The Marginal Return on Resolution Time in the Workout Process of Defaulted Corporate Debts

Transcription

1 The Marginal Return on Resolution Time in the Workout Process of Defaulted Corporate Debts Natalie Tiernan Office of the Comptroller of the Currency Deming Wu a Office of the Comptroller of the Currency deming.wu@occ.treas.gov First version: July 2015 This version: May 2016 a The views expressed in this paper are those of the authors, and do not necessarily reflect those of the Office of the Comptroller of the Currency or the U.S. Department of the Treasury. We thank participants at the OCC Risk Analysis Division Seminar for helpful comments.

2 The Marginal Return on Resolution Time in the Workout Process of Defaulted Corporate Debts Abstract We examine how debt resolution time and the discount rate affect the recovery rates of defaulted corporate debts. The optimal time to end a defaulted debt workout process is when the marginal return and marginal cost on additional workout time are equal. But empirical evidence in this area is scant. Using a sample of defaulted corporate debts over the period from 1987 through 2012, we find that the average nominal marginal return on resolution time is close to 6 percent per year, and the average discounted marginal return on resolution time is close to zero. This finding rejects the early resolution bias hypothesis, which predicts either a large negative or a large positive discounted marginal return on resolution time. In addition, we find that recovery rate estimates decrease by 1.1% when the discount rate increases by 1%. JEL classification: G32; G33; G34 Key words: Recovery rate; Defaulted debt; Resolution time; Marginal return; Discount rate; LGD

3 1. Introduction When a borrower defaults on a loan or a bond, the debt resolution (i.e., workout) process starts. At any point during this process, debt holders face a choice between ending the workout process and extending it for an additional amount of time. 1 Rational debt holders would end the debt workout process when the marginal return and marginal cost on additional workout time are equal. However, because of data limitations, no prior studies have thoroughly examined the marginal return on workout time in the workout process of defaulted corporate debts. To help fill this gap, this study estimates the marginal returns on additional resolution time using a sample of large North American defaulted corporate debts over the period between 1987 and Estimating the marginal returns on defaulted debt workout time 2 has important implications in the current debate over the appropriate discount rate to use when calculating economic loss of corporate defaults. A major challenge of global banking regulators is to establish consistency in the implementation of the Basel III regulatory capital framework. 3 In response to this challenge, the Basel Committee on Banking Supervision (BCBS) established the Regulatory Consistency Assessment Program (RCAP) in 2012 to assess inconsistencies in banks risk-weighting of banking and trading book assets. The RCAP studies found material variances in banks 1 For example, a group of debt holders can influence the length of the workout process by compromising to reach a settlement or not. There is evidence that the presence of hedge funds on an unsecured creditors committee favors a firm s likelihood of emergence from Chapter 11 bankruptcy, which requires a longer workout process than the straight liquidation procedure usually preferred by senior secured creditors (Jiang, Li, and Wang, 2012). 2 This paper uses the terms resolution time, workout time, and workout period interchangeably. 3 For instance, the Basel Committee on Bank Supervision has published a series of reports on the subjects of consistency and risk sensitivity (Basel Committee on Banking Supervision, 2013a, 2013b, 2014b, 2014a). There are also independent studies on these subjects (Barakova and Palvia, 2014; Firestone and Rezende, 2015). 1

4 regulatory capital ratios that arise from factors other than differences in the riskiness of banks portfolios (Basel Committee on Banking Supervision, 2013a, 2014b, 2014a). In particular, variation in loss given default (LGD) estimates was the largest contributor to variations in riskweighted assets for large corporate exposures. These variances undermine confidence in banks regulatory capital ratios. Understanding the different causes of excessive variability in banks regulatory capital ratios is thus critical for regulators to promote public confidence in the regulatory capital framework. Our study sheds light on two important factors that may generate inconsistency in banks estimations of corporate default LGD: the discount rate used in the calculation of LGD and the length of time between default and emergence from default (i.e., resolution time) in the workout process of defaulted corporate debts. Under the U.S. final rule of the Basel III regulatory capital framework (Office of the Comptroller of the Currency and Federal Reserve System, 2013), the LGD of a defaulted corporate credit exposure equals the economic loss divided by the exposure at default (EAD). The economic loss must reflect the net present value of cash flows as of the default date using a discount rate appropriate to the risk of the defaulted exposure. However, neither the U.S. final rule nor the original Basel III Accord (Basel Committee on Banking Supervision, 2011) provides further explanation about how to choose the appropriate discount rate in the LGD calculation. The ambiguities in the Basel Capital Accords have led to a wide disagreement among banking practitioners, academics, and regulators over the appropriate discount rate to use to estimate LGD (Frye, 2000; Maclachlan, 2004; Brady et al., 2007; Jacobs, 2009). Consequently, there are three broad choices of discount rates used in the LGD calculation: the risk free rate, the opportunity cost of funds, and a comparable risky rate of return (e.g. contract rate (pre-petition rate) or return of holding the defaulted debts). If two banks use different discount rates in their 2

5 LGD calculations, it will be difficult for regulators to compare their LGD estimates on an applesto-apples basis. Additionally, when a bank determines that a loan is in default, it places it into a workout program and tries to recover the loss from the obligor. The length of this workout process depends on the context of the default, the debt and obligor characteristics, macroeconomic conditions, and other relevant factors. Consequently, regulators are concerned that differences in defaulted debt workout processes may cause substantial differences in LGD parameters. For instance, if quickly resolved defaults tend to have lower LGDs, a downward bias in LGD estimates could arise if banks include only resolved defaults in the LGD reference data. This bias is sometimes referred to as early resolution bias. Nevertheless, whether this is indeed a concern and what the magnitude of this bias is are empirical questions. The marginal return on defaulted debt workout time offers a theoretically coherent and practical approach for choosing a discount rate that is consistent with the economic loss principle. Specifically, the optimal stopping point of a workout process is when the nominal marginal return on workout time equals the nominal marginal cost on workout time. Therefore, if debt holders end the workout process rationally and if the discount rate used in the calculation of economic loss is close to the nominal marginal cost on workout time, we would expect the discounted marginal return on workout time to be equal or close to zero. We refer to our expectation of a discounted marginal return on resolution time equal or close to zero as the zero marginal return hypothesis. Alternatively, the early resolution bias hypothesis would imply a significantly large positive or negative discounted marginal return on resolution time. We empirically estimate the nominal and discounted marginal returns on resolution time. Overall, we find that the average nominal marginal return on resolution time is close to six 3

6 percent in our sample of defaulted corporate debts over the period of In addition, the average discounted marginal return on resolution time is close to zero, which supports the zero marginal return hypothesis and rejects the early resolution bias hypothesis. A second contribution of this paper is that we estimate the average effect of changes in discount rates on the estimates of recovery rates. Because of data limitations, most banks rely heavily on the Moody s Default and Recovery Database (Moody s DRD) and the S&P LossStats Database when developing their LGD models. However, both Moody s DRD and S&P LossStats use a defaulted obligation s pre-petition interest rate for discounting purposes. Furthermore, although Moody s DRD and S&P LossStats take into account the timing of cash flows before a resolution when calculating discounted recovery amounts, such cash flow data are not available to external users. Therefore, a bank faces the challenge of converting the recovery rate estimates from Moody s DRD and S&P LossStats to its own recovery rate estimates if it wants to use a different discount rate than the pre-petition interest rate. More specifically, a bank cannot consistently apply an alternative discount rate to the precise cash flow data when rediscounting the nominal final recovery at the resolution date back to the default date. Our paper addresses these challenges by estimating econometric models that link discount rates and recovery rates using the Moody s DRD database. Specifically, this econometric model allows us to estimate the average increase in recovery rate estimates when the discount rate is increased by one percentage point. While it is well recognized that the choice of discount rate will affect the recovery rate estimate, the magnitude of this effect depends on the cash flow pattern of the workout process and the resolution time of each defaulted facility. For instance, if the duration of the workout process of a defaulted debt is short, a change in the discount rate will have a small effect on the recovery rate estimate. On the other hand, a change in the discount 4

7 rate will have a substantial impact on the recovery rate estimate if the duration of the workout process is long. We find that a one percent increase in the discount rate is associated with a 1.1% decrease in the recovery rate estimate on average. Therefore, this empirical finding provides a practical solution for comparing recovery rate estimates based on different discount rates. It also allows a bank to map LGD estimates based on external data to its internal estimates even though it uses a different discount rate than that of the external data. 4 The remainder of this paper is organized as follows. Section 2 provides background information and reviews the related literature. Section 3 describes the data and empirical design. Section 4 presents and discusses the estimation results, and Section 5 concludes. 2. Background and related literature The workout process for a defaulted corporate debt involves either private renegotiation with the firm s creditors or bankruptcy proceedings. Private renegotiations are generally less costly than bankruptcies in terms of direct expenses, but are successful only when all creditors agree to the terms of the settlement. An example of a private renegotiation is a distressed exchange, where a defaulted firm offers to exchange all or parts of its defaulted outstanding debt for new securities of lesser value, and all creditors agree to those terms. Gilson, John, and Lang (1990) find that private renegotiations are more likely to succeed when a defaulted firm has more intangible assets, owes more of its debt to banks, owes fewer lenders, and has fewer distinct classes of debt outstanding. In cases where private renegotiation is unsuccessful, a firm can file for bankruptcy under either Chapter 7 (liquidation) or Chapter 11 (reorganization) of the U.S. 4 Such a mapping should consider whether the bank s portfolio has characteristics that are similar to the data underlying this study. 5

8 Bankruptcy Code. 5 Bankruptcy proceedings establish a well-defined priority structure of creditor classes for claims on the defaulted firm. Under Chapter 7, a case trustee is charged with liquidating the defaulted firm s assets in order to maximize the return to the firm s unsecured creditors. Under Chapter 11, a debtor firm typically has 120 days to propose a plan of reorganization, 6 after which creditors may file competing plans. Final acceptance of a Chapter 11 reorganization plan requires approval from creditors within each impaired creditor class (e.g., secured creditors, unsecured creditors entitled to priority, general unsecured creditors, and equity security holders) that represent more than one-half the number and two-thirds the value of the class s claims. 7 Our paper studies two important aspects of the workout process of defaulted corporate debts and their effects on recovery rates, namely the discount rate used in the calculation of LGD and the length of time between default and emergence from default (i.e., resolution or workout time). There are ambiguities in the U.S. final rule and the original Basel Capital Accords (Basel Committee on Banking Supervision, 2004, 2011) regarding the choice of an appropriate discount rate in the LGD calculation. To partially address these ambiguities, the BCBS (Basel Committee on Banking Supervision, 2005) published guidance on the LGD calculation. According to this guidance, when recovery streams are uncertain and involve risk that cannot be diversified away, 5 Alternatively, creditors meeting certain requirements may file an involuntary Chapter 11 bankruptcy petition on behalf of the defaulted firm. 6 The bankruptcy court can shorten or lengthen this 120-day period. Bris, Welch, and Zhu (2006) find that only 22% of the defaulted firms in their sample of 300 bankruptcies occurring in New York and Arizona from met the 120-day deadline. 7 The bankruptcy court has the power to impose the final settlement plan on claimholders or classes that oppose it, as long as the court has determined the plan is feasible, proposed in good faith, and in compliance with the law. 6

