Default and recovery

~9 min read

🎯 Interview frequent

Why it matters

Expected loss — the number that ultimately justifies a spread — is built from exactly two ingredients: how likely is default, and how much do you get back if it happens. Every credit interview eventually asks you to combine these two numbers, usually with a CDS or bond spread as the starting point.

Core concepts

Expected loss decomposition. \(\text{EL} \approx PD \times LGD \times EAD\), where \(PD\) is probability of default over the horizon, \(LGD\) is loss given default, and \(EAD\) is exposure at default. Recovery rate \(R = 1 - LGD\); a commonly cited rough assumption for senior unsecured corporate debt is \(R \approx 40\%\), but this is a convention, not a law — actual recovery varies enormously by seniority, industry, and cycle.
What counts as a default. Ratings agencies and CDS documentation define it broadly: missed coupon or principal payment, bankruptcy filing, and — for CDS specifically — sometimes a “distressed exchange” where bondholders are pressured into accepting worse terms to avoid a formal default. The precise definition matters a great deal for CDS settlement and historical default-rate statistics.
The interview hazard-rate approximation. For a flat hazard rate \(\lambda\) and CDS par spread \(s\): \(s \approx \lambda \times LGD\). So a 100bp spread at 40% assumed recovery implies \(\lambda \approx 100\text{bp} / 0.6 \approx 167\)bp of hazard per year. Survival probability under constant hazard: \(P(\tau > t) = e^{-\lambda t}\) — a 5-year survival at that hazard is \(e^{-0.0167 \times 5} \approx 92\%\), so 5-year cumulative default probability \(\approx 8\%\).
Recovery varies systematically by seniority. Historically: secured/first-lien loans recover the most (often 60–80%+), senior unsecured bonds recover moderately (call it 35–50% on average, wide dispersion), subordinated debt recovers the least. This is the empirical face of the waterfall discussed in Seniority & capital structure — theory and data agree here.
Recovery is cyclical, not a fixed constant. Recovery rates are meaningfully lower in systemic, industry-wide downturns (when many firms in the same sector default simultaneously and asset sales flood a depressed market) than in idiosyncratic, single-name defaults where a healthier buyer can acquire distressed assets near fair value. Modeling recovery as a fixed 40% ignores this correlation between PD and LGD in a real credit cycle — a subtlety interviewers like to probe.
Recovery is realized value, not a quoted market price at default. The actual recovery an investor achieves depends on how the default is resolved: a negotiated out-of-court restructuring, a formal Chapter 11 reorganization (potentially converting debt to new equity), or a liquidation (Chapter 7) — each with very different timelines and realized values relative to the “trading price at 30 days post-default” convention CDS auctions use to settle.
PD and LGD are correlated, and that correlation is the tail risk. In a severe, broad recession, default probability rises across many names and recovery falls simultaneously (more distressed sellers, fewer buyers, depressed collateral values) — the reason portfolio credit losses are fat-tailed rather than well-approximated by independent, identically-distributed default draws.

Mental model

  Expected Loss  =  PD  x  LGD  x  EAD
                     |      |
                     |      +-- LGD = 1 - Recovery Rate
                     |               Recovery varies by seniority (see topic 06)
                     |               and is LOWER in systemic downturns
                     |
                     +-- CDS/spread-implied PD is usually HIGHER than
                         historical/real-world PD (risk premium + liquidity)

  Interview shortcut:  spread s ≈ hazard rate λ × LGD
                        survival to time t ≈ e^(-λt)

Interview questions

A 5-year CDS trades at a 200bp par spread, and you assume 40% recovery. Estimate the hazard rate and 5-year cumulative default probability. Answer: \(\lambda \approx 0.02 / 0.6 \approx 3.33\%\) per year. Survival to year 5 \(\approx e^{-0.0333 \times 5} \approx 84.6\%\), so cumulative 5-year default probability \(\approx 15.4\%\). (Flat-hazard, continuous-payment approximation — good enough for a screen, not for a term sheet.)
Why is CDS-implied (risk-neutral) default probability typically higher than the historical default rate for a same-rated bond? Answer: The spread compensates for expected loss plus a risk premium (investors demand extra return for bearing correlated, fat-tailed default risk) plus liquidity/technical costs. Historical default rates are simply realized frequencies — there’s no premium embedded, just the observed outcome. The gap is the market’s price of uncertainty, analogous to implied vs. realized volatility in options.
Why shouldn’t you assume a flat 40% recovery rate when modeling expected losses across an entire portfolio through a full credit cycle? Answer: Because PD and LGD are correlated — in a systemic downturn, more issuers default simultaneously and recovery falls (distressed asset sales flood a depressed market, fewer healthy buyers exist). Treating recovery as a fixed constant independent of the default environment understates tail risk; portfolio credit losses are fatter-tailed than an independent-draws model would suggest.
A senior secured loan and a senior unsecured bond from the same defaulted issuer show very different recoveries. Explain why, tying it back to capital structure. Answer: The secured loan has a direct claim on specific pledged collateral and is paid from that collateral’s value before any unsecured creditor sees a cent (absolute priority). The unsecured bond only has a claim on whatever’s left in the general asset pool after secured claims and administrative costs are satisfied — so its recovery is both lower and more variable, since it depends on total enterprise value net of the secured claim, not on a specific asset.
What’s the difference between “recovery rate” as used in a CDS auction settlement and the recovery an investor might actually realize by holding through a Chapter 11 reorganization? Answer: CDS auction recovery is a market-clearing price for the deliverable obligation observed roughly 30 days after the credit event — a point-in-time trading price, often depressed by forced/technical selling immediately after default. An investor who holds through a full Chapter 11 process may receive a package of new debt, new equity, and/or cash whose realized value (often over a longer horizon, once the reorganized entity stabilizes) can differ meaningfully from that initial post-default trading price in either direction.

Watch

Credit default swaps — Khan Academy. Protection buyer/seller mechanics and the running spread as the price of default protection.
Credit default swaps (CDS) intro — Khan Academy. A short, mechanical second pass at the contract and payout on a credit event.