Distressed Debt Prices and Recovery Rate Estimation Robert Jarrow Joint Work with Xin Guo and Haizhi Lin May 2008
Introduction � Recent market events highlight the importance of understanding credit risk. � Credit risk pricing and hedging involves understanding: 1. interest rates (stochastic discounting), 2. default process (when payments stop), and 3. recovery rate process (what happens after default). � Points 1 and 2 well-studied. � Point 3, less so...
Introduction Three sources of knowledge on recovery rates. 1. Industry papers: estimate recovery rates (not transparent, not validated by academic community), and study their properties (correlation with business cycle, dependence on …rm characteristics, ...) 2. Academic papers - use industry generated recovery rates to study their properties. 3. Academic papers - use pre-default debt and CDS prices to implicitly estimate recovery rates.
Introduction Potential problems with existing knowledge. � Are we sure recovery rates are estimated correctly? If not, then... � academic papers study mis-speci…ed estimates, � academic papers have no base to compare implicit estimates.
Introduction Purposes Primary - provide direct estimates of recovery rates using distressed debt prices. Secondary - …t a model for defaulted debt prices. (it turns out, to solve one, must also solve the other)
Introduction Results 1. Recovery rate estimates are sensitive to the date selected for estimation (signi…cant di¤erences between using the recorded default date and 30 days after). 2. Prices support the belief that the market often recognizes default before default is recorded. 3. An extended recovery rate model provides a poor …t to distressed debt prices after the recorded default date (extension implicit in using 30 day after to estimate recovery rate). 4. We estimate a new recovery rate process and use it to price distressed debt. The model …ts market prices well.
Prologue Structural models � Use management’s information set. � Default can be viewed as the …rst hitting time of the …rm’s asset value to a liability determined barrier. � If the …rm’s asset value follows a continuous process, the value of a …rm’s debt does not exhibit a jump at default. � No implications for risky debt prices subsequent to default. Reduced Form Models � Use market’s information set. � Default modeled as the …rst jump time of a point process. � Debt prices exhibit a negative jump at default. � No implications for risky debt prices subsequent to default.
Prologue 5 5 s e ri e s 1 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 3 0 -Se p -2 0 0 4 2 7 -F e b -2 0 0 5 2 7 -J u l -2 0 0 5 2 4 -De c -2 0 0 5 Figure: Delta Airlines. Bankruptcy on September 14, 2005. Consistent with the standard structural model. 30-day di¤erent from default date.
Prologue 1 0 0 s e ri e s 1 9 0 8 0 7 0 6 0 5 0 4 0 0 3 -Oc t-2 0 0 4 3 0 -No v -2 0 0 4 2 7 -J a n -2 0 0 5 2 6 -M a r-2 0 0 5 Figure: Trico Marine Service Inc. Bankruptcy on December 18, 2004. Inconsistent with the structural model. (market recognized default earlier?) 30-day approximately same as default date.
Prologue 1 00 s e rie s 1 90 80 70 60 50 40 29-Se p-2004 26-Fe b-2005 26 -J u l-2 00 5 23-De c -2005 Figure: Winn Dixie Stores. Bankruptcy on February 21, 2005. Consistent with the standard reduced form model. 30-day di¤erent from default date.
Prologue 9 0 s e ries 1 8 0 7 0 6 0 5 0 4 0 3 0 2 0 0 3 -Ap r-2 0 0 5 3 0 -J u n -2 0 0 5 2 6 -Se p -2 0 0 5 2 3 -De c -2 0 0 5 Figure: Northwest Airlines. Bankruptcy on September 14, 2005. Partially consistent with both the reduced form and structural. 30-day di¤erent from default date.
Set Up Fix a particular …rm. � Let B t denote the price of its risky debt (a particular issue with a given maturity, coupons (‡oating or …xed), and embedded options). � De…ne the economic default date τ as the time when the market knows default has happened. � The recorded default date τ � where τ � � τ is given in our data set. � Let B d t denote the risky debt price given economic default has already happened, i.e. for t � τ , B d t = B t . � Let r t be riskless spot rate of interest. � Let p t ( T ) be price of a riskless coupon bond with the same maturity T and coupons as the risky bond under consideration.
Cross-Sectional Models 1. Recovery of Face Value (RFV): B d τ = δ τ F where F is the face value of the debt (normalized to $ 100) 2. Recovery of Treasury (RT): B d τ = δ τ p τ ( T ) 3. Recovery of Market Value (RMV): B d τ = δ τ B τ �
Cross-Sectional Models � Purpose of these models is to provide the necessary inputs to price risky debt and credit derivatives prior to default . � Recovery rate estimation procedure is: � …x a defaulted company � …x a date τ to observe debt prices, then � estimate the recovery rate. � Single point estimate of the recovery rate per company. Look cross-sectionally across companies to obtain estimate. � For example, Moody’s uses "30-day" post-default date for τ .
