Capital, equity and leverage · RiskAtoms Academy

By the end you will be able to

1Tell accounting equity apart from regulatory capital: CET1, Additional Tier 1 and Tier 2.
2Calculate leverage as equity ÷ assets, as a multiple, and as the Basel leverage ratio.
3Calculate a CET1 ratio from capital and risk-weighted assets, and say how it differs from the leverage ratio.
4Show how leverage amplifies gains and losses for shareholders.

Why it matters

When Lehman Brothers failed in 2008, it held roughly 30 dollars of assets for every dollar of equity. At that leverage, a fall of about 3% in the value of its assets was enough to wipe out its owners.

Core explanation

Equity is not the same as capital

Leverage. Buy a £300,000 house with a £30,000 deposit and a £270,000 mortgage, and you are leveraged 10 times. If the house rises 10%, your deposit grows by 100%: it doubles. If the house falls 10%, your deposit is gone. Leverage amplifies both ways. Banks run at far higher leverage than most households: Example Bank plc funds 6% of its assets with equity, a multiple of 16.7×.

ExploreThe leverage amplifier

Equity as % of assets6% · 16.7×

Gain or loss on assets−1.0%

On assets−1.0%

On equity−16.7%

With 16.7× leverage, every 1% on assets is 16.7% on equity. A loss of 6% of assets would wipe out the equity entirely.

Why accounting equity is not enough. Equity, from L1.8.01, is assets minus liabilities. But regulators ask a sharper question: which part of the funding could actually absorb losses in a crisis? That is regulatory capital. It starts from equity and makes two kinds of change.

Take things out. Some assets would be worth little if the bank were in trouble: goodwill from past takeovers, software, tax assets that need future profits to be used. These deductions come off equity. What is left is Common Equity Tier 1 (CET1), the core capital.
Add some debt back in. Some bonds are designed to absorb losses. Additional Tier 1 (AT1) bonds are written down or turned into shares while the bank is still alive. Tier 2 subordinated debt absorbs losses when the bank fails. CET1 plus AT1 is Tier 1; add Tier 2 for total capital.

Example Bank plc	£bn
Accounting equity	£30.0bn
less goodwill and intangibles	−£5.0bn
less other deductions (for example, tax assets)	−£1.0bn
= CET1 capital (= Tier 1: it has no AT1)	£24.0bn
plus Tier 2 subordinated debt	£8.0bn
= Total capital	£32.0bn

Two ways to measure capital strength. The risk-based ratio divides capital by risk-weighted assets: a pound of cash needs no capital, a pound of risky business loan needs a lot. The leverage ratio divides Tier 1 capital by a plain exposure measure, with no risk weights at all. Each covers the other's weakness: risk weights can be wrong, and a flat ratio ignores risk.

Insurers: the same idea, different words

Under Solvency II, an insurer compares its own funds with its Solvency Capital Requirement (SCR). Example Insurance SE has own funds of €9,300m against an SCR of €5,000m: a solvency ratio of 186%. The SCR plays the role that risk-weighted assets times a minimum ratio play for a bank.

The formal version

The capital ratio brings in new notation: risk weights and a sum over the assets. Here it is one piece at a time.

Simple leverage, and why it amplifies, follow in two lines:

\text{Leverage multiple} = \frac{\text{Assets}}{\text{Equity}}, \qquad \frac{\text{Loss}}{\text{Equity}} = \frac{\text{Loss}}{\text{Assets}} \times \frac{\text{Assets}}{\text{Equity}}

Try it

Here is Example Bank plc again, now with its capital ratios. Apply 2% loan losses. Which ratio falls further in relative terms, and why? Then try a fall in securities prices instead.

Interactive balance sheetExample Bank plc

£ billion, year end

Assets · £500.0bn

Liabilities and equity · £500.0bn

assets liabilities equityDashed outline: size before any shock.

Assets: what it owns

Total assets£500.0bn

Liabilities and equity: how it is funded

Liabilities
Wholesale funding£80.0bn
Equity

Total liabilities and equity£500.0bn

Cash and central bank reservesasset · 10.0% of total assets

Notes and coins, plus the bank's account at the central bank. The most liquid asset there is.

Risk to watch: Liquidity: this is what pays depositors who withdraw on a bad day.

Apply a shock

Loan losses0.0%

Share of loans written off as borrowers default.

Fall in securities prices0.0%

Investment securities and trading assets lose value, for example after a jump in interest rates.

Loss charged to equity

£0.0bn

Equity

£30.0bn → £30.0bn

Share of equity lost

0.0%

CET1 ratio

12.0%

Core capital ÷ risk-weighted assets.

Basel leverage ratio

4.4%

Tier 1 capital ÷ exposure measure.

Equity ÷ assets

6.0%

How much of the balance sheet the owners fund.

Leverage multiple

16.7×

Assets for every 1 of equity.

