CFA Level I · CFA Level I Exam

Credit Risk: formula sheet

Full chapter guide

Key formulas

Expected loss: EL = PD × LGD × EAD; If the question gives LGD as a percentage of exposure, EL as a percentage is PD × LGD. Multiply by EAD for a currency amount.
Loss given default: LGD = 1 − recovery rate; LGD is a percentage of the exposure. The recovery rate is a share of the amount owed. For the currency loss, use EAD × LGD.
Recovery rate: Recovery rate = 1 − LGD (as a percentage of exposure); Recovery is the amount recovered divided by the amount owed.
Loss if default occurs: Loss = EAD × LGD; This is a currency amount and is conditional on default. It is not the expected loss.
Recovery rate: Recovery rate = Amount recovered ÷ Claim amount; Expressed as a percentage of the claim owed to that creditor.
Loss given default: LGD = 1 − Recovery rate; Can also be stated in currency: LGD = Exposure × (1 − Recovery rate).
Pari passu sharing: Each creditor's share = Available amount for the class × (Own claim ÷ Total claims of the class); Applies when a class of equal-ranking claims cannot be paid in full.
Absolute priority order: Secured → Senior unsecured → Subordinated → Preferred equity → Common equity; Each class is paid in full before the next receives anything, in the strict rule.
Expected loss: Expected loss = Probability of default × Loss given default; Seniority affects only the LGD term.
Investment grade boundary: Investment grade: BBB- or higher (S&P, Fitch); Baa3 or higher (Moody's). High yield: BB+ / Ba1 or lower; A split rating (for example BBB- from one agency and BB+ from another) is a common trap; check each agency's scale.
Notching rule of thumb: Issue rating = issuer rating ± notches for seniority and security; Subordinated or unsecured-behind-secured: notch down. Strong collateral or senior ranking: level or up. Exact notches vary by agency.
Expected loss: Expected loss = Probability of default × Loss severity; Loss severity = 1 − recovery rate. Issuer ratings mostly reflect default probability; issue ratings also reflect recovery.
Approximate price effect of a spread change: %ΔPrice ≈ −Modified duration × ΔSpread; Use for downgrade (migration) risk when the yield change comes from a wider spread. Ignores convexity.
Debt to EBITDA: Debt/EBITDA = Total debt ÷ EBITDA; Leverage. Higher means weaker credit. Roughly, years of EBITDA needed to repay debt.
Net debt to EBITDA: Net debt/EBITDA = (Total debt − Cash and equivalents) ÷ EBITDA; Use when the question gives cash and asks for net leverage.
EBITDA interest coverage: EBITDA ÷ Interest expense; Coverage. Higher is better.
EBIT interest coverage: EBIT ÷ Interest expense; More conservative than EBITDA coverage because it deducts depreciation and amortization.
FFO to debt: FFO ÷ Total debt; FFO = funds from operations. Higher is better.
Free operating cash flow to debt: FOCF ÷ Total debt; FOCF is operating cash flow after capex. Higher is better.
Debt to capital: Total debt ÷ (Total debt + Shareholders' equity); Balance-sheet leverage. Higher means weaker credit.
Four Cs: Capacity, Collateral, Covenants, Character; Capacity is the primary source of repayment. Collateral is a secondary source.
Credit spread: Credit spread = Yield on risky bond − Yield on benchmark bond of similar maturity; Quoted in basis points. 1 bp = 0.01%.
Price change using duration only: %ΔPrice ≈ −ModDur × ΔSpread; Use ΔSpread as a decimal (50 bps = 0.0050). Assumes benchmark yield is unchanged.
Price change with convexity: %ΔPrice ≈ −ModDur × ΔSpread + ½ × Convexity × (ΔSpread)²; The convexity term is always positive, so it reduces the loss when spreads widen and adds to the gain when they narrow.
Return impact of a spread change: Return ≈ Yield income (carry) − ModDur × ΔSpread + ½ × Convexity × (ΔSpread)²; For a one-year horizon, carry is roughly the yield. Add benchmark-yield effects if given.
G-spread: G-spread = Bond YTM − Interpolated government YTM at same maturity; Uses a single point on the government curve.
Z-spread: Price = Σ CFt ÷ (1 + zt + Z)^t; zt are the spot rates on the benchmark spot curve, usually the government curve. Z is the same constant added to every spot rate.
Equity as a call option: Equity at maturity = max(A − K, 0); A = asset value, K = face value of debt (strike). Equity holders keep the upside above debt.
Debt as risk-free bond minus a put: Debt at maturity = min(A, K) = K − max(K − A, 0); Today: risky debt value = PV of K − value of put on assets. Equity + debt = assets.
Approximate credit spread: Credit spread ≈ PD × LGD; Annual probability of default times loss given default. A rough link, not exact.
Expected loss: Expected loss = PD × LGD × exposure; LGD = 1 − recovery rate.
Credit valuation adjustment: CVA = Σ [expected exposure_t × PD_t × LGD × discount factor_t]; PD_t is the marginal (period-specific) probability of default in period t, not the cumulative probability of default up to t. Sum across all periods.
Risky value: Value with credit risk = risk-free value − CVA; CVA is always a reduction in value for the party holding the exposure.
Constant hazard rate: Survival to t = e^(−λt); PD over t = 1 − e^(−λt); λ is the default intensity. Approximately λ ≈ spread ÷ LGD.
Debt service coverage ratio (revenue bonds): DSCR = Net revenue available for debt service ÷ Debt service; Higher is stronger. A ratio below 1 means project revenue cannot cover debt service.
Overcollateralization: Overcollateralization = Collateral value − Bond principal outstanding; This is the loss cushion before bondholders lose money. It is internal enhancement.
Excess spread: Excess spread = Interest collected on pool − Interest paid on bonds − Fees and expenses; Often trapped in a reserve to absorb losses. It is internal enhancement.
Internal vs external enhancement: Internal: subordination, overcollateralization, excess spread, reserve accounts. External: bond insurance, letters of credit, guarantees; External forms add counterparty (third-party) credit risk.
Sovereign credit factors: Ability to pay + Willingness to pay; local-currency debt is generally lower risk than foreign-currency debt; Legal recourse against a sovereign is limited, so willingness matters.

