Recoveries on Defaulted Debt Michael B. Gordy Federal Reserve Board <michael.gordy@frb.gov> May 2008 The opinions expressed here are my own, and do not reflect the views of the Board of Governors or its staff. M.B. Gordy (FRB) Recoveries May 2008 1 / 17
Overview Recovery is the post-default value of a debt instrument. Research on credit risk has focused overwhelmingly on default risk, often treating recovery as a nuisance parameter. Credit spreads and capital contributions roughly linear in expected recovery, and recovery varies tremendously: variation across debt instruments of an obligor; variation from obligor to obligor within a year; variation in average recovery from year to year. Today s talk will review empirical stylized facts on recovery and approaches to modeling. How to measure recovery on defaulted debt instruments? The effect of the business cycle on recovery. An obligor-level perspective on recovery. M.B. Gordy (FRB) Recoveries May 2008 2 / 17
Variation across and within debt class Source: Figure 6.1 in D. Duffie & K.J. Singleton, 2003. Underlying data from Moody s. M.B. Gordy (FRB) Recoveries May 2008 3 / 17
Recovery rate distribution may be bimodal Source: Figure 12.2 in A. Resti & A. Sironi, 2007. Data for a medium-sized European bank. M.B. Gordy (FRB) Recoveries May 2008 4 / 17
How should recovery be defined? Post-default market price as theoretical ideal. Ideal measure when distressed debt is traded in a liquid market. Ties recovery to the default event. Gain/Loss from default date through resolution is a return on vulture investment. Trouble is that market may not exist for some classes of debt. Traded prices may be sensitive to liquidity. Most studies based exclusively on this measure. Recovery at emergence ( workout recovery). Might be in cash (liquidation) or new securities (reorganization). Must net out the administrative costs of the workout. Main problem is rate at which to discount back to date of default. Best (only?) data available on non-traded or thinly traded instruments. M.B. Gordy (FRB) Recoveries May 2008 5 / 17
Post-default price predicts workout recovery? Recovery at emergence from S&P LossStat database. M.B. Gordy (FRB) Recoveries May 2008 6 / 17
Systematic recovery risk? Prior to default, recovery is uncertain. If this risk is idiosyncratic, then it is diversifiable, so should demand no risk premium. Recovery parameter in pricing model can be estimated using historical recovery data for similar instruments. If only data are for workout recoveries, then risk-free yield curve gives appropriate discount! If recoveries correlated with state of credit cycle, then recovery risk is not fully diversifiable. Pricing requires the risk-neutral expected recovery, typically lower than historical average. For discounting workout recoveries, need appropriate spread over risk-free rate. In principle, the hurdle rate for a monoline vulture fund would give a good proxy. Might approximate by risk-free yield curve plus a constant. Original coupon rate is widely used but absurd. M.B. Gordy (FRB) Recoveries May 2008 7 / 17
Recovery risk in capital models For a large portfolio, VaR at q percentile converges to expected portfolio loss conditional on stress event corresponding to q th percentile worst state of the world. Consider a simple book value capital model. Calling our stress event X q, capital contribution for loan l is E[LGD l p l X q ] = E[LGD l X q ] p l (X q ) where p is default probability as function of X and LGD is 1 R. If recovery risk is purely idiosyncratic, then E[LGD l X q ] = E[LGD l ] = ELGD l, and so uncertainty in recovery is immaterial in large portfolio. But if recovery depends on credit cycle, we need to estimate a suitable downturn LGD. M.B. Gordy (FRB) Recoveries May 2008 8 / 17
Basel II treatment Internal Ratings-Based approach of Basel II based on an asymptotic model of this sort. Model extended to mark-to-market loss (maturity effects). Foundation IRB imposes rule-based LGD. Advanced IRB uses bank estimates of downturn LGD (DLGD) corresponding to economic downturn conditions. DLGD is no less than long-run default-weighted average historical LGD for facility type. Recognition that sensitivity of LGD to economic cycle can vary across exposures. Need data spanning at least one complete economic cycle. Explicit recognition that best practice is in early stages here. Pykhtin (Risk, 2003) offers a simple model of DLGD that is consistent with IRB model. M.B. Gordy (FRB) Recoveries May 2008 9 / 17