9 net present value calculations must reflect the time value of money and a risk premium appropriate to the undiversifiable risk. However, when there is no uncertainty in recovery streams (e.g., recoveries derived from cash collateral), net present value calculations need only reflect the time value of money, and a risk free discount rate is appropriate. Furthermore, the BCBS guidance suggests that a bank may use an effective interest rate in accordance with International Accounting Standards (IAS) 39 (International Accounting Standards Board, 2004) as the discount rate, given that the stream of net recoveries is adjusted in a way that is consistent with this principle. In practice, the BCBS guidance on the discount rate is subject to different interpretations, which has led to a wide disagreement among banking practitioners, academics, and regulators over the appropriate discount rate to use to estimate loss given default (LGD). Consequently, there are three broad choices of discount rates in the calculation of LGD: the risk free rate; the lender s opportunity cost (e.g., weighted average cost of capital (WACC), or cost of equity); A comparable risky rate of return (e.g. contract rate (pre-petition rate), ex-post returns of holding defaulted debts, and a rate of return on a distressed index). For instance, Asarnow and Edwards (1995) argue for the use of the contract rate as the LGD discount rate because on an ex post basis, it eliminates potential distortions owing to the specific timing of the accounting recognition of write-offs. 8 Acharya, Bharath, and Srinivasan (2007) and Düllmann and Gehde-Trapp (2004), however, use the high-yield bond index as the discount rate in their studies to account for systematic risk during the workout period. 9 Araten, Jacobs, and Varshney (2004), on the other hand, employ a vulture discount rate of 15% to 8 See Asarnow and Edwards (1995, p.4). 9 Frye (2003) is another study that cautions against ignoring systematic variation in risk when choosing a discount rate. 7

10 estimate the LGD of commercial loans at JP Morgan Chase from , arguing that the rate appropriately accounts for the riskiness of distressed-instrument cash flows. 10 Other studies argue for the use of returns of holding defaulted debts. For example, Brady et al. (2007) and Jacobs (2009) calculate the returns of defaulted debts using 30-day post-default trading prices and the ultimate recovery values of the defaulted instrument. Specifically, Brady et al. (2007) report an overall average discount rate of 14.0% in their study using defaulted bond and loan data from S&P LossStats from , and Jacobs (2009) reports a rate of 29.2% using defaulted bond and loan data from Moody s Ultimate Recovery Database from Maclachlan (2004), on the other hand, uses data from a single bank from and finds the discount rate on corporate bonds to be similar to the BB yield and the discount rate on small and medium enterprise loans to be similar to the loans original contract rate. One major challenge in calculating defaulted debt returns, however, is that the market for defaulted debts is very limited and highly illiquid due to asymmetric information and adverse selection problems. For instance, holders of defaulted secured loans often do not need to sell those loans if they know they can recover through the collateral instead. In fact, based on the Moody s Default and Recovery Database, only a small number of defaulted debts have market prices, and most of them are senior unsecured bonds. For this reason, it is unclear whether market prices of defaulted debts are representative given the limited participation in this market. Our paper contributes to this literature by proposing a theoretically coherent and practical approach for choosing a discount rate that is consistent with the economic loss principle. Specifically, if debt holders end the workout process rationally, then a reasonable choice of discount rate is the nominal marginal return on resolution time. 10 See Araten, Jacobs, and Varshney (2004, p.2). 8

11 Moreover, to the best of our knowledge, our study is the first that thoroughly examines the relationship between recovery rates and resolution time using data that covers multiple types of debt and a relatively long time period which includes the recent crisis. Although there are a couple of recent studies that examine the effects of resolution time on recovery rates, these studies have different focuses, sample designs, and empirical designs than ours. For instance, Dermine and De Carvalho (2006) use a sample of 374 defaulted short-term loans granted to small and medium-size companies by one single bank in Portugal during , to study the univariate relationship between resolution time and cumulative recovery rates. Khieu, Mullineaux, and Yi (2012), on the other hand, employ Moody s data and multivariate analysis but focus on the recoveries of loans and revolvers over the period of In addition, their study uses recovery rates that are calculated based only on the settlement method. 11 Furthermore, these studies have yielded mixed results. For instance, Dermine and De Carvalho (2006) find that the sample average cumulative recovery rate increases over time, while Khieu, Mullineaux, and Yi (2012) find a negative relationship between recovery rates and resolution time. Our paper enriches the literature by providing further and more comprehensive evidence on the relationship between recovery rates and resolution time for large North American defaulted corporate debts. Importantly, our paper covers a longer sample period from 1987 to 2012, which encompasses the most recent financial crisis, and more debt types (e.g., term loans, revolvers, senior unsecured bonds, senior secured bonds, and subordinated bonds). Furthermore, we examine the effects of resolution time on both nominal and discounted recovery rates. Finally, our study includes a more comprehensive set of control variables (collateral types, discount rates, 11 The settlement method for computing recovery rates is described in Section 3.1. Our study allows for the computation of recovery rates based upon either the settlement method, liquidity method, or trading price method, as determined by the judgment of Moody s analysts. 9

12 seniority index, debt-level and firm-level characteristics, and time fixed effects) than the existing studies. 3. Data and empirical design 3.1. Data The LGD data is from Moody s DRD database, which covers more than 1,000 corporate default events of North American commercial and industrial companies since 1987, each with more than US$50 million in total debt at the time of default. Moody s has opted to exclude financial institutions, which are highly regulated. Moody s DRD covers four types of defaults: Bankruptcy: A company files for Chapter 11 or Chapter 7 in a U.S. Bankruptcy Court; Distressed exchange: A company exchanges all or parts of securities for new securities of lesser value; Default and cure: A company defaults on debt then cures the default outside of the 30 day grace period; Other restructuring: Any other non-bankruptcy restructuring with a loss. Because there are only a few observations of Default and cure and Other restructuring, this study will focus on bankruptcies and distressed exchanges. Moody s DRD offers three different methods for calculating ultimate recovery: the settlement method, the liquidity method, and the trading price method. The settlement method calculates the recovery using values of settlement instruments at or close to emergence from the default resolution process. The liquidity method calculates the recovery using values of settlement instruments at the time of a liquidity event, such as the maturity of an instrument, the call of an instrument, or a subsequent default event. Lastly, the trading price method calculates the recovery using the trading price of the defaulted instrument taken at or post-emergence. For a given default, the database also indicates the preferred method, which reflects the best valuation and is most representative of the actual recovery of that default based on the knowledge and 10

13 experience of Moody s analysts. The most common preferred method is the settlement method. The analyses in this study are based on recovery rates using the preferred method indicated by Moody s DRD. 12 To obtain ultimate recovery, each nominal recovery is discounted back to the last time when interest was paid using the instrument s pre-petition coupon rate. The starting point for discounting for the settlement method is the first point in time when each settlement instrument can be priced. The starting point for the liquidity method is the date of the liquidity event. The starting point for the trading price method is the date of the first available trading price at or following emergence from default. We merge Moody s DRD data with Compustat and the Center for Research on Securities Prices stock prices database (CRSP) to obtain information on firms income and financial condition, their long-term credit ratings, and stock prices and returns Definitions of LGD, recovery rate, and nominal recovery rate Under the Basel III regulatory capital framework, the LGD of a defaulted debt equals the economic loss divided by EAD: (economic loss) recovery LGD = 1 1 (recovery rate). EAD = EAD = (1) In the above equation, the (discounted) recovery rate equals the present discounted value at the default date of net recovery cash flows divided by EAD: PVt k k = 1 (recovery rate)=, EAD n (2) 12 For completeness, we include a robustness check of our results using recovery rates based upon each method separately. 11

14 where PV t k denotes the present discounted value of the net recovery received at time t k and n is the number of cash flows received during the workout period. In addition, the nominal recovery rate is defined as the sum of undiscounted net recovery cash flows divided by EAD: CFt k k = 1 (nominal recovery rate)=, EAD n (3) where CF denotes undiscounted value of net recovery received at time t t k k and n is the number of cash flows received during the workout period. The relationship between discounted and undiscounted cash flows is defined by the following two equations: where r denotes the discount rate. Continuously compounding: PV = CF exp( rt ), (4) t t k k i tk Annual compounding: PV = CF (1 + r), (5) tk According to Eq. (1), LGD is completely determined by the recovery rate. For this reason, we focus our regression analyses on discounted and nominal recovery rates. tk 3.3. Marginal returns on resolution time The nominal marginal return on resolution time is defined as: (nominal recovery rate) (nominal marginal return)=. (resolution time) (6) Similarly, the discounted marginal return on resolution time is defined as: (recovery rate) (discounted marginal return)=. (resolution time) (7) As discussed before, a rational debt holder would stop the workout process when the nominal 12

15 marginal return on additional resolution time equals the nominal marginal cost. For this reason, a reasonable choice of discount rate in the calculation of economic loss is the nominal marginal cost on additional resolution time (or equivalently, the marginal return on additional resolution time). More specifically, if the discount rate used in the present value calculation equals the nominal marginal return on resolution time, we would expect the discounted marginal return on resolution time to be equal or close to zero. Alternatively, if quickly resolved defaults tend to have lower or higher LGDs than defaults resolved over longer periods, we would expect the discounted marginal return on resolution time to be substantially below or above zero. Therefore, we formulate the marginal return and early resolution hypotheses as follows: H1 ( Zero marginal return hypothesis): The discounted marginal return on resolution time is close to zero. H2 ( Early resolution bias hypothesis): The discounted marginal return on resolution time is substantially above or below zero Empirical design We use the following two regressions to estimate the average nominal and discounted marginal returns on resolution time: (nominal recovery rate) = a + a (resolution time) + a (discount rate) it, 0 1 it, 2 it, + A (debt characteristics) + A (firm characteristics) 3 it, 1 4 it, 1 + A (other control variables) +(error term), 5 it, 1 it, (8) (recovery rate) = b + b (resolution time) + b (discount rate) it, 0 1 it, 2 it, + B (debt characteristics) + B (firm characteristics) 3 it, 1 4 it, 1 +B (other control variables) +(error term). 5 it, 1 it, (9) In the regression of nominal recovery rate in Eq. (8), the coefficient of resolution time captures the average nominal marginal return on resolution time. Although Eq. (8) assumes a linear relationship between these two variables, we also perform robustness checks using regressions that allow for nonlinearity. 13

