Capital Structure in Banks: formula sheet

Key formulas

Balance sheet identity

Assets = Liabilities + Equity

Equity is the residual. Book capital = Assets − Liabilities.

Leverage multiple

Leverage = Assets ÷ Equity

Also called the equity multiplier. Inverse is the equity-to-assets ratio.

Equity ratio

Equity ratio = Equity ÷ Assets

Loss as a share of assets that wipes out equity, ignoring other effects.

Return on equity

ROE = Net income ÷ Equity = ROA × (Assets ÷ Equity)

Leverage scales ROA into ROE. Losses are scaled the same way.

ROE with funding cost

ROE = [r_A × A − r_D × D] ÷ E, where D = A − E

Ignores taxes and costs. Use when asset yield and debt cost are given.

Economic capital

Economic capital ≈ Unexpected loss at a confidence level = Loss quantile − Expected loss

Expected loss is covered by pricing and provisions. Capital covers the unexpected part.

Capital buffer

Buffer = Actual capital ratio − Required minimum ratio

Positive buffer means room to absorb losses before breaching the requirement.

Economic capital (credit)

Economic capital = Credit VaR (at confidence level) − Expected loss

Covers unexpected loss only. Expected loss is covered by pricing and provisions.

Expected loss

EL = PD × LGD × EAD

Use the same horizon for PD, usually one year.

RAROC

RAROC = (Revenues − Costs − Expected loss + Return on economic capital) ÷ Economic capital

The return on capital term is optional. Many questions omit it. Use only the items the question gives.

Simple RAROC

RAROC = (Revenue − Costs − Expected loss) ÷ Economic capital

Compare the result with the hurdle rate.

Value-creation test

RAROC > hurdle rate → adds shareholder value

Equal to the hurdle rate means break-even.

Diversification effect

Σ stand-alone capital ≥ diversified total capital

Holds when correlations are below 1. The gap is the diversification benefit.

Capital adequacy ratio

Capital ratio = Eligible capital ÷ RWA

Use CET1, Tier 1 or Total capital in the numerator to get the matching ratio. RWA is the same denominator for all three.

Minimum ratios (Pillar 1)

CET1 ≥ 4.5%; Tier 1 ≥ 6%; Total capital ≥ 8% of RWA

These are before any buffer.

Capital conservation buffer

CCB = 2.5% of RWA, in CET1

CET1 requirement including CCB = 7%. Tier 1 = 8.5%. Total = 10.5%.

Countercyclical buffer

CCyB = 0% to 2.5% of RWA, in CET1

Bank-specific rate = exposure-weighted average of national CCyB rates, weighted by private-sector credit exposures by jurisdiction.

G-SIB surcharge

Surcharge = 1.0%, 1.5%, 2.0%, 2.5% or 3.5% of RWA, in CET1

Set by the bucket from the G-SIB score. Highest requirement (all buffers): CET1 = 4.5% + 2.5% + CCyB + surcharge.

Leverage ratio

Leverage ratio = Tier 1 capital ÷ Total exposure measure ≥ 3%

No risk weights. Exposure includes off-balance-sheet items and derivatives per the Basel rules. G-SIB leverage buffer = 50% of the G-SIB surcharge.

Total CET1 requirement

Required CET1 = 4.5% + CCB 2.5% + CCyB + G-SIB surcharge

Add the buffers to the 4.5% minimum, all measured on RWA.

MM Proposition I (no taxes)

V(levered) = V(unlevered)

Firm value is independent of the debt-equity mix, assuming no frictions.

MM Proposition II (no taxes)

Re = R0 + (R0 − Rd) × (D ÷ E)

Cost of equity rises linearly with debt-to-equity. R0 is the unlevered cost of capital; Rd is the cost of debt, assumed risk-free-like in this form.

WACC

WACC = (E ÷ V) × Re + (D ÷ V) × Rd × (1 − t)

V = D + E. Set t = 0 for the pure MM case. Under MM with no taxes, WACC equals R0 at any leverage.

Leverage ratio

Leverage = Assets ÷ Equity; Equity ratio = Equity ÷ Assets

Higher leverage amplifies ROE up and down.

Return on equity under leverage

ROE = ROA × (Assets ÷ Equity) − Cost of debt × (Debt ÷ Equity)

Useful when ROA is pre-interest return on assets. Check the question's definition of ROA.

Quick revision

• Capital absorbs unexpected losses and protects depositors and the financial system.
• Common Equity Tier 1 is the highest-quality capital and is the core going-concern layer.
• Additional Tier 1 is going-concern capital that must be able to absorb losses while the bank operates.
• Tier 2 is gone-concern capital that absorbs losses in resolution or failure.
• Capital ratio = eligible capital ÷ risk-weighted assets.
• Leverage ratio uses Tier 1 capital over a non-risk-weighted exposure measure.
• Buffers sit above minimums; breaching them triggers restrictions such as limits on distributions.
• The countercyclical buffer is set by national authorities and varies with credit conditions.
• Economic capital is a model-based estimate of capital needed at a chosen confidence level.
• Regulatory capital is rule-based; economic capital is internal and risk-sensitive.
• Higher leverage raises return on equity when returns are good and magnifies losses when they are bad.
• Equity is costlier than debt per rupee or dollar, but more equity lowers default risk and funding cost.

Common mistakes

• Treating equity as an asset or as cash the bank holds. Fix: Capital is a funding source on the liability side. It says how assets are financed, not what the bank holds.
• Dividing equity by equity ratio the wrong way, using Equity ÷ Assets as leverage. Fix: Leverage = Assets ÷ Equity (greater than 1). Equity ratio = Equity ÷ Assets (less than 1).
• Using credit VaR as economic capital without subtracting expected loss. Fix: Economic capital = credit VaR − EL, when the question defines it that way. Expected loss is handled through pricing and provisions.
• Forgetting to deduct expected loss in the RAROC numerator. Fix: RAROC is risk-adjusted, so expected loss always comes out of the return.
• Using total assets instead of RWA as the denominator of the risk-based ratio. Fix: Risk-based ratio uses RWA. Leverage ratio uses the exposure measure. Read the question for the word 'risk-weighted'.
• Saying a bank breaching the conservation buffer must be closed or is below the minimum. Fix: Buffers are above the minimum. Breaching them triggers automatic restrictions on distributions, not a failure of the minimum requirement.
• Treating debt as cheaper so WACC must fall with leverage under MM. Fix: Under no-friction MM, Re increases exactly to offset cheaper debt, so WACC stays at R0.
• Using D ÷ V instead of D ÷ E in Proposition II. Fix: Proposition II uses debt-to-equity, D ÷ E. WACC weights use D ÷ V and E ÷ V.

Exam tips

• Questions often ask for both the return effect and the risk effect of leverage. Give both.
• Be exact on the three meanings of capital: book, regulatory and economic. Options are built to blur them.
• Do the quick scaling check (loss ÷ equity ratio) before building a full balance sheet.
• Watch the direction of the ratio: leverage above 1, equity ratio below 1.
• Link capital to moral hazard and deposit insurance when the question asks why banks hold capital.
• Look for whether the question gives credit VaR or unexpected loss. This decides if you subtract EL.
• Always check that expected loss is deducted in the RAROC numerator.
• When asked why a unit's allocated capital is lower than its stand-alone capital, answer diversification.