CMA Final · Risk Management in Banking and Insurance

Credit Risk Management: formula sheet

Full chapter guide

Key formulas

Expected loss: EL = PD × LGD × EAD; PD is probability of default, LGD is loss given default, EAD is exposure at default. Treat it as an introduction here; the detailed measurement is a separate topic.
Loss given default: LGD = 1 − Recovery rate; Both are expressed as a proportion of exposure at default.
Concentration share: Concentration (%) = Exposure to one borrower, group or sector ÷ Total exposure × 100; Use it to spot concentration. Compare the result against the bank's internal limits and regulatory exposure norms.
Expected loss: EL = PD × LGD × EAD; Used to price loans and set provisions; PD is probability of default, LGD is loss given default, EAD is exposure at default.
Exposure limit (percentage of capital): Maximum exposure = Limit % × Capital base; Use the capital base specified by the regulator or bank policy for the limit in the question; do not assume the percentage unless given.
Headroom under a limit: Headroom = Limit − Existing exposure; A new proposal is within limit only if proposed exposure ≤ headroom.
Portfolio share of a sector: Sector share = Sector exposure ÷ Total portfolio × 100; Compare with the internal sector cap to test concentration.
Altman Z-score (original, listed manufacturing companies): Z = 1.2×X1 + 1.4×X2 + 3.3×X3 + 0.6×X4 + 1.0×X5; X1 = working capital ÷ total assets; X2 = retained earnings ÷ total assets; X3 = EBIT ÷ total assets; X4 = market value of equity ÷ book value of total liabilities; X5 = sales ÷ total assets.
Altman Z-score zones (original model): Z > 2.99 safe; 1.81 to 2.99 grey; Z < 1.81 distress; Cut-offs differ for the Z′ (private firms) and Z″ (non-manufacturers) versions. Say which model you use.
Transition matrix property: Σ of probabilities in each row = 100%; Row = current grade; column = grade at end of period. Default is usually an absorbing state.
Probability of default from a matrix: PD (1 year) = value in the row of the current grade, column 'Default'; For two years, multiply the matrix by itself, assuming migrations are independent across years.
Expected loss: EL = PD × LGD × EAD; Links the rating (which gives PD) to the loss estimate.
Debt service coverage ratio: DSCR = (PAT + depreciation + interest on term loan) ÷ (interest + instalment of term loan); Common capacity test. Banks usually look for a figure comfortably above 1.
Expected loss: EL = PD × LGD × EAD; Use PD and LGD as decimals. EL is in rupees. All three must refer to the same horizon.
Loss given default: LGD = 1 − Recovery rate; Recovery rate is net of workout costs if the question says so.
Exposure at default: EAD = Drawn amount + CCF × Undrawn commitment; CCF is the credit conversion factor, given in the question.
Portfolio expected loss: EL(portfolio) = Σ EL of each exposure; Expected losses add up simply, whatever the correlation.
Unexpected loss, single exposure with fixed LGD and EAD: UL = EAD × LGD × √[PD × (1 − PD)]; Assumes LGD is certain and default is a yes/no event. Sound only under this simplification.
Credit VaR: Credit VaR = Loss at chosen confidence level − EL; Some texts define credit VaR as the loss quantile itself. Follow the definition in the question.
Net loss rate or EL rate: EL rate = EL ÷ EAD = PD × LGD; Useful to compare pricing across loans.
Risk-weighted asset (funded exposure): RWA = Exposure (net of eligible provisions/collateral, where allowed) × Risk weight; Use the exposure value the question gives. Apply the risk weight as a percentage.
Off-balance sheet exposure: Credit equivalent = Notional amount × Credit conversion factor (CCF); RWA = Credit equivalent × Risk weight; Convert first, then apply the counterparty's risk weight.
Capital adequacy ratio (CRAR): CRAR = Eligible capital ÷ Total RWA × 100; Total RWA should include credit, market and operational risk RWA when given.
Tier 1 ratio: Tier 1 ratio = Tier 1 capital ÷ Total RWA × 100; Tier 1 = Common Equity Tier 1 + Additional Tier 1.
Minimum capital required: Required capital = Total RWA × Minimum CRAR %; Compare with actual capital to find surplus or shortfall.
Capital for operational/market risk to RWA: RWA equivalent = Capital charge × (100 ÷ Minimum CRAR %); Use the minimum ratio the question states, for example ×11.11 at 9%.
IRB inputs: Expected loss = PD × LGD × EAD; IRB risk weights are driven by PD, LGD and EAD (and maturity). Foundation: own PD. Advanced: own PD, LGD, EAD.
Net exposure after collateral (comprehensive approach): E* = max{0, E × (1 + He) − C × (1 − Hc − Hfx)}; E = exposure, He = haircut on exposure, C = collateral value, Hc = haircut on collateral, Hfx = currency mismatch haircut. Capital is then computed on E*.
Simple netting of loans and deposits: Net exposure = Loan outstanding − Eligible deposit set off; Applies only when there is a legally enforceable netting right. Floor at zero.
Guarantee substitution: Covered portion takes the guarantor's risk weight; uncovered portion keeps the borrower's risk weight; Applies for eligible guarantees. Risk-weighted assets = covered × guarantor RW + uncovered × borrower RW.
Risk-weighted assets and capital: RWA = Exposure × Risk weight; Capital required = RWA × minimum capital ratio; Use the ratio given in the question. Do not assume a figure.
Credit default swap payout: Payout = Notional × (1 − Recovery rate); Applies on a credit event under cash settlement. Annual premium = Spread × Notional.
Expected loss: EL = PD × LGD × EAD; Collateral and guarantees reduce LGD or EAD, and so reduce EL.
NPA test (term loans): Overdue > 90 days → NPA; Interest or principal overdue for more than 90 days. Standard assets are not overdue beyond this.
Sub-standard asset: NPA for ≤ 12 months; Secured sub-standard asset: provision 15% of outstanding. If the exposure is unsecured, the rate is 25% (15% + 10% additional). An exposure is unsecured where the realisable value of the security, as assessed by the bank, approved valuers or RBI's inspecting officers, is not more than 10% ab initio (from the start) of the outstanding.
Doubtful asset: Sub-standard for 12 months; Secured portion: 25% (up to 1 year), 40% (1-3 years), 100% (over 3 years). Unsecured portion: 100%.
Loss asset: Provision = 100% of outstanding; Applies to the amount not written off.
Unsecured sub-standard exposure: Provision = 25% of outstanding; Where the realisable value of security is not more than 10% ab initio of the outstanding (as assessed by the bank, approved valuers or RBI), the sub-standard rate is 25%, not 15%.
Doubtful provision: Provision = 100% × unsecured portion + rate × secured portion; Unsecured portion = outstanding − realisable value of security.
Net NPA: Net NPA = Gross NPA − provisions held; Net NPA ratio = Net NPA ÷ Net advances.
Gross NPA ratio: Gross NPA ÷ Gross advances × 100; Key measure of asset quality.
Provision Coverage Ratio: PCR = Provisions held against NPAs ÷ Gross NPA × 100; Shows how much of NPAs is already covered.
Standard asset provision: Provision = standard asset rate for the sector × outstanding; Standard asset provision rates vary by sector: 0.25% for direct advances to agriculture and SMEs, 0.40% for other (general) standard advances, 0.75% for commercial real estate - residential housing (CRE-RH), and 1% for commercial real estate (CRE). Use the rate given in the question.