16 By the same token, the coefficient of resolution time in the regression of recovery rate in Eq. (9) captures the average discounted marginal return on resolution time. Consequently, we will reject the zero marginal return hypothesis if the coefficient on resolution time is substantially below or above zero. A large positive coefficient on this variable may imply that the discount rate is lower than the marginal return on resolution time. Conversely, a large negative coefficient may imply that the discount rate is higher than the marginal return on resolution time. Another important explanatory variable in our study is the discount rate. The coefficient of this variable in the recovery rate regression in Eq. (9) measures the average effect of changes in discount rates on the recovery rate estimates. On the other hand, because the nominal recovery rate is unrelated to the discount rate, we would expect this coefficient to be close zero in Eq. (8). Following findings in the literature, we include additional explanatory variables such as debt characteristics, firm characteristics, macroeconomic conditions, and industry conditions in our regressions. Previous empirical studies document that recovery rates vary by debt type, seniority and collateral type, finding that bank loans and senior debt as well as debt secured by more liquid types of collateral or guarantees tend to be associated with higher recovery rates (Acharya, Bharath, and Srinivasan, 2007; Qi and Zhao, 2011). Firm characteristics may also impact recovery rates, as profitability, the strength of the firm s balance sheet, and the ability of the firm s assets to be re-deployed should all lead to higher recoveries (Khieu, Mullineaux, and Yi, 2012). In addition, debt resolution processes that occur during macroeconomic downturns are associated with lower recovery rates (Frye, 2000; Schuermann, 2004; Mora, 2015), and previous studies have found a negative relationship between the aggregate default rate and the recovery rate (Gupton, Gates, and Carty, 2000; Hu and Perraudin, 2002; Frye, 2003; Düllmann and Gehde-Trapp, 2004; Altman et al., 2005). Additionally, work by Shleifer and Vishny (1992) 14

17 argues theoretically that industry conditions can impact a defaulted firm s ability to liquidate assets to their highest-valued use. Namely, competitor firms in the same industry would be the likeliest to re-employ a defaulted firm s assets to their highest-valued use, but an episode of industry-wide distress could instead lead to fire-sales of those assets to outsiders who value the assets less, leading to lower recovery rates. This fire-sale effect exacerbates the fundamental negative effect on asset values arising from reduced business opportunities during periods of industry distress. Empirical studies by Brown, Ciochetti, and Riddiough (2006); Acharya, Bharath, and Srinivasan (2007); and Mora (2015) provide supporting evidence of this effect. Table 1 summarizes the definitions of dependent and all explanatory variables included in regressions as well as the additional variables mentioned in this study. For debt characteristics, we define the following categories of debt types: senior unsecured bonds, senior secured bonds, subordinated bonds, term loans, and revolvers. Following Qi and Zhao (2013), we also include the seniority index (i.e., 1-percent above-percentage pari passu/2). We define the following five groups of collateral types: unsecured, liquid assets, guarantees, core assets, other assets. One important difference in the definitions of collateral type groups between this study and Qi and Zhao (2011) is that this study defines collateral type groups based on the levels of liquidity of different collateral types. For instance, the category of liquid assets includes Cash, All Current Assets, Inventory and Accounts Receivable, Inventory, and Accounts Receivable. The category of core assets includes less liquid collateral types, such as All Assets, Oil and Gas Properties, Real Estate, All Non-current Assets, Most Assets. Finally, the category of other assets includes illiquid collateral types, such as Capital Stock, PP&E, Other, Second Lien on all assets, Equipment, Intellectual Property, Third Lien on all assets, and Intercompany Debt. 15

18 Firm-level explanatory variables include firm size, leverage, earnings-to-assets ratio, profitability, coverage, tangibility, Tobin s Q, current ratio, cash ratio, bonds debt ratio, and utility dummy. We also calculate the distance-to-default measure using Merton s model (Merton, 1974; Bharath and Shumway, 2008). To control for macroeconomic and industry conditions, we include the monthly aggregate default rate, industry default rate, and three-month T-bill rate. 4. Empirical results 4.1. Summary statistics Table 2 reports the summary statistics of continuous variables in the final sample. As this table shows, the final sample consists of 4,959 defaulted debts, including 4,958 observations with non-missing discount rates, and 3,041 observations with matched financial information. The average nominal recovery rate in the sample is 66.4%, and the average (discounted) recovery rate is 58.8%. 13 Moreover, the average discount rate is 8.1%, and the median is 8.6%, with half of the discount rates in the sample falling between 5.8% and 10.8%. 14 In addition, the average resolution time is 1.2 years (14.6 months). 15 The average firm size in the sample is approximately 13 In comparison, Asarnow and Edwards (1995) report an average (discounted) recovery rate of 65% on over 800 loans that defaulted at Citibank between 1970 and Additionally, Gupton, Gates, and Carty (2000) report an average (discounted) recovery rate of 69.5% for senior secured loans versus 52.1% for unsecured loans. 14 As was noted in Section 3.1, these discount rates correspond to pre-petition coupon rates in the Moody s DRD database. 15 Using Moody s Ultimate Recovery Database from 1987 to 2009, Jacobs (2009) finds an average time to resolution of 1.4 years for all defaulted debts. Using the same database over the period of , Khieu, Mullineaux, and Yi (2012) find an average time to resolution of 13.8 months for term loans and revolvers. Gupton, Gates, and Carty (2000) find an average time to default resolution of 1.44 years (approximately 17.3 months) using a sample of 181 large U.S. 16

19 $2 billion, and the average leverage ratio of these firms is 60.8%. Finally, the average aggregate default rate over the sample period is 1.1%. Panel A of Table 3 reports the summary statistics of discounted and nominal recovery rate by year over the sample period of As this table shows, the recovery rate varies substantially by year. For instance, the lowest value of the average recovery rate is 43.8%, which occurred in 1989, and the highest average recovery rate, which is 82.6%, occurred in Moreover, as Figure 1 shows, both discounted and nominal recovery rates are lower during recession periods. This result is consistent with findings in previous studies such as Frye (2000), Schuermann (2004), and Mora (2015). Furthermore, our Figures 2 and 3 tend to agree with the results in Altman et al. (2005). Namely, no clear relationship emerges when we compare the discounted recovery rate in our data with real GDP growth in Figure 2. Additionally, in Figure 3 the discounted recovery rate is negatively correlated with the aggregate default rate over most of our sample period. 16 Figure 4 plots the average recovery rate along with the market return over time. 17 Panel B of Table 3 reports the summary statistics of the recovery rate by debt and default types. Among all debt types, subordinate bonds have the lowest average recovery rate, followed by senior unsecured bonds. Term loans and revolvers, on the other hand, have the highest bank loans that defaulted during , a result that reflects an average across Chapter 11 bankruptcies, prepackaged Chapter 11 bankruptcies, and defaults that were not formal bankruptcies. 16 This particular result is also cited in many other studies. See, for example, Düllmann and Gehde-Trapp (2004); Frye (2003); Gupton, Gates, and Carty (2000); and Hu and Perraudin (2002). However, we show in Section 4.5 that this negative correlation may have broken down during the recent crisis. 17 Market returns in Figure 3 are trailing 12-month value-weighted market returns. 17

20 recovery rates. Moreover, recovery rates are higher in distressed exchanges than in bankruptcies across all debt types, averaging 81.7% and 54.8% respectively. 18 Panel C of Table 3 reports the summary statistics of the recovery rate by collateral and default types, which shows that more liquid collateral types tend to have higher recovery rates than less liquid collateral types. Among all collateral type groups, the guarantees group has the highest recovery rate, followed by the liquid assets group, the core assets group, and the other assets group. The unsecured group has the lowest recovery rate. Panel D of Table 3 reports the summary statistics of the recovery rate by debt and collateral types and largely confirms the results of Panels B and C, although unsecured term loans have a lower recovery rate of 40.0% compared to senior unsecured bonds at 48.2%. In general, the results presented in Table 3 indicate that recovery rates can vary widely depending on time period, debt type, default type, and collateral type. In terms of the resolution time variable, Panel A of Table 4 reports the summary statistics of resolution time by year and default type. As we would expect, workout processes involving bankruptcy take longer to resolve than those involving a distressed exchange. For example, the average time to resolve a distressed exchange over our sample period was 1 month, versus 16.9 months for bankruptcies. 19 Average resolution time was highest in 1988 at 30.6 months, and 18 Franks and Torous (1994) report similar recovery rates of 80.1% for distressed exchanges and 50.9% for Chapter 11 reorganizations in their study, which uses a sample of 82 firms defaulting over the period from Other studies have reported different summary statistics of resolution time by default type, which could be attributed to differences in sample period and sample size from this study. For example, Gilson, John, and Lang (1990) use a sample of 169 financially-distressed firms from , and find that private debt restructurings take an average of 15.4 months, with exchange offers in particular taking an average of 6.6 months. The authors also find that firms filing for Chapter 11 in their sample spend an average of 8.1 months attempting to restructure 18