Simplified: losses are charged before tax, deductions and off-balance-sheet items are held fixed, and risk-weighted assets fall only with the written-down assets.

Worked example

Example Bank plc's capital ratios

Work from the balance sheet to the two regulatory ratios. Try each step before revealing it.

From equity to ratios

Step 1 of 5

1
CET1 capital
Equity £30.0bn − deductions £6.0bn = £24.0bn.

Regulatory lens

The Basel III framework, set by the Basel Committee on Banking Supervision and put into law by each jurisdiction, sets minimums as a share of risk-weighted assets: CET1 4.5%, Tier 1 6% and total capital 8%. On top sits a capital conservation buffer of 2.5% of CET1, plus extra buffers for the economic cycle and for the largest, systemically important banks. The leverage ratio minimum is 3% of Tier 1 capital, higher for the largest banks. The EU applies Basel through its Capital Requirements Regulation and Directive, the UK through the PRA, and the US through the federal banking agencies. Insurers in the EU must hold own funds of at least 100% of the SCR under Solvency II.

Sparks

SparkRepo 105

The examiner's report into Lehman Brothers' failure found that it used accounting moves called “Repo 105” to move tens of billions of dollars of assets off its balance sheet around quarter ends, making its reported leverage look lower than it was. Leverage ratios are only as good as the balance sheet they are built on.

SparkA ratio born from a crisis

Before 2008, international rules relied on risk-weighted ratios. Several banks that failed or needed rescue had reported healthy risk-based ratios while running very high leverage. Basel III added the leverage ratio as a simple backstop that risk weights cannot shrink.

Key takeaways

Leverage multiplies returns and losses: a loss of x% of assets is x × (assets ÷ equity) % of equity.
Regulatory capital starts from accounting equity, removes items like goodwill to reach CET1, and adds loss-absorbing debt (AT1, Tier 2).
CET1 ratio = CET1 ÷ risk-weighted assets. Basel III's minimum is 4.5%, plus buffers.
Leverage ratio = Tier 1 ÷ exposure measure, with no risk weights. Basel III's minimum is 3%.
Insurers make the same comparison under Solvency II: own funds ÷ SCR, at least 100%.

Reaction

Check what stuck

Question 1 · objective 1

Which of these is deducted from accounting equity to reach CET1 capital?

ACustomer depositsBGoodwill from a past acquisitionCGovernment bonds heldDRetained earnings

Question 2 · objective 2

A bank has total assets of £600bn and equity of £24bn. What is its leverage multiple (assets ÷ equity)?

×

Question 3 · objective 3

A bank has CET1 capital of €15bn and risk-weighted assets of €120bn. What is its CET1 ratio, in %?

%

Question 4 · objective 4

A bank's equity is 5% of its assets. Its assets lose 1% of their value. What percentage of its equity is lost?

%

Question 5 · objective 3

Why do regulators use a leverage ratio as well as a risk-based capital ratio?

ABecause the leverage ratio is easier to raiseBAs a backstop: if risk weights turn out to be too low, the leverage ratio still limits total borrowingCBecause the leverage ratio counts goodwill as capitalDBecause risk-based ratios apply only to insurers

Glossary

Leverage: Funding assets with borrowed money rather than the owners' money. Measured as equity ÷ assets or assets ÷ equity.
Regulatory capital: The part of a bank's funding that can absorb losses, as defined by its regulator.
CET1: Common Equity Tier 1: ordinary shares and retained earnings, less deductions. The highest-quality capital.
Additional Tier 1: Additional Tier 1: perpetual bonds that are written down or converted into shares if the bank's capital falls too low.
Tier 2: Tier 2: mainly subordinated debt. It absorbs losses if the bank fails, after equity and AT1.
Deductions: Items taken off accounting equity to reach CET1 because they would be worth little in a crisis, such as goodwill.
Risk-weighted assets: Risk-weighted assets: each exposure multiplied by a risk weight, plus charges for market and operational risk.
Exposure measure: The denominator of the leverage ratio: assets, plus off-balance-sheet items, minus items deducted from Tier 1.
SCR: Solvency Capital Requirement: the capital an insurer must hold under Solvency II.

Deep Dives & Origins

Deep Dives

Admati and Hellwig, The Bankers' New Clothes: What's Wrong with Banking and What to Do about It (Princeton University Press, 2013). Beginner.
Hull, Risk Management and Financial Institutions (Wiley), the chapters on Basel I, II and III. Intermediate.

Origins

BCBS, Basel III: A global regulatory framework for more resilient banks and banking systems (December 2010, revised June 2011).
BCBS, Basel III: Finalising post-crisis reforms (December 2017), including the leverage ratio framework.
Anton R. Valukas, Report of Examiner, In re Lehman Brothers Holdings Inc. (US Bankruptcy Court, SDNY, March 2010).
Directive 2009/138/EC (Solvency II), articles 100 and 101 on the SCR.

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