 December 2019.
T. Taylor, “The Herfindahl-Hirschman Index: Story, Primer, Alternatives”, Conversable Economist, 18 February 2020 (on Hirschman 1945, Herfindahl 1950, Hirschman 1964 in the American Economic Review 54(5), 761, and Rosenbluth 1961).
Basel Committee on Banking Supervision, Principles for Sound Liquidity Risk Management and Supervision, BIS, September 2008, paragraph 43 (FX swap markets).
Financial Stability Board, Holistic Review of the March Market Turmoil, 17 November 2020.

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