21 lowest in 2010 at 5.1 months. The average resolution time by year is plotted in Figure 5 along with the variable s 25 th and 75 th percentile values. As the figure shows, average resolution time exhibits a downward trend over the period. In addition, no discernible patterns emerge around recession periods, but the low average resolution time and the compressed 25 th and 75 th percentile range during the financial crisis are quite different relative to previous years. Figure 6 compares the average recovery rate and average resolution time by year. Before 2005, the recovery rate and resolution time appear to be negatively correlated. That is, years in which recovery rates were low (high) appear to also have long (short) resolution times. However, since 2005, the relationship appears to be more positively correlated. Panel B of Table 4 shows the summary statistics of resolution time by debt and default types. In bankruptcies, bond defaults take longer to resolve than term loans and revolvers. For example, senior unsecured bonds take the longest to resolve at an average of 20.1 months, but term loans take the least time to resolve at 14.6 months. Resolution time is relatively stable across debt types for distressed exchanges, however. Panel C reports the summary statistics of resolution time by collateral and default types. For both distressed exchanges and bankruptcies, defaults on debts unsecured by collateral take the longest to resolve, at 1.1 months and 18.8 months respectively. Bankruptcies that involve core assets as collateral take the least amount of time to their debt before seeking bankruptcy protection, and an average of 20.4 additional months in Chapter 11. Bris, Welch, and Zhu (2006), in their sample of 300 bankruptcies occurring in New York and Arizona from , report an average resolution time of 709 days (23.3 months) for Chapter 7 bankruptcies and 828 days (27.2 months) for Chapter 11 bankruptcies. The authors find that the longer resolution time associated with Chapter 11 bankruptcies is not a result of the procedure itself, rather it arises due to a self-selection effect. In addition, Franks and Torous (1994) find that distressed exchanges required an average workout period of 17.7 months whereas Chapter 11 bankruptcies required 29.6 months. 19

22 resolve at 13.4 months, followed by liquid assets at 16.5 months. Panel D of Table 4 presents the summary statistics of resolution time by debt and collateral types. Unsecured term loans and unsecured revolvers have the longest resolution times, at 28.3 and 23.1 months, respectively. However, the largest proportion of term loans and revolvers are secured by core assets, with average resolution times of 11.3 and 10.9 months respectively, which provides the overall result in Panel B, namely that term loans and revolvers tend to have the lowest average resolution times. Among the bonds, senior secured bonds with guarantees have the shortest average resolution time at 4 months, and senior secured bonds secured by other assets have the longest average resolution time at 18.9 months. Panel E of Table 4 reports the summary statistics of the discounted recovery rate by resolution time. All distressed exchanges are resolved in less than one year and have a recovery rate of 81.7%. Approximately 45% of the bankruptcies in our sample are resolved in less than one year, and 89% are resolved within 3 years. The discounted recovery rate for bankruptcies is non-monotone with respect to resolution time. For example, the average recovery rate is decreasing by year for resolution times between 0 and 3 years, and then rises to a high of 69.9% for resolutions taking between 4 and 5 years. A similar exercise is presented in Panel F for nominal recovery rates. This table shows that bankruptcies resolved between 0 and 3 years have an average nominal recovery rate of between 60.1% and 60.7%. However, those recoveries taking longer than 3 years have average nominal recovery rates that are much higher. Workout processes taking between 4 and 5 years, for example, have average nominal recovery rates of 95.9%. Table 5 reports the summary statistics of the discount rate. 20 As shown in Panel A, the 20 It should be noted that within Moody s DRD, the discount rate used is the pre-petition contract rate. 20

23 average discount rate across our data sample from is 8.1%. For bankruptcies only, the average discount rate was 8.8% and for distressed exchanges it was 4.6%. Figure 7 plots the average discount rate over time along with the variable s 25 th and 75 th percentile values. Overall, the average discount rate appears to be relatively stable between 1987 and The average discount rate then fell during , rose pre-crisis in 2006 and 2007, and then fell to its lowest values in Given this behavior, there appears to be a slight downward trend in the discount rate over our sample period. Figure 8 compares the behavior of the recovery rate and the discount rate over our sample period. Panel B of Table 5 reports the summary statistics of the discount rate by debt and default types. Average discount rates tend to be higher for bonds than for term loans and revolvers across default types. Subordinated bonds have the highest discount rate across default types, reflecting the increased risk of these securities relative to senior bonds, term loans and revolvers. Revolvers tend to have the lowest discount rate, at 6.9% for bankruptcies and 0.8% for distressed exchanges. Panel C presents the summary statistics of the discount rate by collateral and default types. Across default types, bonds and loans secured by guarantees, liquid assets, and core assets have the lowest discount rates. The highest discount rates are associated with unsecured debts. Lastly, Panel D reports the summary statistics of the discount rate by debt and collateral types. This panel largely reflects the results found in Panels B and C Regressions of nominal recovery rates Tables 6 and 7 report the estimation results from regressions of nominal recovery rates on resolution time, discount rate, additional debt and firm characteristics, and macroeconomic conditions. The core explanatory variables of interest are resolution time and discount rate. The coefficient of resolution time measures the average nominal marginal return on resolution time, 21

24 and the coefficient of discount rate measures the effect of a change in the discount rate on the nominal recovery rate estimation. Table 6 assumes a linear relationship between the nominal recovery rate and resolution time. To capture a potential nonlinear relationship, Table 7 reports two regressions that use different transformations of resolution time. Specifically, regression (1) of Table 7 uses the log of resolution time in years, and regression (2) of Table 7 uses six indicators that divide the resolution time into six categories (i.e., less than one year, one to two years, two to three years, three to four years, four to give years, and above five years). Table 6 consists of 5 regressions. Regression (1) includes only debt-level variables as explanatory variables. Regression (2) adds firm-level variables, and regression (3) adds macroeconomic variables. Regression (4) adds time fixed effects but excludes macroeconomic variables. Regression (5) includes both time fixed effects and macroeconomic variables. Table 6 shows that the average nominal marginal return on resolution time is close to six percent. For instance, the coefficient of resolution time is 6.08% in in regression (5), which includes all control variables. In addition, this coefficient is positive and statistically significant in all regressions. Except for regression (2), the values of this coefficient are very close to each other. The lowest value of this coefficient, which is reported in regression (2), is 4.64%. In addition, Table 6 shows that the nominal recovery rate is largely unrelated to the discount rate. For instance, the coefficient of discount rate is economically insignificant in all five regressions and statistically insignificant in four regressions. Even though this coefficient is statistically significant in regression (1), its value is very close to zero (0.73%). Furthermore, regression (1) includes the least number of control variables among all five regressions. Although Table 7 confirms the existence of nonlinearity in the relationship between the 22

25 nominal recovery rate and resolution time, it also confirms that the estimation results in Table 6 and Table 7 are qualitatively similar. For instance, the coefficient of log (resolution time) is 6.35% in regression (1) of Table 7, which implies that the nominal marginal return on resolution time is 5.3% at the sample mean of 1.2 years of resolution time. In regression (2) of Table 7, the base category of resolution time is resolution time less than one year. Therefore, the coefficient of resolution time between 1 and 2 years, which is 3.62%, captures the change in nominal recovery rate from the less than one year category to the between 1 and 2 years category. Similarly, the coefficient of resolution time between 3 and 4 years, which is 17.4%, captures change in average nominal recovery rate from the less than one year category to the between 3 and 4 years. Therefore, if we average this coefficient over three years, the average nominal marginal return on resolution time is 5.8% Regressions of discounted recovery rates Tables 8 and 9 report estimation results from regressions of (discounted) recovery rates on resolution time, discount rate, additional debt and firm characteristics, and macroeconomic conditions. These two tables are structured like Tables 6 and 7, respectively. More specifically, Table 8 assumes a linear relationship between the nominal recovery rate and resolution time, and Table 9 uses different transformations of resolution time to capture potential nonlinearity. Similarly to Tables 6 and 7, the core explanatory variables of interest in Tables 8 and 9 are resolution time and discount rate. The coefficient of resolution time measures the average discounted marginal return on resolution time, and the coefficient of discount rate measures the effect of a change in the discount rate on the recovery rate estimation. Overall, Tables 8 and 9 show that the average discounted marginal return on additional resolution time is small. For instance, the highest value of the coefficient of resolution time is 23

26 1.56 % in Table 8. In addition, the coefficient of log (resolution time) is insignificant in regression (1) of Table 9, which captures the nonlinear effect of resolution time. Furthermore, except for resolution time between 4 and 5 years, the coefficients for all categories of resolution time are insignificant in regression (2) of Table 9. Even though the coefficient of resolution time between 4 and 5 years is 12.06%, when this value is averaged across four years, the average annual marginal return is only 3.02%. For comparison purposes, the coefficient of resolution time between 4 and 5 years is 33.6% in the regression of nominal recovery rate in Table 7. Because the average discounted marginal return on resolution time is close to zero, we fail to reject the zero marginal return hypothesis. For robustness testing, Table 10 presents the regressions of discounted recovery rates on subsamples of different debt types. This table shows that the coefficient on resolution time is insignificant and is close to zero for the subsamples of senior secured bonds, subordinated bonds, term loans, and revolvers. The only exception is the subsample of senior unsecured bonds, in which the coefficient on resolution time is positive and statistically significant. The positive marginal returns on resolution time of senior unsecured bonds may imply that senior unsecured bond holders can get more concessions from other participants in the workout process if they can successfully prolong the workout process. More specifically, there may be significant differences in the recovery experiences between holders of secured and unsecured debts. For debts that are secured by collateral, debt holders can seize the collateral and obtain the recovery. As a result, their recovery rates may depend more on the realized values of the collateral and less on the resolution time. On the other hand, senior unsecured bonds are not secured by collateral. Therefore, prolonging the workout process may be an effective weapon for holders of senior unsecured bonds to force other participants to make more concessions during the resolution 24

27 process. Consequently, the final resolution time may reflect the conflicts and compromises among management, shareholders, and different type of debt holders. Table 11 runs regressions on subsamples over different sub-periods and with different resolution cut-off years. Overall, we find that that early resolution bias is minimal if the reference data covers a relatively long period (e.g., 5 years or longer) and if relevant risk factors are included in the regression. The only exception is regression (8), which covers the period of with 2012 as the resolution cut-off year. The coefficient of resolution time in regression (8) is negative and statistically significant (-8.01%), which is consistent with the early resolution bias hypothesis. Therefore, the early resolution bias appears to be only a recent phenomenon when the reference data cover only a relatively short period after As an additional robustness test, Table 13 reports the regressions of discounted recovery rates over subsamples of the dataset based upon Moody s three methods for calculating ultimate recovery: the settlement method, trading price method, and liquidity method. The dependent variable in regression (1) is the discounted recovery rate calculated using the settlement method. Regressions (2) and (3) are based upon the discounted recovery rate calculated using the trading price method and liquidity method, respectively. The results show that the zero marginal return hypothesis cannot be rejected when the recovery rate is calculated using the settlement method, but evidence in favor of rejecting the hypothesis is present for the trading price and liquidity methods. However, these results should be interpreted with some caution. First, the regressions in Table 13 rely upon recovery rate calculations that are not necessarily those chosen by Moody s analysts to be the most representative of the actual recovery of each default. Second, important differences exist among the three calculation methods. The settlement and liquidity method recovery rates are calculated based upon the value of the settlement instrument, 25