Quick revision

Credit risk is the risk of loss from a borrower failing to pay in full and on time.
Expected loss = probability of default × loss given default, applied to exposure.
Loss severity = 1 − recovery rate, when both are stated as a share of exposure.
Senior claims are paid before junior claims, so seniority raises expected recovery.
For the same issuer, senior debt usually has higher recovery and a lower spread than junior debt.
Ratings are opinions, can lag events, and can change sharply, so they are not a full substitute for analysis.
The four Cs are capacity, collateral, covenants and character.
Capacity is the borrower's ability to repay from cash flow, so leverage and coverage matter.
A credit spread is the extra yield over a benchmark that pays for default and other risks, such as liquidity.
Wider spreads mean the market demands more compensation for credit risk.
The structural model views equity as a call option on the firm's assets, and debt as a risk-free bond minus a put option on those assets. Default occurs when asset value falls below the debt's face value at maturity. The reduced-form model treats default as a random event with an intensity.
Securitized debt depends on the asset pool and its structure; municipal credit depends on the source of repayment.

Common mistakes

Using the recovery rate in place of LGD in the expected loss formula. Fix: Always convert first: LGD = 1 − recovery rate.
Treating loss if default occurs as the expected loss. Fix: Expected loss includes PD. Loss given default is conditional on default.
Treating all senior debt as equal to secured debt. Fix: Secured means backed by specific collateral. Senior is about rank in the queue. Senior unsecured ranks below secured debt for the collateral.
Giving pari passu creditors different recoveries. Fix: Equal-ranking claims share the shortfall in proportion to claim size, so each gets the same recovery percentage.
Treating BB+ or Ba1 as investment grade. Fix: Memorise that the lowest investment grade rating is BBB- (Baa3). Anything one step lower is high yield.
Assuming the issue rating always equals the issuer rating. Fix: Remember notching: seniority and collateral change recovery, so a subordinated bond is usually rated below the issuer rating.
Calling a restriction on dividends or new debt an affirmative covenant. Fix: Ask whether it forces an action or limits one. Limits are negative covenants.
Treating collateral as the main assessment of credit quality. Fix: Capacity comes first. Collateral only helps recovery after cash flow has failed.
Getting the sign wrong: showing a price rise when the spread widens. Fix: Wider spread means higher yield means lower price. Write the minus sign first.
Using basis points as whole numbers, for example 4.5 × 80 = 360%. Fix: Convert bps to decimals (80 bps = 0.0080) or divide the product by 100 to get a percentage.

Exam tips

Look for the recovery rate in the stem and convert it to LGD before anything else.
Wrong options often match PD alone, loss given default alone, or the senior bond answer. Compute before choosing.
Read whether the question asks for a conditional loss or an expected loss.
With no penalty for wrong answers, never leave a question blank. Eliminate the option that ignores PD, then pick.
Remember that recovery usually rises with seniority and collateral.
Most questions are conceptual: pick the option that matches higher rank means higher recovery and lower LGD.
With three options, eliminate any that give a junior class a higher recovery than a senior class under strict priority.
Watch the wording: pari passu means equal rank, not equal claim size.