Default Risk

Default risk enters valuation through a single arithmetic chain: expected loss equals the probability of default multiplied by the loss given default, applied to the exposure at default. Loss given default is itself one minus the recovery rate, so a bond with a 3 percent annual default probability and a 60 percent expected recovery carries an expected loss of roughly 1.2 percent of exposure per year.

Probabilities are quoted in two forms that candidates must not blend. A marginal (or conditional) default probability is the chance of default during one period given survival to the start of it; a cumulative default probability is the chance of default at any point up to a horizon. Cumulative rates build from marginal rates through survival: the probability of surviving several years is the product of the annual survival probabilities, and one minus that product is the cumulative default probability.

Credit analysis reduces default probability to capacity, collateral, covenants and character. Capacity dominates: leverage measured as debt to EBITDA, coverage measured as EBITDA or EBIT to interest expense, and the stability of free cash flow relative to scheduled maturities. An issuer defaults when it cannot roll or service obligations, which makes the maturity profile and access to liquidity as important as the level of debt.

Collateral and covenants shift the outcome conditional on distress rather than the probability of distress itself, though tight maintenance covenants can accelerate a default that a looser structure would defer. Above the issuer sits the cycle: default rates are strongly countercyclical, clustering in recessions when revenue, asset values and refinancing windows deteriorate together. Correlation across issuers is therefore a portfolio-level feature of default risk, not an anomaly.

The yield spread over a benchmark government curve compensates for expected credit loss plus a credit risk premium for the uncertainty and illiquidity around that loss. Because the spread bundles these components, an observed spread cannot be read as a pure default probability; risk-neutral probabilities extracted from spreads systematically exceed historical default frequencies.

Ratings agencies express default risk on ordinal scales, with the investment-grade boundary at Baa3 or BBB minus. Their transition matrices show the annual probability of moving between rating categories, including to default, and are the standard empirical evidence that default risk rises steeply and non-linearly as ratings fall. Credit default swap premiums provide a continuously updated market view of the same risk, and their divergence from cash bond spreads is watched as a basis signal.

Compute expected loss from a stated default probability and recovery rate, and reverse the calculation to back out an implied recovery. Move between marginal and cumulative default probabilities using survival products. Estimate the price impact of a spread change as approximately minus modified duration times the spread change, adding the convexity term for large moves, and recognise that downgrade risk transmits through exactly this channel without any default occurring.

Equally important are the distinctions: default probability versus loss severity, expected loss versus unexpected loss, issuer credit rating versus issue rating where seniority and structural subordination alter recovery. Candidates should also be able to rank claims in a bankruptcy waterfall and explain why senior secured, senior unsecured and subordinated debt of the same issuer share a default probability but not a recovery rate.