28 but that valuation is taken at different times. The settlement method reflects the value of that instrument at or close to emergence from default, whereas the liquidity method reflects the value at the date of a liquidity event such as the maturity date of the instrument or a subsequent default date. Hence, the settlement method represents the earliest valuation of the settlement instrument, and the liquidity date represents a later valuation. The results in Table 13 indicate that the later liquidity method valuation of the settlement instrument is larger in our dataset than the earliest settlement method valuation. The trading price method, in contrast, is based upon the first available trading price of the pre-petition instrument at emergence from default. Thus, while the settlement method and trading price method represent valuations around the same point in time, the underlying instrument in each valuation is different Recovery rate and discount rate Overall, we find that recovery rate estimates decrease by 1.1% for a 1% increase in discount rates, as the coefficient of discount rate is close to -1.1% in almost all regressions of recovery rate in Tables 8 and 9. In addition, this coefficient is statistically significant in all regressions. By contrast, the coefficient of discount rate is small and statistically insignificant in almost all regressions of nominal recovery rates in Tables 6 and 7. Table 12 tests the robustness of the effects of discount rates on the recovery rates by including the nominal recovery rate as a control variable. Using the nominal recovery rate as a control variable would capture the effects of all other explanatory variables, including omitted variables. Therefore, this approach is less susceptible to the omitted variable biases. This table shows that the coefficient on discount rate is -1.23%, which reinforces the findings of Tables 8 and 9. 26

29 4.5. Recovery rate and aggregate default rate We also explore the relationship between the recovery rate and the aggregate default rate. In regression (3) of both Tables 6 and 8, the coefficient on the aggregate default rate variable is between -11% and -13%. It should be noted that regression (3) does not include the quarterly time fixed effects, however. When quarterly time fixed effects are included in regression (5) of each table, the coefficient of aggregate default rate is inflated to between -33% and -40%. This instability is likely to be caused by multicollinearity arising from high correlation between the macroeconomic variables and time fixed effects. To avoid the multicollinearity problem, Table 11 does not include the quarterly time fixed effects. In regressions (1) through (7), this coefficient is negative and statistically significant, and is between -10% to -17%. However, this coefficient is no longer stable and changes signs in regressions (8) and (9). Both regressions (8) and (9) cover a relatively short period. For instance, regression (8) covers a six-year period from 2007 through 2012, while regression (9) covers a three-year period from 2007 through Overall, these results suggest that in order to obtain stable estimates on the effects of macroeconomic variables on recovery rate, the reference data needs to cover a relatively long period. Alternatively, these results may indicate that the negative relationship between the recovery rate and aggregate default rate broke down during the recent financial crisis. 5. Conclusions We have examined how resolution time and the discount rate affect the recovery rate of defaulted corporate debts. Using a sample of defaulted corporate debts over the period from 1987 through 2012, we find that the average nominal marginal return on resolution time is close to six percent, and the average discounted marginal return on resolution time is close to zero. We 27

30 interpret this latter result as evidence that holders of defaulted debts end workout processes rationally, when nominal marginal returns and marginal costs (i.e. the discount rate) on additional workout time are equal. This finding rejects the early resolution bias hypothesis, which predicts either a large negative or a large positive discounted marginal return on resolution time. In addition, we find that recovery rate estimates decrease by 1.1% on average when the discount rates increases by 1%. Additionally, recovery rates decrease by 11% on average when the aggregate default rate increases by 1%. Finally, we find that the negative relationship between the recovery rate and the aggregate default rate broke down during the recent financial crisis. References Acharya, V.V., Bharath, S.T., Srinivasan, A., Does industry-wide distress affect defaulted firms? Evidence from creditor recoveries. Journal of Financial Economics 85, Altman, E.I., Brady, B., Resti, A., Sironi, A., The link between default and recovery rates: Theory, empirical evidence, and implications. Journal of Business 78, Araten, M., Jacobs, M., Varshney, P., Measuring LGD on commercial loans: An 18-year internal study. RMA Journal 86, Asarnow, E., Edwards, D., Measuring loss on defaulted bank loans: A 24-year study. The Journal of Commercial Lending 77, Barakova, I., Palvia, A., Do banks internal Basel risk estimates reflect risk? Journal of Financial Stability 13, Basel Committee on Banking Supervision, Basel II: International convergence of capital measurement and capital standards: A revised framework. Bank for International Settlements. Basel Committee on Banking Supervision, Guidance on paragraph 468 of the framework document. Bank for International Settlements. Basel Committee on Banking Supervision, Basel III: A global regulatory framework for more resilient banks and banking systems - revised version June Bank for International Settlements. 28

31 Basel Committee on Banking Supervision, 2013a. Analysis of risk-weighted assets for credit risk in the banking book. Bank for International Settlements. Basel Committee on Banking Supervision, 2013b. The regulatory framework: Balancing risk sensitivity, simplicity and comparability. Bank for International Settlements. Basel Committee on Banking Supervision, 2014a. Assessment of Basel III regulations United States of America. Bank for International Settlements. Basel Committee on Banking Supervision, 2014b. Reducing excessive variability in banks regulatory capital ratios. Bank for International Settlements. Bharath, S.T., Shumway, T., Forecasting default with the Merton distance to default model. Review of Financial Studies 21, Brady, B., Chang, P., Miu, P., Ozdemir, B., Schwartz, D., Discount rate for workout recoveries: An empirical study. SSRN Working Paper Series. Bris, A., Welch, I., Zhu, N., The costs of bankruptcy: Chapter 7 liquidation versus Chapter 11 reorganization. The Journal of Finance 61, Brown, D.T., Ciochetti, B.A., Riddiough, T.J., Theory and evidence on the resolution of financial distress. Review of Financial Studies 19, Dermine, J., De Carvalho, C.N., Bank loan losses-given-default: A case study. Journal of Banking & Finance 30, Düllmann, K., Gehde-Trapp, M., Systematic risk in recovery rates an empirical analysis of US corporate credit exposures. In: EFMA 2004 Basel Meetings. Firestone, S., Rezende, M., Are banks internal risk parameters consistent? Evidence from syndicated loans. Journal of Financial Services Research, Franks, J.R., Torous, W.N., A comparison of financial recontracting in distressed exchanges and Chapter 11 reorganizations. Journal of Financial Economics 35, Frye, J., Depressing recoveries. Risk 13, Frye, J., A false sense of security. Risk, Gilson, S.C., John, K., Lang, L.H., Troubled debt restructurings: An empirical study of private reorganization of firms in default. Journal of Financial Economics 27, Gupton, G.M., Gates, D., Carty, L.V., Bank loan loss given default. Moody s Investors Service, Global Credit Research November, Hu, Y.-T., Perraudin, W., The dependence of recovery rates and defaults. Working Paper, Birbeck College and Bank of England. 29

32 International Accounting Standards Board, IAS 39: Financial instruments: Recognition and measurement. International Accounting Standards Board. Jacobs, M., An empirical study of the returns on defaulted debt and the discount rate for loss-given-default. SSRN Working Paper Series. Jiang, W., Li, K., Wang, W., Hedge funds and Chapter 11. Journal of Finance 67, Khieu, H.D., Mullineaux, D.J., Yi, H.-C., The determinants of bank loan recovery rates. Journal of Banking & Finance 36, Maclachlan, I., Choosing the discount factor for estimating economic LGD. Working Paper, Australia and New Zealand Banking Group Ltd. Merton, R.C., On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, Mora, N., Creditor recovery: The macroeconomic dependence of industry equilibrium. Journal of Financial Stability 18, Office of the Comptroller of the Currency, Federal Reserve System, Regulatory capital rules: Regulatory capital, implementation of Basel III. Federal Register 78, Qi, M., Zhao, X., Comparison of modeling methods for loss given default. Journal of Banking & Finance 35, Qi, M., Zhao, X., Debt structure, market value of firm and recovery rate. Journal of Credit Risk 9, Schuermann, T., What do we know about loss given default? Working Paper, Wharton Financial Institutions Center. Shleifer, A., Vishny, R.W., Liquidation values and debt capacity: A market equilibrium approach. Journal of Finance 47,

33 Table 1 Variable definitions This table summarizes the definitions of dependent and explanatory variables included in regressions and additional variables mentioned in this study. Variable Description Nominal recovery rate Nominal recovery rate is the sum of undiscounted net recovery cash flows divided by EAD. Recovery rate Recovery rate is the present discounted value at the default date of net recovery cash flows divided by EAD. LGD Loss given default equals one minus the recovery rate. Resolution time (year) Resolution time in years. This variable is continuous. For instance, 1 year and 3 months will be Discount rate The discount rate used in the LGD calculation Distressed exchange This dummy variable equals 1 if the default type is distressed exchange. Seniority index The seniority index is proposed by Qi and Zhao (2013) and equals (1-percent above-percent pari passu/2) Debt type Senior unsecured bonds Senior secured bonds Subordinated bonds Term loans Revolvers Collateral group Firm size Distance-to-default Leverage Earnings-to-assets ratio Profitability Coverage Tangibility Tobin s Q Current ratio Cash ratio Bonds debt ratio Utility dummy Aggregate default rate Industry default rate T-bill rate Industry distance-to-default Market return Maturity longer than 5 years Unsecured Liquid assets ( Cash, All Current Assets, Inventory and Accounts Receivable, Inventory, Accounts Receivable ) Guarantees Core assets ( Oil and Gas Properties, All Assets, Real Estate, All Noncurrent Assets, Most Assets ) Other assets ( Capital Stock, PP&E, Other, Second Lien on all assets, Equipment, Intellectual Property, Third Lien on all assets, Intercompany Debt ) The natural logarithm of total assets (expressed in millions of U.S. dollars) 1-year distance-to-default calculated using Merton s model Debt to assets ratio Earnings to assets ratio EBITDA/sales ratio EBITDA/Interest expenses ratio Property, plant and equipment to assets ratio (ppentq/assets) Market value of assets to book value of assets ratio Current assets to current liabilities ratio Cash and short-term investments/assets ratio Bonds to total debt ratio This dummy variable equals one if the firm is in the utility sector Aggregate default rate Industry default rate 3-month Treasury bill rate Industry distance-to-default Trailing 12 month value-weighted market return This dummy variable equals one if the maturity of the debt is greater than 5 years and zero otherwise. 31

