An empirical study of the returns on defaulted debt

Abstract

This study empirically analyses the historical performance of defaulted debt from Moody's Ultimate Recovery Database (1987–2010). Motivated by a stylized structural model of credit risk with systematic recovery risk, we argue and find evidence that returns on defaulted debt co-vary with determinants of the market risk premium, firm specific and structural factors. Defaulted debt returns in our sample are observed to be increasing in collateral quality or debt cushion of the issue. Returns are also increasing for issuers having superior ratings at origination, more leverage at default, higher cumulative abnormal returns on equity prior to default, or greater market implied loss severity at default. Considering systematic factors, returns on defaulted debt are positively related to equity market indices and industry default rates. On the other hand, defaulted debt returns decrease with short-term interest rates. In a rolling out-of-time and out-of-sample re-sampling experiment we show that our leading model exhibits superior performance. We also document the economic significance of these results through excess abnormal returns, implementing a hypothetical trading strategy, of around 5%–6% (2%–3%) assuming zero (1 bp per month) round-trip transaction costs. These results are of practical relevance to investors and risk managers in this segment of the fixed income market.

Keywords:

• distressed debt
• recoveries
• default
• credit risk

JEL Classification::

• C15
• C52
• G24
• G33
• G34
• G00
• G10
• G21

Notes

¹ Standard portfolio separation theory implies that, all else equal, during episodes of augmented investor risk aversion, a greater proportion of wealth is allocated to risk-free assets (Tobin, 1958; Merton, 1971), implying lessened demand, lower price, and augmented expected returns across all risky assets.

² The probable reason why we are closer to the higher end of estimates, such as Keenan et al. (2000), is that we have included several downturn periods, such as the early 1990s and the recent ones.

³ Our research also has a bearing on the related and timely issue of the debate about the so-called ‘pro-cyclicality’ of the Basel capital framework (Gordy, 2003), an especially relevant topic in the wake of the recent financial crisis, where a critique of the regulation is such that banks wind up setting aside more capital just at the time that they should be using capital to provide more credit to businesses or to increase their own liquidity positions, in order to help avoid further financial dislocations and help revitalize the economy.

⁴ Note that this is also the approach underlying the regulatory capital formulae (BCBS, 2004), as developed by Gordy (2003).

⁵ This could also be interpreted as the ith PD segment or an obligor rating.

⁶ Vasicek (2002) demonstrates that under the assumption of a single systematic factor, an infinitely granular credit portfolio, and LGD that does not vary systematically, a closed-form solution for capital exists that is invariant to portfolio composition.

⁷ We can interpret this as an LGD segment (or rating) or debt seniority class.

⁸ Indeed, for many asset classes the Basel II framework mandates constant correlation parameters equally across all banks, regardless of particular portfolio exposure to industry or geography. However, for certain exposures, such as wholesale non-High Volatility Commercial Real Estate (non-HVCRE), this is allowed to depend upon the PD for the segment or rating (BCBS, 2004).

⁹ Alternatively we can estimate the vector of parameters (μ, , ρ_i,s , , r)^T by Full-Information Maximum Likelihood (FIML), given a time series of default rates and realized recovery rates. The resulting estimate can be used in Equation 3.8 – in conjunction with estimates of the market volatility σ_M , debt-specific volatility , the MRP (r_M – r_f ), and the risk-free rate r_f – in order to derive the theoretical return on defaulted debt within this model (Maclachlan, 2004). Also see Jacobs (2011) for how these quantities can be estimated from prices of defaulted debt at default and at emergence of different seniority instruments.

¹⁰ Experts at Moody’ compute an average of trading prices from 30 to 45 days following the default event, where each daily observation is the mean price polled from a set of dealers with the minimum/maximum quote thrown out.

¹¹ Based upon extensive data analysis in the Robust Statistics package of the S-Plus statistical computing application, we determined 35 observations to be statistical outliers. The optimal cut-off was determined to be about 1000%, above which we removed the observation from subsequent calculations. There was a clear separation in the distributions, as the minimum RDD in the outlier subset is about 17 000%, more than double the maximum in the nonoutlier subset.

¹² We have two sets of collateral types: the 19 lowest level labels appearing in MURD™ (Guarantees, Oil and Gas Properties, Inventory and Accounts Receivable, Accounts Receivable, Cash, Inventory, Most Assets, Equipment, All Assets, Real Estate, All Noncurrent Assets, Capital Stock, PP&E, Second Lien, Other, Unsecured, Third Lien, Intellectual Property and Intercompany Debt), and a 6-level grouping of that we constructed from these (Cash, Accounts Receivables and Guarantees; Inventory, Most Assets and Equipment; All Assets and Real Estate; Noncurrent Assets and Capital Stock; PP&E and Second Lien; and Unsecured and Other Illiquid Collateral). The latter high-level groupings were developed with in consultation with recovery analysis experts at Moody's Investors Services.

¹³ In the terminology of GLMs, the link function connects some function of a response variable (usually the random variable weighted by density, in the case of the expected value) to a linear function of explanatory variables.

¹⁴ To this end, we employ an alternating direction stepwise model selection algorithm in the mass() library of R statistical software. There were five candidate leading models that were tied as best, we eliminated two of them that we judged to have economically unreasonable features.

¹⁵ These are described in Jacobs (2011).

¹⁶ Moody's investment grade rating in Model 3 is on the borderline, having a p-value of 0.06, with significance at the 5% level.

¹⁷ The estimation was performed in S+ 8.0 using built-in optimization routines.

¹⁸ See Maddala (1981) for a discussion of this concept in the context of probit and logit regressions.