Risk Management in Banks and Basel Accords: formula sheet

Key formulas

Risk management process

Identify → Measure → Monitor and report → Control or mitigate → Review

Use this sequence as the skeleton of any descriptive answer.

Three lines of defence

1st: business units; 2nd: risk and compliance functions; 3rd: internal audit

Business units own risk, the risk function oversees it, and audit gives independent assurance.

Main risk categories

Credit risk + Market risk + Liquidity risk + Operational risk (plus others such as reputational and strategic)

Credit and market risk were the original Pillar 1 capital risks under Basel I. Basel II added operational risk. Liquidity risk is not a Pillar 1 capital charge. It is covered by separate liquidity standards, the LCR and NSFR, under Basel III.

Governance chain

Board → Risk Management Committee of the Board → Management committees (credit, ALCO, operational risk) → CRO and risk department

State who approves, who oversees and who executes.

Credit risk

Risk of loss if a borrower or counterparty fails to meet its obligations

Linked to loans, investments, guarantees and derivatives. Use this definition word for word in answers.

Market risk

Market risk = interest rate risk + equity price risk + foreign exchange risk + commodity price risk (on market-sensitive positions)

Say 'arising from movements in market prices'. Do not confuse it with credit risk.

Operational risk

Loss from inadequate or failed internal processes, people and systems, or external events

Includes legal risk. Strategic and reputational risk are normally excluded from the regulatory definition.

Liquidity gap

Liquidity gap in a time bucket = Cash inflows (maturing assets) − Cash outflows (maturing liabilities). A negative gap means a shortfall in that bucket.

Liquidity is judged by cash flow mismatches across time buckets.

Interest rate gap

Gap = Rate sensitive assets (RSA) − Rate sensitive liabilities (RSL)

Positive gap: earnings rise if rates rise. Negative gap: earnings fall if rates rise. This assumes a parallel rate move.

Expected loss

EL = PD × LGD × EAD

PD is probability of default, LGD is loss given default, EAD is exposure at default. Provisions are meant to cover expected loss; capital covers unexpected loss.

Risk-weighted asset for credit risk

Credit RWA = Exposure × Risk weight

Exposure here is after any eligible credit risk mitigation. Capital required = RWA × minimum capital ratio.

Exposure ceiling

Maximum exposure = Ceiling % × Capital funds

Use the percentage in the current RBI exposure norms for single and group borrowers. Capital funds is as defined by RBI, so do not use total assets.

Loss given default

LGD = 1 − Recovery rate

Recovery rate is the share of exposure recovered after default, net of costs.

Net exposure after collateral (simple approach)

Net exposure = Exposure − Eligible collateral value (after haircut)

Eligible collateral is cut by a haircut for price volatility. Net exposure cannot be negative for capital purposes.

Liquidity Coverage Ratio (LCR)

LCR = Stock of high quality liquid assets (HQLA) ÷ Total net cash outflows over the next 30 calendar days × 100

Basel III requires LCR to be at least 100%. It covers a 30-day stress scenario. Check the current RBI minimum and any relaxation before quoting.

Net Stable Funding Ratio (NSFR)

NSFR = Available stable funding ÷ Required stable funding × 100

Basel III requires at least 100%. It looks at a one-year horizon and limits reliance on short-term funding for long-term assets.

Net cash outflows

Net cash outflows = Total expected cash outflows − Minimum of (total expected cash inflows, 75% of total expected cash outflows)

Under Basel III, inflows are capped at 75% of outflows, so net outflows are never below 25% of gross outflows.

Liquidity gap

Gap in a time bucket = Rate or cash inflows (assets) − outflows (liabilities) in that bucket

A negative gap means outflows exceed inflows in that bucket. Compare the gap with the limit set by the board.

Rate sensitivity gap

Gap = Rate sensitive assets (RSA) − Rate sensitive liabilities (RSL)

A positive gap means net interest income rises when rates rise. A negative gap means it falls.

Change in net interest income

Change in NII ≈ Gap × Change in interest rate

Applies to a given bucket over a given period. For a one-year view use the cumulative one-year gap.

Scaling VaR to a longer horizon

VaR for N days = 1-day VaR × √N

Holds under the assumption of independent, identically distributed daily returns. Basel's market risk approach used a 10-day horizon.

Parametric VaR

VaR = Position value × z × σ (for the chosen horizon)

z is about 1.65 at 95% and 2.33 at 99% confidence for a one-tailed normal distribution. σ is the standard deviation of returns.

Capital adequacy ratio (CRAR)

CRAR = (Eligible capital ÷ Risk-weighted assets) × 100

Capital is Tier 1 plus Tier 2 under the rules. Risk-weighted assets are exposures multiplied by risk weights.

Risk-weighted asset for one exposure

RWA = Exposure amount × Risk weight

Add up RWA across all assets, including off-balance-sheet items after conversion to credit equivalents.

Basel minimum under Basel I and II

Minimum total capital = 8% of RWA

Under Basel I this covered credit risk (market risk added in 1996). Basel II extended RWA to include market and operational risk.

RBI minimum under Basel II

Minimum CRAR = 9% of RWA

RBI prescribed 9%, higher than the Basel 8%.

Basel II total RWA

Total RWA = Credit RWA + Market-risk RWA + Operational-risk RWA

Capital charges for market and operational risk are converted to RWA by multiplying by 12.5 (the reciprocal of 8%).

Three pillars of Basel II

Pillar 1: Minimum capital | Pillar 2: Supervisory review | Pillar 3: Market discipline

Learn the order and the purpose of each.