34 Table 2 Summary statistics of continuous variables, This table reports the summary statistics of continuous variables. Variables are defined in Table 1. Firm size is the natural logarithm of total assets (expressed in millions of U.S. dollars). All other values are expressed in real value. N Mean Median Std P25 P75 Nominal recovery rate % 74.9% 44.6% 22.4% 103.0% Recovery rate % 63.8% 39.1% 20.3% 100.0% LGD % 36.2% 39.1% 0.0% 79.8% Resolution time (year) Resolution time (month) Discount rate % 8.6% 4.0% 5.8% 10.8% Seniority index % 50.0% 25.9% 30.2% 72.4% Firm size Distance-to-default Leverage % 62.5% 23.8% 40.9% 82.2% Earnings-to-assets ratio % -1.5% 9.5% -7.5% 0.5% Profitability % 5.9% 26.8% -0.6% 13.8% Coverage % 0.0% 169.6% 0.0% 130.1% Tangibility % 42.1% 23.2% 22.0% 58.9% Tobin s Q % 107.5% 63.9% 90.9% 133.3% Current ratio % 98.2% 84.3% 56.2% 129.7% Cash ratio % 3.7% 7.9% 1.5% 9.0% Bonds debt ratio % 62.9% 29.4% 39.0% 83.3% Aggregate default rate % 1.0% 0.6% 0.5% 1.6% Industry default rate % 1.3% 2.3% 0.7% 2.4% T-bill rate % 2.1% 2.3% 1.2% 5.0% Industry distance-to-default Market return % 2.5% 21.0% -16.0% 15.9% 32

35 Table 3 Summary statistics of recovery rate by different categories, This table reports the summary statistics of recovery rate by different categories (year, default type, debt type, collateral type, and resolution time). Panel A: Summary statistics of recovery and nominal recovery rate by year, Recovery rate Nominal recovery rate Year N Mean Median Std Mean Median Std % 100.0% 36.2% 83.2% 100.9% 33.9% % 56.4% 38.4% 68.6% 71.7% 48.6% % 37.1% 32.9% 56.0% 48.4% 43.2% % 42.6% 40.0% 54.1% 50.0% 45.3% % 64.7% 40.4% 70.9% 79.9% 51.2% % 57.3% 38.2% 66.8% 70.1% 42.9% % 72.8% 38.4% 73.0% 85.9% 45.8% % 84.8% 35.2% 76.0% 88.9% 39.1% % 76.5% 39.3% 87.0% 92.0% 61.0% % 86.5% 38.0% 73.4% 101.9% 43.1% % 78.1% 38.5% 71.6% 83.3% 43.9% % 36.8% 37.2% 53.4% 40.2% 41.6% % 61.5% 39.7% 64.8% 77.2% 44.6% % 45.3% 39.3% 61.4% 59.3% 47.7% % 42.7% 40.7% 59.5% 48.4% 48.3% % 37.9% 37.2% 54.6% 40.2% 41.2% % 74.8% 35.7% 75.3% 84.7% 39.1% % 100.0% 35.7% 79.9% 100.0% 37.8% % 90.6% 31.1% 86.6% 100.0% 35.9% % 100.0% 39.0% 81.6% 102.8% 42.0% % 100.0% 30.5% 88.9% 102.5% 32.9% % 69.7% 40.1% 64.2% 80.7% 41.3% % 74.5% 38.6% 65.6% 81.3% 39.6% % 74.8% 41.1% 60.7% 75.3% 41.8% % 100.0% 38.2% 79.4% 100.0% 44.5% % 62.8% 38.4% 71.9% 72.3% 60.8% Total 4, % 63.8% 39.1% 66.4% 74.9% 44.6% Panel B: Summary statistics of recovery rate by debt and default types, Recovery rate Bankruptcy Distressed exchange Debt type N Mean Median Std N Mean Median Std Senior unsecured bonds 1, % 31.4% 36.1% % 86.8% 30.0% Senior secured bonds % 60.0% 33.9% % 100.0% 28.0% Subordinated bonds % 8.2% 27.6% % 66.6% 33.6% Term loans % 90.1% 35.0% % 100.0% 17.1% Revolvers % 100.0% 27.8% % 100.0% 7.1% Total 4, % 55.1% 39.4% % 100.0% 28.4% 33

36 Table 3 (continued) Panel C: Summary statistics of recovery rate by collateral and default types, Recovery rate Bankruptcy Distressed exchange Collateral group N Mean Median Std N Mean Median Std 1 Unsecured 2, % 19.9% 35.0% % 79.3% 31.4% 2 Liquid assets % 100.0% 13.3% % 100.0% 6.9% Accounts receivable % 100.0% 21.5% % 100.0% 0.0% All current assets % 100.0% 9.9% % 100.0% 0.0% Cash % 100.0% 0.0% % 52.7%. Inventory % 100.0% 14.7% % 100.0% 0.0% Inventory and accounts receivable % 100.0% 9.6% % 100.0% 0.0% 3 Guarantees % 100.0% 4.9% % 100.0%. 4 Core assets 1, % 100.0% 29.1% % 100.0% 13.5% All assets 1, % 100.0% 29.1% % 100.0% 12.2% All non-current assets % 77.7% 27.9% % 99.6% 48.0% Most assets % 79.7% 26.6%.... Oil and gas properties % 100.0% 4.8% % 100.0% 0.0% Real estate % 100.0% 34.3% Other assets % 55.5% 35.3% % 100.0% 25.5% Capital stock % 66.8% 30.2% % 100.0% 28.7% Equipment % 20.9% 36.0% % 100.0% 0.0% Intellectual property % 37.4% 32.6%.... Intercompany debt % 12.7%..... Other % 53.5% 37.7%.... PP&E % 58.5% 31.4% % 100.0% 25.0% Second lien % 42.8% 39.5% % 100.0% 25.0% Third lien % 37.7% 37.0% % 100.0%. Panel D: Summary statistics of recovery rate by debt and collateral types, Recovery rate Collateral group Unsecured Liquid assets Guarantees Core assets Other assets Debt type N Mean N Mean N Mean N Mean N Mean Senior unsecured bonds 1, % Senior secured bonds % % % % Subordinated bonds % Term loans % % % % % Revolvers % % % % % 34

37 Table 4 Summary statistics of resolution time by different categories, This table reports the summary statistics of resolution time by different categories (year, default type, debt type, and collateral type). Panel A: Summary statistics of resolution time by year and default type, Resolution time(month) All Bankruptcy Distressed exchange Year N Mean Median Std N Mean Median Std N Mean Median Std Total 4, , Panel B: Summary statistics of resolution time by debt and default types, Resolution time(month) Bankruptcy Distressed exchange Debt type N Mean Median Std N Mean Median Std Senior unsecured bonds 1, Senior secured bonds Subordinated bonds Term loans Revolvers Total 4,

38 Table 4 (continued) Panel C: Summary statistics of resolution time by collateral and default types, Resolution time(month) Bankruptcy Distressed exchange Collateral group N Mean Median Std N Mean Median Std Unsecured 2, Liquid assets Guarantees Core assets 1, Other assets Total 4, Panel D: Summary statistics of resolution time by debt and collateral types, Resolution time (month) Collateral group Unsecured Liquid assets Guarantees Core assets Other assets Debt type N Mean N Mean N Mean N Mean N Mean Senior unsecured bonds 1, Senior secured bonds Subordinated bonds Term loans Revolvers Panel E: Summary statistics of recovery rate by resolution time, Recovery rate Bankruptcy Distressed exchange N Mean Median Std N Mean Median Std Resolution time Less than 1 year (0) 1, % 53.6% 38.8% % 100.0% 28.4% Between 1 and 2 years (1) 1, % 53.6% 39.7%.... Between 2 and 3 years (2) % 41.2% 40.9%.... Between 3 and 4 years (3) % 61.0% 38.3%.... Between 4 and 5 years (4) % 80.3% 36.6% years or longer (5) % 43.8% 36.5%.... Panel F: Summary statistics of nominal recovery rate by resolution time, Nominal recovery rate Bankruptcy Distressed exchange N Mean Median Std N Mean Median Std Resolution time Less than 1 year (0) 1, % 60.1% 41.2% % 100.0% 30.4% Between 1 and 2 years (1) 1, % 64.1% 45.6%.... Between 2 and 3 years (2) % 52.1% 49.1%.... Between 3 and 4 years (3) % 74.9% 49.0%.... Between 4 and 5 years (4) % 102.5% 51.0% years or longer (5) % 71.8% 69.0%

39 Table 5 Summary statistics of discount rate by different categories, This table reports the summary statistics of discount rate by different categories (year, default type, debt type, and collateral type). Panel A: Summary statistics of discount rate by year and default type, Discount rate All Bankruptcy Distressed exchange Year N Mean Median Std N Mean Median Std N Mean Median Std % 9.5% 3.9% % 10.8% 2.6% % 8.9% 4.4% % 10.1% 5.6% % 10.0% 5.6% % 13.0% 1.0% % 11.4% 4.3% % 11.4% 3.0% % 11.3% 6.1% % 11.3% 4.9% % 11.5% 3.4% % 0.0% 7.4% % 11.0% 3.6% % 11.0% 2.6% % 8.9% 6.7% % 10.4% 4.6% % 10.5% 4.5% 8 6.7% 8.8% 5.8% % 10.0% 3.7% % 10.0% 3.1% % 0.0% 7.1% % 9.3% 4.1% % 9.3% 2.5% % 0.0% 6.3% % 9.3% 3.7% % 9.3% 3.4% 4 1.8% 0.0% 3.6% % 9.8% 2.6% % 9.8% 2.6% % 11.0% 1.5% % 9.8% 3.2% % 9.8% 3.2% % 9.4% 2.4% % 9.4% 2.4% % 10.3% 2.6% % 8.9% 3.5% % 9.0% 2.6% % 0.0% 6.0% % 9.8% 2.4% % 9.8% 2.1% % 10.0% 5.7% % 8.3% 3.1% % 8.3% 2.7% % 6.0% 5.4% % 8.0% 3.7% % 8.3% 3.0% % 0.0% 4.4% % 7.1% 3.9% % 7.1% 3.5% % 4.2% 5.9% % 6.8% 4.1% % 7.1% 3.6% % 0.0% 4.9% % 7.9% 3.3% % 7.9% 2.6% % 4.3% 5.6% % 9.0% 2.8% % 9.0% 2.6% 3 6.4% 9.6% 5.6% % 9.7% 2.9% % 9.9% 2.1% 4 4.5% 4.4% 5.2% % 6.3% 4.2% % 7.5% 3.1% % 0.0% 4.1% % 5.3% 4.1% % 6.3% 3.4% % 0.0% 4.4% % 5.5% 4.3% % 5.7% 4.1% % 0.0% 4.9% % 7.6% 3.8% % 8.4% 3.1% % 0.0% 4.3% % 7.4% 3.3% % 7.5% 3.4% % 5.0% 3.2% Total 4, % 8.6% 4.0% 4, % 8.9% 3.4% % 0.0% 5.3% Panel B: Summary statistics of discount rate by debt and default types, Discount rate Bankruptcy Distressed exchange Debt type N Mean Median Std N Mean Median Std Senior unsecured bonds 1, % 9.5% 2.7% % 6.9% 5.0% Senior secured bonds % 10.0% 3.4% % 8.0% 6.2% Subordinated bonds % 10.6% 3.2% % 9.8% 4.9% Term loans % 7.2% 3.4% % 0.0% 3.7% Revolvers % 7.0% 3.0% % 0.0% 2.4% Total 4, % 8.9% 3.4% % 0.0% 5.3% 37

