Analysis of Financial Institutions: formula sheet

Key formulas

Net interest income

NII = Interest income − Interest expense

Core earnings measure for a bank. Check the vignette for the exact labels.

Net interest margin

NIM = NII ÷ Average interest-earning assets

Use average earning assets, not total assets, if earning assets are given.

Interest spread

Spread = Yield on earning assets − Cost of interest-bearing liabilities

Differs from NIM because NIM also reflects funding from non-interest-bearing sources such as equity.

Loan-to-deposit ratio

Loans ÷ Deposits

A high value suggests reliance on wholesale funding and tighter liquidity.

Efficiency ratio

Non-interest expense ÷ (NII + Non-interest income)

Lower is better. It measures cost per unit of revenue.

Equity multiplier (leverage)

Total assets ÷ Total equity

Banks have high values, so ROE is very sensitive to asset returns.

Return on assets

ROA = Net income ÷ Average total assets

Typically small for banks, so compare with peers.

Capital adequacy (risk-based)

Capital ratio = Regulatory capital ÷ Risk-weighted assets

Compare with the regulatory minimum. Higher means a bigger buffer. Tier 1 and total capital versions both exist.

Leverage ratio

Leverage ratio = Tier 1 capital ÷ Total exposure (or total assets)

Does not use risk weights, so it checks for risk-weight manipulation.

Asset quality: nonperforming loans

NPL ratio = Nonperforming loans ÷ Total loans

Higher is worse. Also watch loan loss reserves ÷ NPLs (coverage).

Reserve coverage

Coverage = Loan loss reserve ÷ Nonperforming loans

Higher means more cushion against expected losses.

Net interest margin

NIM = Net interest income ÷ Average earning assets

Core earnings measure for a lending-based bank.

Return on equity / assets

ROE = Net income ÷ Average equity; ROA = Net income ÷ Average assets

Check quality of earnings: stable, recurring income is better than one-offs.

Efficiency ratio

Efficiency ratio = Noninterest expense ÷ Total revenue

Lower is better. A rising ratio can signal weak cost control.

Liquidity coverage ratio

LCR = High-quality liquid assets ÷ Net cash outflows over 30 days

Regulatory minimum is 100%. Higher means more short-term resilience.

Net stable funding ratio

NSFR = Available stable funding ÷ Required stable funding

Regulatory minimum is 100%. It looks at funding over one year.

Loan-to-deposit ratio

Loans ÷ Deposits

A high value suggests reliance on less stable wholesale funding.

CET1 capital

CET1 = common equity (shares + retained earnings + other reserves) − regulatory deductions

Deductions include goodwill and other intangibles. Always deduct them before computing any ratio.

Tier 1 and total capital

Tier 1 = CET1 + Additional Tier 1; Total capital = Tier 1 + Tier 2

Tier 1 is going-concern capital. Tier 2 is gone-concern capital.

Risk-based capital ratios

Ratio = capital measure ÷ risk-weighted assets

Basel III minimums: CET1 4.5%, Tier 1 6%, total capital 8%. Use the matching numerator for each ratio.

Capital conservation buffer

CET1 needed = 4.5% + 2.5% = 7.0% of RWA

Add any countercyclical or surcharge buffer the vignette gives. Falling into the buffer restricts distributions.

Leverage ratio

Leverage ratio = Tier 1 capital ÷ total exposure

Minimum 3% under Basel III. Not risk-weighted.

Liquidity coverage ratio

LCR = stock of high-quality liquid assets ÷ total net cash outflows over 30 days ≥ 100%

Net outflows = outflows − inflows, with inflows capped at 75% of outflows. HQLA is after haircuts.

Net stable funding ratio

NSFR = available stable funding ÷ required stable funding ≥ 100%

Looks at a one-year horizon. Stable funding means capital and long-term, sticky liabilities.

Capital headroom

Headroom (currency) = (actual ratio − required ratio) × RWA

Useful when the question asks how much capital a bank can lose or distribute.

NPL ratio

NPL ratio = Non-performing loans ÷ Gross loans

Higher means weaker asset quality. Use gross loans unless told otherwise.

Allowance (coverage) ratio

Coverage ratio = Loan loss allowance ÷ Non-performing loans

Below 100% means the allowance does not cover all NPLs, though collateral may cover the gap.

Allowance to loans

Allowance ratio = Loan loss allowance ÷ Gross loans

Shows the cushion against the whole book.

Allowance roll-forward

Ending allowance = Beginning allowance + Provision − Write-offs + Recoveries

Use it to find a missing item. Write-offs reduce the allowance. Recoveries add to it.

Net charge-offs

Net charge-offs = Write-offs − Recoveries

Often expressed as a percentage of average loans.

