Lay out what recovery rates are and how they move with default rates.
The idea
The recovery rate is the share of a defaulted claim's face value that creditors get back, commonly measured as the bond's market price shortly after default as a percentage of face value. Loss given default is one minus the recovery rate. Expected loss then combines exposure at default (EAD), the probability of default (PD) and LGD. EL = EAD × PD × LGD. Recovery depends on seniority and security. Senior secured claims recover more than senior unsecured, which recover more than subordinated claims, and under absolute priority each class is paid in full before the next receives anything. Empirically recovery rates are negatively correlated with default rates. In years when many firms default, recoveries are lower because the assets of defaulted firms sell into a weak market. The exam point is that treating recovery as a fixed average, independent of defaults, understates losses in bad years and so understates tail credit risk.
Formulas
Expected credit loss
EL = PD × LGD × EAD
- PD
- the probability of default over the horizon
- LGD
- loss given default, as a share of the exposure
- EAD
- the exposure at default
LGD is one minus the recovery rate. Because recovery falls when defaults rise, a fixed average LGD understates losses in bad years.
A practice question
How is a bond's recovery rate commonly measured?
- As one minus the probability of default over the bond's life.Why not: That is a survival probability; recovery measures what creditors get back after default.
- As the bond's market price shortly after default, expressed as a percentage of face value. - correct
- As the bond's price on the day before default as a percentage of face value.Why not: Uses the pre-default price, which still reflects the market's hope of repayment.
- As the coupon rate divided by the yield to maturity at issue.Why not: Unrelated to recovery; this ratio has no link to losses on default.
Recovery is what bondholders get back per unit of face value; loss given default is 1 minus the recovery rate.
A harder one
A firm defaults with net asset-liquidation proceeds of USD 90 million. Its claims are senior secured debt of USD 40 million (secured on specific assets worth more than the claim), senior unsecured debt of USD 80 million and subordinated debt of USD 60 million. Assuming absolute priority holds, what is the recovery rate on the senior unsecured debt?
- 62.5% - correct
- 50.0%Why not: Spreads proceeds across all claims pro rata, ignoring the priority ranking.
- 75.0%Why not: Treats secured and unsecured senior debt as pari passu and ignores the subordinated debt.
- 100.0%Why not: Ignores the senior secured claim, which is paid first.
The secured claim takes USD 40 million first, leaving USD 50 million for USD 80 million of senior unsecured claims: 50/80 = 62.5%, and subordinated debt receives nothing.
The hardest tier
A risk manager models portfolio credit losses with recovery fixed at the long-run average of 40%, independent of the default rate. How will the 99.9% loss estimate compare with one that uses the observed relationship between defaults and recoveries?
- It will be too high, because recoveries are always above the long-run average in bad years.Why not: Reverses the empirical relationship: bad years bring low recoveries.
- It will be too low, because in the worst years high default rates coincide with low recoveries. - correct
- It will be unbiased, because over-estimates in good years offset under-estimates in bad years.Why not: Offsetting averages do not help a tail measure, which depends on the bad years.
- It will be unaffected, because tail losses depend only on default correlation and not on recovery.Why not: Tail losses depend on both default rates and loss severity; a stochastic LGD changes the tail.
Because high default years carry high LGD, a fixed average recovery understates tail losses even if the expected loss is about right.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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