40 Table 5 (continued) Panel C: Summary statistics of discount rate by collateral and default types, Discount rate Bankruptcy Distressed exchange Collateral group N Mean Median Std N Mean Median Std Unsecured 2, % 9.8% 3.1% % 7.9% 5.2% Liquid assets % 7.2% 3.2% % 0.0% 2.7% Guarantees % 6.1% 3.8% 1 0.0% 0.0%. Core assets 1, % 7.2% 3.1% % 0.0% 3.4% Other assets % 9.4% 3.3% % 0.0% 5.6% Total 4, % 8.9% 3.4% % 0.0% 5.3% Panel D: Summary statistics of discount rate by debt and collateral types, Discount rate Collateral group Unsecured Liquid assets Guarantees Core assets Other assets Debt type N Mean N Mean N Mean N Mean N Mean Senior unsecured bonds 1, % Senior secured bonds % 2 6.8% % % Subordinated bonds % Term loans % % 8 5.3% % % Revolvers % % 8 3.8% % % 38

41 Table 6 Regressions of nominal recovery rates: Baseline regressions This table presents the regressions of nominal recovery rates on resolution time, discount rate, additional debt and firm characteristics, and macroeconomic conditions. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and Variables are defined in Table 1. The dependent variable is the nominal recovery rate. The core variables of interest are resolution time and discount rate. The coefficient of resolution time measures the nominal marginal return on resolution time. The coefficient of discount rate measures the effect of changes in discount rate on nominal recovery rate estimations. This table consists of 5 regressions. Regression (1) includes only debt-level variables as explanatory variables. Regression (2) adds firm-level variables, and regression (3) adds macroeconomic variables. Regression (4) adds time fixed effects but excludes macroeconomic variables. Regression (5) includes both time fixed effects and macroeconomic variables. *, ** and *** indicate statistical significance at the 10%, 5% and 1% level, respectively. (1) (2) (3) (4) (5) Resolution time (year) *** *** *** *** *** [0.0054] [0.0066] [0.0073] [0.0073] [0.0073] Discount rate *** [0.0015] [0.0021] [0.0021] [0.0020] [0.0021] Distressed exchange *** *** *** *** *** [0.0152] [0.0218] [0.0211] Seniority index *** *** *** [0.0004] [0.0004] Aggregate default rate *** [0.0131] Industry default rate *** [0.0029] T-bill rate *** [0.0037] Senior secured bonds *** *** [0.0414] [0.0502] [0.0490] Subordinated bonds *** *** *** [0.0164] [0.0223] [0.0218] Term loans * [0.0386] [0.0469] [0.0460] Revolvers [0.0382] [0.0449] [0.0437] Collateral: liquid assets or guarantees *** *** *** [0.0392] [0.0487] [0.0481] Collateral: core assets *** *** *** [0.0373] [0.0463] [0.0452] Collateral: other assets ** *** *** [0.0394] [0.0492] [0.0480] Maturity longer than 5 years *** *** *** [0.0114] [0.0157] [0.0154] Distance-to-default *** *** [0.0000] [0.0000] Leverage *** *** [0.0004] [0.0226] *** [0.0004] *** [0.0458] *** [0.0219] [0.0421] [0.0405] *** [0.0474] *** [0.0422] *** [0.0447] *** [0.0153] *** [0.0000] [0.0004] [0.0227] *** [0.0004] *** [0.0795] *** [0.0031] *** [0.0415] *** [0.0442] *** [0.0220] [0.0404] [0.0389] *** [0.0466] *** [0.0411] *** [0.0434] *** [0.0149] *** [0.0000] [0.0004] 39

42 Earnings-to-assets ratio [0.0008] [0.0008] [0.0008] [0.0008] Profitability *** *** *** *** Tangibility Current ratio *** [0.0001] *** [0.0001] *** [0.0001] *** [0.0001] Cash ratio *** [0.0013] *** [0.0013] ** [0.0013] ** [0.0013] Bonds debt ratio Coverage [0.0000] [0.0000] ** [0.0000] [0.0000] Tobin s Q * [0.0002] ** [0.0002] *** [0.0001] *** [0.0001] Firm size [0.0047] [0.0049] [0.0060] [0.0061] Utility dummy *** [0.0253] *** [0.0269] *** [0.0409] *** [0.0397] Constant *** [0.0269] *** [0.0642] *** [0.0677] *** [0.0953] *** [0.2847] Time fixed effects No No No Yes Yes N Adjusted R Log likelihood

43 Table 7 Regressions of nominal recovery rate: Nonlinear effects of resolution time The regressions in this table estimate the nonlinear effects of resolution time on nominal recovery rate. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and The resolution cut-off year is 2014 in all regressions. Variables are defined in Table 1. The dependent variable is the nominal recovery rate. The core variables of interest are resolution time and discount rate. The coefficient of resolution time measures the nominal marginal return on resolution time. The coefficient of discount rate measures the effect of changes in discount rate on nominal recovery rate estimations. This table consists of two regressions. All regressions include time fixed effects, debt-level, firm-level, and macroeconomic variables. In addition, each regression uses different transformations of resolution time to capture the nonlinearity. Specifically, regression (1) uses log of resolution time in years. Regression (2) use indicators that divide the resolution time into six categories (i.e., less than one year, one to two years, two to three years, three to four years, four to give years, and above five years). *, ** and *** indicate statistical significance at the 10%, 5% and 1% level, respectively. (1) (2) Log(resolution time) *** [0.0093] Resolution time between 1 and 2 years ** [0.0178] Resolution time between 2 and 3 years *** [0.0252] Resolution time between 3 and 4 years *** [0.0397] Resolution time between 4 and 5 years *** [0.0443] Resolution time longer than 5 years *** [0.0581] Discount rate [0.0021] Distressed exchange *** [0.0308] Seniority index *** [0.0004] Aggregate default rate *** [0.0803] Industry default rate *** [0.0031] T-bill rate *** [0.0421] Senior secured bonds *** [0.0451] Subordinated bonds *** [0.0220] Term loans [0.0411] Revolvers [0.0399] [0.0021] *** [0.0231] *** [0.0004] *** [0.0797] *** [0.0033] *** [0.0422] *** [0.0437] *** [0.0220] [0.0401] [0.0384]

44 Collateral: liquid assets or guarantees *** [0.0476] Collateral: core assets *** [0.0423] Collateral: other assets *** [0.0443] Maturity longer than 5 years *** [0.0150] Distance-to-default *** [0.0000] Leverage [0.0004] Earnings-to-assets ratio [0.0008] Profitability *** Tangibility Current ratio *** [0.0001] Cash ratio * [0.0013] Bonds debt ratio Coverage [0.0001] Tobin s Q *** [0.0001] Firm size [0.0061] Utility dummy *** [0.0405] Constant *** *** [0.0461] *** [0.0408] *** [0.0431] *** [0.0149] *** [0.0000] [0.0004] [0.0008] *** *** [0.0001] ** [0.0013] [0.0000] *** [0.0001] [0.0060] *** [0.0396] *** [0.2857] [0.2883] Time fixed effects Yes Yes N Adjusted R Log likelihood

45 Table 8 Regressions of discounted recovery rate: Baseline regressions This table presents the regressions of discounted recovery rates on resolution time, discount rate, additional debt and firm characteristics, and macroeconomic conditions. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and Variables are defined in Table 1. The dependent variable is the discounted recovery rate. The core variables of interest are resolution time and discount rate. The coefficient of resolution time measures the discounted marginal return on resolution time. The coefficient of discount rate measures the effect of changes in discount rate on recovery rate estimations. This table consists of 5 regressions. Regression (1) includes only debt-level variables as explanatory variables. Regression (2) adds firm-level variables, and regression (3) adds macroeconomic variables. Regression (4) adds time fixed effects but exclude macroeconomic variables. Regression (5) include both time fixed effects and macroeconomic variables. *, ** and *** indicate statistical significance at the 10%, 5% and 1% level, respectively. (1) (2) (3) (4) (5) Resolution time (year) ** * *** ** [0.0039] [0.0047] [0.0053] [0.0055] [0.0055] Discount rate *** *** *** *** *** [0.0013] [0.0018] [0.0017] [0.0017] [0.0017] Distressed exchange *** *** *** *** *** [0.0131] [0.0187] [0.0181] Seniority index *** *** *** [0.0004] [0.0004] Aggregate default rate *** [0.0109] Industry default rate *** [0.0024] T-bill rate *** [0.0030] Senior secured bonds *** *** [0.0338] [0.0415] [0.0403] Subordinated bonds *** *** *** [0.0133] [0.0180] [0.0176] Term loans ** [0.0313] [0.0390] [0.0378] Revolvers [0.0312] [0.0374] [0.0360] Collateral: liquid assets or guarantees *** *** *** [0.0320] [0.0400] [0.0391] Collateral: core assets *** *** *** [0.0305] [0.0383] [0.0370] Collateral: other assets ** *** *** [0.0324] [0.0409] [0.0395] Maturity longer than 5 years *** *** *** [0.0096] [0.0132] [0.0129] Distance-to-default *** *** [0.0000] [0.0000] Leverage *** *** [0.0196] *** [0.0004] *** [0.0380] *** [0.0176] [0.0350] [0.0334] *** [0.0388] *** [0.0349] *** [0.0373] *** [0.0129] *** [0.0000] [0.0197] *** [0.0004] *** [0.0676] *** [0.0026] *** [0.0346] *** [0.0369] *** [0.0177] [0.0338] [0.0323] *** [0.0382] *** [0.0341] *** [0.0363] *** [0.0125] *** [0.0000]

