Recovery Rate Modeling: How Credit Risk Models Treat What You Get Back
Corporate Financial Distress, Restructuring, and Bankruptcy by Edward I. Altman, Edith Hotchkiss, and Wei Wang (Wiley, ISBN 978-1-119-48180-5)
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Chapter 16 tackles the piece of credit risk that got ignored for decades: recovery rates. Everyone obsessed over probability of default. But what you actually recover when a borrower defaults matters just as much for pricing, capital requirements, and portfolio risk.
The three variables of credit risk
Every credit asset comes down to three things:
- Probability of default (PD): will they fail?
- Loss given default (LGD): how much do you lose? (LGD = 1 minus recovery rate)
- Exposure at default (EAD): how much was outstanding?
Basel II made banks separate expected losses (provisions) from unexpected losses (economic capital). Recovery rate estimation became central to both.
Recovery rate is usually measured as the market price just after default. “Ultimate recovery” measures what creditors actually receive at the end of Chapter 11 restructuring. S&P and Fitch launched separate recovery ratings in the early 2000s. Moody’s argues their regular ratings already embed both PD and RR.
First-generation structural models: RR is endogenous
Merton’s 1974 framework treats default as happening when firm asset value falls below liabilities. Bondholders get the lesser of face value or asset value. Recovery is whatever assets remain.
In this world, PD and RR move inversely. Better firm health means lower default risk and higher expected recovery. More debt means higher PD and lower recovery. Higher asset volatility means higher PD and lower recovery.
The logic is clean. The practical problems are real:
- Firms default before maturity, not just at it
- Complex capital structures need seniority specifications
- Absolute priority rules get violated in practice (Weiss 1990, Franks and Torous 1994)
- Lognormal distributions overstate recovery rates
Second-generation structural models: mixed treatment
These models let default happen anytime when asset value hits a barrier, not just at maturity. But they split on recovery:
Exogenous barrier models (Longstaff-Schwartz 1995, Collin-Dufresne-Goldstein 2001): RR is a fixed ratio independent of PD. You estimate it from historical recovery data for similar firms.
Endogenous barrier models (Leland 1994, Leland-Toft 1996): Shareholders choose when to default to maximize equity value. Recovery equals the default boundary minus deadweight costs, scaled by total debt face value.
Both generations still struggle with unobservable firm asset values, inability to model credit rating migrations, and the “sudden surprise” problem (Duffie and Lando 2000).
Reduced-form models: RR is exogenous and separate
Jarrow-Turnbull (1995), Duffie-Singleton (1999), and others treat default as a random event driven by a hazard rate process. PD and RR are modeled independently.
Duffie-Singleton allows stochastic RR that can correlate with the default hazard rate and depend on macro variables. But the core assumption remains: you don’t need to estimate firm asset values.
The tradeoff: reduced-form models handle sudden defaults better but lose the economic intuition of why firms fail.
Empirical performance is mixed. Duffee (1999) found difficulty explaining credit spread term structures across firms of different credit quality.
Credit VaR models: RR as a plug-in parameter
CreditMetrics, CreditRisk+, CreditPortfolioView, and KMV’s CreditPortfolioManager all treat RR as either a constant input or a stochastic variable (often beta-distributed) independent from PD.
Default mode (DM) models only consider default vs. survival. Mark-to-market (MTM) models also capture credit migrations. Both approaches assume PD and RR don’t depend on each other.
This matters because Basel II let banks use their own recovery estimates under the advanced IRB approach. If banks revise recoveries down during bad years without accounting for the PD-RR correlation, capital requirements could be systematically understated.
The PD-RR relationship: why independence is wrong
The second half of Chapter 16 (covered in the next post) dives into empirical evidence. But the theoretical case is already clear from Frye (2000):
When the economy tanks, defaults rise AND collateral values fall. Recovery rates drop just when you need them most. This creates a negative correlation between PD and RR.
Altman, Brady, Resti, and Sironi (2005) found supply-demand effects matter too. In high-default years, the flood of defaulted securities exceeds buyer demand, pushing secondary market prices (and measured recoveries) down.
Monte Carlo simulations show assuming PD and RR are uncorrelated vastly understates both expected and unexpected losses. Banks using models that ignore this correlation may hold insufficient reserves.
The procyclicality problem gets worse: low recoveries during high-default periods amplify the credit cycle, especially under Basel II’s advanced approach where banks set their own recovery assumptions.
What this means for practitioners
If you’re pricing distressed debt, modeling portfolio risk, or setting bank capital requirements, recovery rate isn’t a static input you look up in a table. It moves with the credit cycle, industry conditions, seniority, and the supply of defaulted paper in the market.
The next post covers what the data actually shows: average recoveries by seniority, industry, rating, and how they changed from 1978 through 2017.
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