Quick revision

Credit risk is the risk of loss when a borrower or counterparty fails to meet its obligation on time.
Components include default risk, exposure risk, recovery risk, concentration risk and counterparty risk.
Expected loss = PD × LGD × EAD.
PD is the likelihood of default over a stated period, usually one year.
LGD is the share of exposure lost after recoveries; recovery rate = 1 − LGD.
EAD is the amount outstanding at the time of default, including expected drawdown of undrawn limits.
Expected loss is covered by pricing and provisions; unexpected loss is covered by capital.
Risk-weighted assets = exposure × risk weight; capital ratio = capital ÷ RWA.
Collateral, guarantees and netting reduce exposure; credit derivatives and securitisation transfer risk.
A credit policy sets limits, delegation of powers, pricing and monitoring rules.
Credit rating gives an opinion on the likelihood of timely repayment.
Asset classification moves a loan from standard to NPA stages based on overdue period; provisions rise as the asset worsens.

Common mistakes

Treating credit risk and counterparty risk as the same thing. Fix: Counterparty risk is a subset tied to trades and contracts where the exposure value changes before settlement. Default risk on a loan is about the borrower repaying principal and interest.
Calling concentration risk a type of default. Fix: Concentration is about portfolio structure. Each borrower may be sound, yet the bunching makes the portfolio vulnerable to one shock.
Saying management approves the credit policy. Fix: Write that the board approves the policy; management implements it through procedures.
Letting the business team rate and sanction its own loans. Fix: Stress separation of the credit risk function from the business lines and the use of committee approval for larger loans.
Treating internal and external ratings as the same thing Fix: State who assigns it: the bank (internal, for its own decisions, pricing and IRB capital) versus a SEBI-registered agency (external, public, used for standardised risk weights).
Listing the 5 Cs without applying them to the case Fix: Attach a fact and a verdict to each C, then conclude.
Using the sanctioned limit as EAD instead of drawn amount plus CCF × undrawn. Fix: Always compute EAD = drawn + CCF × undrawn. Use the CCF given in the question.
Taking LGD as the recovery rate. Fix: Write LGD = 1 − recovery before any multiplication.
Dividing capital by total assets instead of RWA Fix: CRAR always has RWA in the denominator. Weight every asset first.
Applying the risk weight to the notional of an off-balance sheet item Fix: Multiply by the CCF first, then by the counterparty risk weight.

Exam tips

For 'identify the type' MCQs, look for the root cause in the scenario: loan repayment, trade settlement, bunching of exposure, or foreign country conditions.
In written answers, define first, list sources, then classify. This order earns marks for structure.
Write the expected loss formula only when numbers are given; otherwise just define the terms PD, LGD and EAD.
Show a simple percentage calculation for concentration questions and state your conclusion in words.
Always end with a control or mitigation point to show application, not recall.
Case questions reward application: always use the amounts, ratings and names given before adding theory.
In limit problems, show limit, existing exposure, headroom and proposal in four clear lines, then conclude.
Name the board, the risk committee and the independent credit risk function; examiners look for who does what.