46 Earnings-to-assets ratio [0.0007] [0.0007] [0.0007] [0.0007] Profitability *** [0.0002] *** [0.0002] *** *** Tangibility [0.0002] Current ratio *** [0.0001] *** [0.0001] *** [0.0001] *** [0.0001] Cash ratio *** [0.0011] *** [0.0011] [0.0011] [0.0011] Bonds debt ratio Coverage [0.0000] [0.0000] ** [0.0000] [0.0000] Tobin s Q * [0.0001] ** [0.0001] *** [0.0001] *** [0.0001] Firm size [0.0039] [0.0041] [0.0050] [0.0051] Utility dummy *** [0.0200] *** [0.0214] *** [0.0335] *** [0.0327] Constant *** [0.0226] *** [0.0544] *** [0.0574] *** [0.0791] *** [0.2393] Time fixed effects No No No Yes Yes N Adjusted R Log likelihood

47 Table 9 Regressions of discounted recovery rate: Nonlinear effects of resolution time The regressions in this table estimate the nonlinear effects of resolution time on discounted recovery rate. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and The resolution cut-off year is 2014 in all regressions. Variables are defined in Table 1. The dependent variable is the discounted recovery rate. The core variables of interest are resolution time and discount rate. The coefficient of resolution time measures the discounted marginal return on resolution time. The coefficient of discount rate measures the effect of changes in discount rate on recovery rate estimations. This table consists of 3 regressions. All regressions include time fixed effects, debt-level, firm-level, and macroeconomic variables. In addition, each regression uses a different transformation of resolution time to capture the nonlinearity. Specifically, regression (1) uses log of resolution time in years. Regression (2) uses Resolution time longer than 1 year, a dummy variable that equals 1 if the resolution time is longer than one year. Regression (3) use indicators that divide the resolution time into six categories (i.e., less than one year, one to two years, two to three years, three to four years, four to give years, and above five years). *, ** and *** indicate statistical significance at the 10%, 5% and 1% level, respectively. (1) (2) Log(resolution time) [0.0074] Resolution time between 1 and 2 years [0.0152] Resolution time between 2 and 3 years [0.0206] Resolution time between 3 and 4 years [0.0310] Resolution time between 4 and 5 years *** [0.0322] Resolution time longer than 5 years [0.0417] Discount rate *** [0.0017] *** [0.0017] Distressed exchange *** [0.0258] *** [0.0203] Seniority index *** [0.0004] *** [0.0004] Aggregate default rate *** [0.0673] *** [0.0681] Industry default rate *** [0.0026] *** [0.0028] T-bill rate *** [0.0347] *** [0.0354] Senior secured bonds *** [0.0371] *** [0.0366] Subordinated bonds *** [0.0177] *** [0.0177] Term loans [0.0339] [0.0336] Revolvers

48 [0.0326] [0.0320] Collateral: liquid assets or guarantees *** [0.0384] *** [0.0381] Collateral: core assets *** [0.0344] *** [0.0341] Collateral: other assets *** [0.0365] *** [0.0362] Maturity longer than 5 years *** [0.0125] *** [0.0126] Distance-to-default *** [0.0000] *** [0.0000] Leverage Earnings-to-assets ratio [0.0007] [0.0007] Profitability *** *** Tangibility Current ratio *** [0.0001] *** [0.0001] Cash ratio [0.0011] [0.0011] Bonds debt ratio Coverage [0.0000] [0.0000] Tobin s Q *** [0.0001] *** [0.0001] Firm size [0.0051] [0.0051] Utility dummy *** [0.0330] *** [0.0329] Constant *** [0.2394] *** [0.2412] Time fixed effects Yes Yes N Adjusted R Log likelihood

49 Table 10 Regressions of discounted recovery rate: Subsample of different debt types This table presents the regressions of discounted recovery rates on subsamples of different debt types. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and Variables are defined in Table 1. The dependent variable is the discounted recovery rate. The core variables of interest are resolution time and discount rate. The coefficient of resolution time measures the discounted marginal return on resolution time. The coefficient of discount rate measures the effect of changes in discount rate on recovery rate estimations. The table reports only the coefficients of interest and omits an extensive set of control variables. This table consists of 5 regressions. Regressions (1) through (5) are based on the subsamples of senior unsecured bonds, senior secured bonds, subordinated bonds, term loans, and revolvers, respectively. *, ** and *** indicate statistical significance at the 10%, 5% and 1% level, respectively. (1) (2) (3) (4) (5) Subsample Senior Senior secured Subordinated Term Revolvers unsecured bonds bonds bonds loans Resolution time (year) *** [0.0178] [0.0773] [0.0223] [0.0174] [0.0138] Discount rate *** [0.0033] ** [0.0053] [0.0048] [0.0070] [0.0065] Distressed exchange *** [0.0574] [0.1438] *** [0.0873] *** [0.0611] *** [0.0496] Seniority index *** [0.0010] ** [0.0019] *** [0.0010] *** [0.0014] *** [0.0013] Collateral: liquid assets or guarantees ** [0.1266] [0.1339] *** [0.0634] Collateral: core assets [0.0858] [0.0988] [0.0585] Collateral: other assets [0.0994] [0.0710] Time fixed effects Yes Yes Yes Yes Yes N 1, Adjusted R Log likelihood

50 Table 11 Regressions of discounted recovery rate: Robustness tests on the early resolution bias The regressions in this table test the early resolution bias by running regressions on different subsamples with different resolution cut-off years. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and Variables are defined in Table 1. The dependent variable is the discounted recovery rate. The table reports only the coefficients of interest and omits an extensive set of control variables. *, ** and *** indicate statistical significance at the 10%, 5% and 1% level, respectively. Panel A: Regressions (1) to (4) (1) (2) (3) (4) Sample period Resolution cut-off year Resolution time (year) [0.0052] * [0.0053] [0.0061] [0.0092] Discount rate *** [0.0017] *** [0.0018] *** [0.0019] [0.0028] Aggregate default rate *** [0.0109] *** [0.0114] *** [0.0133] *** [0.0340] Industry default rate *** [0.0024] *** [0.0024] *** [0.0026] * [0.0121] T-bill rate *** [0.0030] *** [0.0032] *** [0.0034] *** [0.0061] Time fixed effects No No No No N 3,006 2,815 2, Adjusted R Log likelihood Panel B: Regressions (5) through (9) (5) (6) (7) (8) (9) Sample period Resolution cut-off year Resolution time (year) *** [0.0068] *** [0.0068] [0.0093] *** [0.0236] [0.1106] Discount rate *** [0.0023] *** [0.0023] *** [0.0027] *** [0.0044] *** [0.0056] Aggregate default rate *** [0.0123] *** [0.0132] *** [0.0164] [0.0323] * [0.0706] Industry default rate *** [0.0025] *** [0.0025] *** [0.0029] [0.0150] ** [0.0288] T-bill rate [0.0053] [0.0057] [0.0068] *** [0.0154] *** [0.0196] Time fixed effects No No No No No N 2,092 1,901 1, Adjusted R Log likelihood

51 Table 12 Regressions of recovery rate: Robustness tests on discount rate effects The regressions in this table test the robustness of the effects of discount rate by including nominal recovery rate as a control variable. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and The resolution cut-off year is 2014 in all regressions. Variables are defined in Table 1. The dependent variable is the recovery rate. The core variables of interest are nominal recovery rate and discount rate. The coefficient of discount rate measures the effect of changes in discount rate on recovery rate estimations. This table consists of 2 regressions. Regression (1) includes discount rate as the only explanatory variable. Regression (2) adds nominal recovery rate. (1) (2) Discount rate *** [0.0011] *** Nominal recovery rate *** [0.0037] Time fixed effects No No N 4,958 4,958 Adjusted R Log likelihood

52 Table 13 Regressions of recovery rate: Robustness tests using different recovery measures The OLS regressions in this table use different measures of recovery that are based on the settlement, trading price, and liquidity methods. The sample of defaulted corporate debts is from the Moody s DRD database, over the period between 1987 and Variables are defined in Table 1. The dependent variable is the discounted recovery rate. The core variables of interest are resolution time and discount rate. The coefficient of resolution time measures the discounted marginal return on resolution time. The coefficient of discount rate measures the effect of changes in discount rate on recovery rate estimations. The table reports only the coefficients of interest and omits an extensive set of control variables. This table consists of 3 regressions. Regressions (1) through (3) are based on the settlement, trading price, and liquidity methods, respectively. *, ** and *** indicate statistical significance at the 10%, 5% and 1% level, respectively. (1) (2) (3) Settlement method Trading price method Liquidity method Resolution time (year) [0.0064] *** [0.0060] *** [0.0169] Discount rate *** [0.0019] *** [0.0018] *** [0.0040] Distressed exchange *** [0.0211] *** [0.0255] *** [0.0704] Seniority index *** [0.0004] *** [0.0005] ** [0.0010] Senior secured bonds *** [0.0447] [0.0431] *** [0.0753] Subordinated bonds *** [0.0196] *** [0.0203] *** [0.0392] Term loans [0.0415] [0.0393] * [0.0654] Revolvers [0.0388] [0.0372] * [0.0660] Collateral: liquid assets or guarantees *** [0.0433] ** [0.0597] *** [0.0807] Collateral: core assets *** [0.0409] *** [0.0397] *** [0.0757] Collateral: other assets ** [0.0436] ** [0.0416] *** [0.0778] Time fixed effects Yes Yes Yes N Adjusted R Log likelihood

53 Fig. 1. Average recovery rates over time ( ). This figure plots average recovery and nominal recovery rates over time. The shaded bars indicate recession periods. 51

54 Fig. 2. Recovery rate and real GDP growth ( ). This figure plots the average recovery rate along with the real GDP growth over time. 52

55 Fig. 3. Average recovery rate and aggregate default rate ( ). This figure plots the average recovery rate along with the aggregate default rate over time. 53

56 Fig. 4. Recovery rate and market return ( ). This figure plots the average recovery rate along with the market return over time. 54

57 Fig. 5. Resolution time over time ( ). This figure plots the average resolution time in months along with the 25th and 75th percentiles over time. 55