Empirical evidence on systematic recovery risk Frye (Risk, 2000) first to show that recovery falls in recession. Altman, Brady, Resti & Sironi (J. Business, 2005) offer a more comprehensive analysis. Acharya, Bharath & Srinivasan (JFE, 2007) show recovery is tied to distress in obligor s own industry. M.B. Gordy (FRB) Recoveries May 2008 10 / 17
Recoveries and the business cycle Source: Altman, Resti & Sironi (2004) based on data for US high yield bond market. M.B. Gordy (FRB) Recoveries May 2008 11 / 17
Digression: Recovery in CDO pricing models Example to illustrate importance of recovery risk, both idiosyncratic and systematic. Conventional CDO pricing models impose fixed recovery rate of 40%. Implies zero spread on super-super-senior tranche of 60 100%, but spread recently 30 40 bps. Most natural way to reconcile tranche spreads is to assume that recovery rate falls as default rate increases, i.e., systematic risk. Fixed recovery rate also implies discrete loss distribution in pool, which can distort pricing of equity tranche. M.B. Gordy (FRB) Recoveries May 2008 12 / 17
Recovery in credit pricing models Credit risk models mainly of two varieties: Structural models, following Merton (1974), in which debt is viewed as a derivative on the obligor s assets. Reduced-form models, following Duffie & Singleton (1999), in which we directly model the term structure of default probabilities. In reduced-form models, recovery is merely a parameter to specify, and is in no way explained within the model. Structural models ought to explain recovery, but in practice do so very poorly. In plain-vanilla Black & Cox (1976) model Asset value evolves smoothly over time. Default occurs when asset value crosses a default threshold. Threshold is exogeneous, typically calibrated as face value of debt. Moody s KMV imposes a slight variant. Implies recovery of 100% less liquidation costs. Need a richer model of the default threshold, built on endogenous behavior of a distressed obligor and its creditors in the end game. M.B. Gordy (FRB) Recoveries May 2008 13 / 17
Instrument-level vs Firm-level recovery Empirical recovery literature has focused on predicting performance at instrument level. But debt claims on defaulted firms are collar options on the borrower s assets. Can also view debt claims as akin to CDO tranches. Here the assets of the firm correspond to the CDO collateral pool. Cannot properly assess expected recovery for an instrument independently from its place in the capital structure. Seniority label is of secondary importance (Keisman). Firm-level recovery studied by Hamilton & Carty (1999) and Carey & Gordy (2007). M.B. Gordy (FRB) Recoveries May 2008 14 / 17
Debt instruments as collar options Seniority Class of Claim Value of Firm at Emergence M.B. Gordy (FRB) Recoveries May 2008 15 / 17
Firm-level vs. Instrument-level Recovery 0.02 0.018 Normal kernel, bandwidth=6 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 Firm Instrument 0 0 10 20 30 40 50 60 70 80 90 100 Recovery at Emergence (percent) Recovery at emergence from S&P LossStat database. M.B. Gordy (FRB) Recoveries May 2008 16 / 17
Implications of firm-level view Carey & Gordy (2007) show that firm-level recovery strongly increasing with share of bank loans in firm s debt. Going from no bank debt to all bank debt increases expected recovery by 35 40 percentage points. Debt structure has bigger effect than systematic risk and borrower characteristics. Offer model in which banks play a crucial role in forcing insolvent borrowers into bankruptcy. Model emphasizes financial covenants in loan agreements, which allow bank to recall loan to distressed borrower. Early foreclosure on such borrowers preserves asset-value available to creditors. Incorporating loan share in estimating expected recovery would improve performance of pricing and risk management models. M.B. Gordy (FRB) Recoveries May 2008 17 / 17