Net interest margin

NIM = Net interest income ÷ Average interest-earning assets

Net interest income = interest income − interest expense. Use average earning assets, not total assets.

Efficiency ratio

Efficiency ratio = Non-interest expense ÷ (Net interest income + Non-interest income)

Lower is better. Definitions vary, so use the one the vignette gives.

Pre-provision profit

Pre-provision profit = Net interest income + Non-interest income − Non-interest expense

Shows earnings power before credit-cost judgments.

Loss ratio

Loss ratio = Incurred losses (including loss adjustment expenses) ÷ Net premiums earned

Measures claims cost per unit of premium. Use premiums earned, not written, unless the question says otherwise.

Expense ratio

Expense ratio = Underwriting expenses ÷ Net premiums written (or earned, as the vignette defines it)

Includes acquisition costs and operating costs. Use the base the vignette uses.

Combined ratio

Combined ratio = Loss ratio + Expense ratio

Below 100% means an underwriting profit; above 100% means an underwriting loss.

Combined ratio after policyholder dividends

Combined ratio after dividends = Combined ratio + Policyholder dividends ÷ Net premiums earned

Used when dividends are paid to policyholders.

Underwriting result

Underwriting profit = Net premiums earned × (1 − Combined ratio)

A combined ratio of 100% is breakeven on underwriting alone.

Overall operating ratio

Operating ratio = Combined ratio − Investment income ratio (investment income ÷ net premiums earned)

Shows whether investment income makes an underwriting loss profitable overall.

Premiums-to-surplus (leverage)

Net premiums written ÷ Policyholders' surplus (capital)

Higher means more underwriting leverage and risk relative to capital.

Quick revision

• CAMELS is a regulator-style bank rating framework: capital adequacy, asset quality, management, earnings, liquidity and sensitivity to market risk.
• Banks earn mainly from net interest income plus fee and trading income.
• Higher capital ratios mean a bigger loss-absorbing cushion, but very high ratios can signal low returns.
• Rising non-performing loans signal weakening asset quality and usually need higher provisions.
• Provisions are charged to earnings, so low provisions can flatter profit and hide risk.
• Check whether earnings growth comes from core income or from one-off gains.
• Liquidity is judged by how easily assets can be turned to cash against short-term funding needs.
• Sensitivity to market risk covers interest rate, currency and trading exposure.
• Insurers are analyzed differently from banks; confirm in the current curriculum whether ratios such as the combined ratio are examinable.
• Always compare a ratio with its own trend and with peers before drawing a conclusion.
• Answer only from the vignette, and note whether the exhibit uses IFRS or US GAAP.

Common mistakes

• Using the current ratio or working capital to judge a bank Fix: Banks have unclassified balance sheets. Use liquidity, funding and capital measures instead.
• Confusing NIM with interest spread Fix: Spread is asset yield minus funding cost. NIM is NII divided by earning assets and includes the benefit of free funds like equity.
• Treating a high capital ratio as proof the bank is healthy. Fix: Check asset quality and earnings. Capital can fall fast if NPLs are rising and reserves are low.
• Reading a higher NPL ratio as good or neutral. Fix: Note the direction for each ratio before comparing. NPL up is worse. Reserve coverage up is better.
• Forgetting to deduct goodwill and intangibles from common equity Fix: Regulatory capital is not accounting equity. Subtract the deductions listed in the vignette first.
• Using total assets instead of risk-weighted assets as the denominator of the capital ratios Fix: Risk-based ratios use RWA. Only the leverage ratio uses total exposure.
• Treating the provision and the allowance as the same thing. Fix: The provision is an income statement expense for the period. The allowance is a balance sheet stock. Link them with the roll-forward.
• Subtracting write-offs from the provision expense in the roll-forward. Fix: Write-offs reduce the allowance directly and do not touch the income statement. Only the provision is expensed.
• Treating a combined ratio under 100% as the only sign of a good insurer. Fix: Check reserve development and investment income as well. A low combined ratio from under-reserving is poor quality.
• Using premiums written for the loss ratio and premiums earned for the expense ratio without noting it. Fix: Use the base the vignette states. Losses are normally compared with premiums earned, because earned premium matches the period of cover.

Exam tips

• Read the vignette for the institution type before doing any math.
• Check whether the question wants NIM or spread. The denominators differ.
• When two answer options both sound sensible, pick the one that uses bank-specific measures such as capital, funding or asset quality.
• Use average balances when both opening and closing figures are given and the question implies a period measure.
• Expect to explain why a change happened, not only to calculate it.
• Tag every number in the vignette with a CAMELS letter before you read the questions in detail.
• Memorise the direction of each ratio. Many wrong options flip higher-is-better with higher-is-worse.
• Expect questions that link components, such as how rising NPLs affect earnings and capital.