Data � December 2000 to October 2007. � Debt Price Data - Advantage Data Corporation - Trade data and broker quotes to get end of day prices 4:45 p.m. � Filter data: � have 50 prices over a 60 day window surrounding recorded default date. � Remove bond issues with missing data on maturity, coupons. � This leaves 96 issues remaining for recovery rate estimation. � Filters imply that all our defaulted debt issues eventually …le for bankruptcy (potential selection bias). � Bond Characteristics - Mergent Fixed Income Database. Default is when a debt issue violates a bond covenant, misses a coupon or principal payment, or …les for bankruptcy. A grace period of 30 days must usually pass before default is recognized for a missed coupon.
Data - Bankruptcy Time Analysis To get a sense for duration of distressed debt market, considering only issues that …le for bankruptcy. N = 1902 Mean Std. Dev. Median N λ Chapter 7 433.22 353.20 433 9 0.80 Chapter 11 454.34 427.08 354 631 0.84 Time in Bankruptcy in Days λ is average time spent in bankruptcy in years.
Cross-sectional Recovery Rates (RFV) Di¤erence Count Avg. Price Std. Dev. Avg. Ratio -30 23 62.19 33.04 1.3199 -20 58 48.99 28.06 1.3510 -10 27 66.74 28.60 1.2382 -5 51 40.42 25.81 1.2114 -2 41 44.60 29.99 1.0541 -1 61 45.05 29.55 0.9796 0 70 48.17 29.39 1 1 71 45.48 28.67 1.0292 2 63 41.27 28.85 1.0284 5 44 48.32 31.48 1.0341 10 45 54.62 28.83 1.0933 20 46 53.86 32.44 1.1473 30 64 42.31 29.30 1.0779 RFV at recorded default 48.17 statistically di¤erent from RFV at 30 day 42.31.
Cross-sectional Recovery Rates (RT) N = 96 RT Estimates Mean 0.4062 Median 0.3452 Standard Deviation 0.2528 First Quartile 0.1692 Third Quartile 0.6374 Lower than the RFV estimates because otherwise identical default free bonds trade at a premium ( > $ 100).
Cross-sectional Recovery Rates (RMV) N = 96 Pre-Default Default Date RMV Estimates Mean 48.4 48.6 1.0230 Median 39 38.5 1.0013 Standard Deviation 30.6 30.7 0.1824 First Quartile 21.5 22 0.9681 Third Quartile 67.55 69.375 1.0597 � Debt prices do not jump on the default date. � Implies that, on average, the debt is "riskless." � Anomalous result: � either the RMV is a poor model for recovery rates, or � the recorded default date does not equal the economic default date.
Time-Series Models R t B d τ r s ds t = m � δ τ e where 8 < F if RFV m = p τ ( T ) if RT : B τ � if RMV . Assumes that risky debt position is sold at τ , and the model prices debt as the value of this position. Equivalently, R t τ � r s ds for t � τ . B d t = B d τ � e This form is independent of model type. Use this to: 1. Determine economic default date. 2. Test accuracy of valuation model.
Time-Series Models - Economic Default Date � Given our de…nition of the economic default date, using debt prices, our estimator is: τ � e � R τ � τ � � 180 � t � τ � f t : B t � B d r s ds g . b τ = inf t � Bound below by 180 days before the recorded default date. � Our estimator depends on the information up to time τ � .
Time-Series Models - Economic Default Date Time Between Economic Default Date and Announced Default Date 25 20 15 s e s a C 10 5 0 0 20 40 60 80 100 120 140 160 180 Days Figure: N = 73.
Time-Series Models - Revised Recovery Rates 8 B τ > if RFV < F b B τ if RT δ τ = p ( τ , T ) > : B τ if RMV . B τ �
Time-Series Models - RFV N = 73 Economic Default Recorded Default Mean 0.4879* 0.5283 Median 0.45 0.5782 Standard Deviation 0.3044 0.3151 First Quartile 0.2 0.2225 Third Quartile 0.76 0.8425 *P value essentially zero.
Time-Series Models - RT N = 73 Economic Default Recorded Default Mean 0.3970* 0.4335 Median 0.3291 0.4776 Standard Deviation 0.2461 0.2600 First Quartile 0.1578 0.1803 Third Quartile 0.6031 0.6610 *P value essentially zero.
Time-Series Models - RMV N = 73 Economic Default Recorded Default Mean 0.8314* 1.0653 Median 0.9094 1.0217 Standard Deviation 0.1775 0.1729 First Quartile 0.7267 0.9976 Third Quartile 0.9649 1.0854 *P value essentially zero. This is consistent with a jump on the economic default date.
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