FRM Part I · FRM Exam Part I

Banks: formula sheet

Full chapter guide

Key formulas

Balance sheet identity: Assets = Liabilities + Equity; Always holds. Equity is the residual and absorbs losses first.
Net interest income (NII): NII = Interest income − Interest expense; Interest income comes from loans and securities; expense comes from deposits and borrowings.
Net interest margin (NIM): NIM = NII ÷ Average interest-earning assets; Use earning assets, not total assets, unless the question says otherwise.
Leverage ratio (simple): Leverage = Total assets ÷ Equity; Higher leverage magnifies both gains and losses on equity.
Equity change from asset loss: Loss in assets ÷ Equity = % fall in equity; Liabilities stay fixed, so the whole loss reduces equity.
Balance sheet identity: Assets = Liabilities + Equity; Losses reduce assets and hit equity first. If assets fall below liabilities, equity is negative and the bank is insolvent.
Total regulatory capital: Total capital = Tier 1 + Tier 2, where Tier 1 = CET1 + AT1; CET1 is the highest quality. Deductions (such as goodwill) apply before the ratios are calculated.
Capital ratio: Capital ratio = Capital ÷ Risk-weighted assets; Use CET1, Tier 1 or total capital in the numerator, depending on the ratio asked.
Risk-weighted assets: RWA = Σ (Exposure × Risk weight); A higher risk weight means more capital is required against that exposure.
Loss absorption capacity: Loss before insolvency = Equity (capital) on the balance sheet; Insolvency occurs when losses exceed equity. Equity ÷ assets shows the percentage fall in asset value the bank can survive.
Tranche loss allocation: Loss to a tranche = min(max(Pool loss − Attachment point, 0), Detachment point − Attachment point); Losses hit the lowest tranche first. Attachment and detachment points are in the same units as the pool loss, such as % of pool or a currency amount.
Pool loss: Pool loss = Pool balance × Default rate × (1 − Recovery rate); Use this to get the loss in currency before applying it to tranches. The recovery rate is the fraction recovered on defaulted loans.
Tranche thickness: Thickness = Detachment point − Attachment point; A thin tranche can be wiped out by a small change in pool loss, so it is highly sensitive to default risk.
Credit enhancement (subordination): Subordination below a tranche = Attachment point of that tranche; The attachment point is the loss the pool can take before this tranche loses anything.
Basel III leverage ratio: Leverage ratio = Tier 1 capital ÷ Total exposure measure; Not risk-weighted. Basel III sets a minimum of 3%. Do not confuse with assets ÷ equity, which is the inverse idea.
Equity multiplier: Equity multiplier = Total assets ÷ Equity; A simple leverage measure. A 5% equity ratio means leverage of 20 times.
Liquidity Coverage Ratio: LCR = Stock of HQLA ÷ Total net cash outflows over 30 days ≥ 100%; Net outflows = outflows − min(inflows, 75% of outflows).
Net Stable Funding Ratio: NSFR = Available stable funding ÷ Required stable funding ≥ 100%; Covers a one-year horizon.
Funding gap: Funding gap = Loans − Deposits; A positive gap must be met by wholesale funding or asset sales.
Loan-to-deposit ratio: Loan-to-deposit = Loans ÷ Deposits; A high value signals reliance on non-deposit funding.

Quick revision

Banks take deposits and make loans, so their liabilities are mostly short-term and assets longer-term.
Capital ratio = capital ÷ risk-weighted assets. Higher risk weights mean lower ratios for the same capital.
Capital absorbs unexpected losses; provisions cover expected losses.
Leverage is assets relative to equity. Higher leverage magnifies gains and losses.
In originate-to-distribute, banks make loans, then sell them to investors instead of holding them.
Securitization tranches pay in order of seniority; the equity tranche takes losses first.
Weak underwriting standards are a known risk of originate-to-distribute because the originator does not keep the loss.
Liquidity risk is being unable to meet cash obligations when due, even if the bank is solvent.
Funding liquidity risk is about raising cash; market liquidity risk is about selling assets without a large price drop.
Heavy reliance on short-term wholesale funding makes a bank vulnerable to runs.
Credit, market and operational risk are the main risks; know which one a scenario describes.

Common mistakes

Treating deposits as assets of the bank. Fix: Deposits are owed to customers, so they are liabilities. The bank's asset is the cash or loan it holds against them.
Saying investment banks mainly take insured retail deposits. Fix: Investment banks rely on wholesale funding such as repo and bonds. Retail deposits are the commercial bank model.
Dividing capital by total assets instead of risk-weighted assets. Fix: If the question says capital ratio or CET1 ratio, use RWA. Only use total assets or exposure if it says leverage.
Treating deposit insurance as having no downside. Fix: Always pair it with moral hazard: insured depositors do not monitor risk, so banks may take more.
Saying securitization eliminates the bank's credit risk. Fix: Remember banks often kept residual tranches, liquidity support, warehoused loans and reputational exposure, so some risk stayed.
Applying losses to the senior tranche first. Fix: Senior is paid first and loses last. Equity loses first.
Using risk-weighted assets as the denominator of the leverage ratio. Fix: The leverage ratio uses total exposure, not risk-weighted. That is its purpose.
Counting all expected inflows against outflows in the LCR. Fix: Inflows are limited to 75% of outflows, so net outflows are at least 25% of gross outflows.

Exam tips

Know which activities define commercial versus investment banks. Option wording often swaps them.
Always check whether a question asks for average earning assets or total assets in a margin calculation.
In loss questions, treat liabilities as fixed and let equity take the whole hit.
Link each balance sheet feature to a risk: long loans funded by short deposits means liquidity and interest rate risk.
Read the sign and units carefully; equity changes are often asked in percentage terms.
Expect short conceptual questions: why banks are regulated, what deposit insurance does, and the tier of a given instrument.
When deposit insurance appears, look for moral hazard as the drawback.
For ratio questions, check whether the denominator is RWA or total assets.