Capital adequacy ratio (CRAR)

CRAR = (Eligible Tier 1 + Tier 2 capital) ÷ Risk-weighted assets × 100

Risk-weighted assets cover credit, market and operational risk. Basel minimum total capital is 8% of RWA; RBI requires 9% for Indian banks, excluding buffers.

Basel minimum CET1 and Tier 1

CET1 ≥ 4.5% of RWA; Tier 1 ≥ 6% of RWA (Basel minimum)

RBI's own minimum for CET1 is 5.5% and for Tier 1 is 7%. Check the latest RBI circular.

Capital Conservation Buffer

CCB = 2.5% of RWA, held in CET1

Applies on top of minimum capital. Falling into it limits dividends and bonuses.

Countercyclical Capital Buffer

CCyB = 0% to 2.5% of RWA, in CET1, set by the regulator

Activated when credit growth is excessive; it is not a permanent buffer.

Leverage ratio

Leverage ratio = Tier 1 capital ÷ Total exposure (on and off balance sheet) × 100

Basel minimum is 3%. RBI sets higher levels for some banks; confirm the current figure.

Liquidity Coverage Ratio

LCR = Stock of HQLA ÷ Total net cash outflows over next 30 days ≥ 100%

Short-term, 30-day stress test.

Net Stable Funding Ratio

NSFR = Available stable funding ÷ Required stable funding ≥ 100%

One-year structural measure; limits reliance on short-term wholesale funding.

CRAR

CRAR (%) = (Tier 1 capital + Tier 2 capital) ÷ Total RWA × 100

Use eligible capital after regulatory deductions and any limits on Tier 2.

Tier 1 capital

Tier 1 = CET1 + Additional Tier 1 (AT1)

CET1 is mainly equity, share premium and reserves, less deductions.

Total capital

Total regulatory capital = Tier 1 + Tier 2

Tier 2 is gone-concern capital.

Risk-weighted asset (funded)

RWA = Asset amount × Risk weight %

Sum across all assets to get credit-risk RWA.

Off-balance-sheet RWA

RWA = Notional amount × Credit conversion factor (CCF) × Risk weight %

CCF converts the contingent item into an on-balance-sheet equivalent.

Total RWA

Total RWA = Credit-risk RWA + Market-risk RWA + Operational-risk RWA

If the question gives only credit risk, state that assumption.

Minimum requirement (Basel III as applied by RBI)

Total capital ≥ 9% of RWA; Tier 1 ≥ 7%; CET1 ≥ 5.5%; plus 2.5% conservation buffer in CET1

Quote the figures as per the RBI master circular in force. Use the figures given in the question if they differ.

Quick revision

• Risk management means identify, measure, monitor and control risk, with the board holding final responsibility.
• The main banking risks are credit, market, liquidity and operational risk, along with others such as reputation and compliance risk.
• Credit risk is the risk that a borrower fails to repay as agreed.
• Market risk comes from changes in interest rates, exchange rates and prices of securities.
• Liquidity risk is the inability to meet payment obligations when they fall due.
• Operational risk arises from failed processes, people, systems or external events.
• Basel I focused mainly on credit risk and minimum capital against risk-weighted assets.
• Basel II rests on three pillars: minimum capital requirements, supervisory review and market discipline.
• Basel III raised the quality and quantity of capital and added a leverage ratio and liquidity standards.
• Regulatory capital is divided into tiers, and the ratio is capital divided by risk-weighted assets.
• Always confirm current RBI minimum ratios and buffers from the latest directions before writing figures.

Common mistakes

• Saying risk management means eliminating risk. Fix: Write that banks take risk to earn returns and manage it within an approved risk appetite and limits.
• Placing responsibility only on the risk department. Fix: State that the Board is ultimately responsible, committees oversee, and business units own day-to-day risk.
• Treating credit risk and market risk as the same because both cause losses. Fix: Credit risk comes from the counterparty's failure to pay. Market risk comes from price movements even when everyone pays.
• Calling a loan default caused by fraud inside the bank a credit risk only. Fix: Ask the cause. Borrower inability is credit risk. Staff collusion or process failure is operational risk, even if a loan is lost.
• Treating credit risk mitigation as removal of credit risk. Fix: Say mitigation reduces loss on default. Mention residual risks such as valuation, enforceability and documentation.
• Confusing exposure norms with risk weights. Fix: Exposure norms cap how much can be lent to a borrower or group. Risk weights decide how much capital is needed against an exposure.
• Treating liquidity risk and solvency risk as the same thing. Fix: Say that liquidity is about timing of cash, solvency is about assets versus liabilities. A solvent bank can still face a liquidity crisis.
• Using total inflows in LCR net outflows without the cap. Fix: Cap inflows at 75% of outflows. Net outflows cannot fall below 25% of gross outflows.
• Saying Basel norms are binding law on Indian banks as issued by the Committee. Fix: State that the Committee only recommends. RBI makes the norms binding by issuing directions.
• Mixing up the pillars, for example calling Pillar 2 market discipline. Fix: Remember the order: 1 capital, 2 supervisors, 3 market. Pillar 3 is disclosure.

Exam tips

• Structure answers as definition, process, governance, RBI expectation, conclusion. It earns marks even when your details are incomplete.
• In case questions, point to the specific failure, such as no independence or no limits, then give the fix.
• Use the exact terms Board, Risk Management Committee, ALCO, CRO and three lines of defence.
• Do not quote circular numbers or limits you are unsure of. Describe the requirement in words.
• Link this topic to credit, market and operational risk and to Basel in the same answer when the question allows.
• Start every answer with a one-line definition. It secures marks even if the case is unclear.
• In case questions, quote the fact that points to the risk, then name it. Examiners reward the link.
• For distinguish questions, use two or three points: source, effect and control.