# The Determinants of Market-Implied Recovery Rates

## Abstract

**:**

## 1. Introduction

## 2. Related Literature

#### 2.1. Factors Driving Historical Recovery Rates

- Debt contract-specific variables: Coupon rate, seniority, collateral.
- Firm-specific variables: Size, asset tangibility, market-to-book ratio, liquidity ratio, interest coverage ratio, profit margin, leverage, firm age.
- Industry-specific variables: industry dummy, utilities dummy, industry sales growth, industry stock return.
- Macroeconomic variables: Bond default rate, GDP growth, S&P500 index return, S&P500 index volatility, unemployment rate, Fama-French factors, economic uncertainty.

#### 2.2. Inferring Recovery Rates from Market Data

## 3. Methodology

#### 3.1. The Recovery Model

_{t}) and a traded term structure of CDS contracts (the j-maturity CDS premium process is denoted by π

_{t}(j)). Assuming that the absolute priority rule is enforced, the equity-holders obtain zero recovery upon default. By contrast, the CDS offers compensation for the loss given default on the underlying reference bond. Consequently, the (risk-neutral) default probability of the issuing firm and the recovery rate on the reference bond affects the CDS premium. Therefore, it is possible to infer market-implied recovery rates from the joint observation of S

_{t}and the collection of π

_{t}(j), since equity and CDS contracts are driven by the same default process, but exhibit distinct recovery rates.

_{i}

^{k}denotes the stock price, where superscript k indexes time (from 0 to N periods) and subscript i indexes the level of the node at time k. In the kth period, i takes value 0 at the top and value k at the bottom.

_{i}

^{k}is the one-period probability of jumping to default (default intensity), and q

_{i}

^{k}is the risk-neutral probability of an up move if the firm survives.

_{i}

^{k}is given by

^{k}is the one-period compound factor.

_{i}

^{k}and the level of the stock price

_{i}

^{k}on the defaultable reference bond

_{u}, u = 1, …, j. For clarity of exposure, λ

^{k}≡ λ

^{k}(T

_{k}

_{−1}, T

_{k}) denotes the probability of jumping to default between settlement dates T

_{k}

_{−1}and T

_{k}. Likewise, φ

^{k}≡ φ

^{k}(T

_{k}

_{−1}, T

_{k}) is the recovery rate prevailing between the settlement dates T

_{k}

_{−1}and T

_{k}. The λ

^{k}and φ

^{k}are obtained from aggregation across all states of the binomial tree.1 In this framework, the no-arbitrage premium π(j) equalizes the two legs of the CDS2

_{obs}(j) to extract the term structure of the market-implied recovery rates (φ

^{k}). That is, for J available CDS maturities, I solve for

#### 3.2. Data and Model Calibration

#### 3.3. Comparison with Historical Recoveries

- The actual recovery rates from CDS auctions are slightly lower than actual recovery rates on the underlying bonds. Chernov et al. (2013) and Gupta and Sundaram (2015) find a downward bias of about 15% of the bond price (which represents a smaller fraction of par) and attribute it to a liquidity premium.
- Market-implied recovery rates from CDS might contain a premium for the CDS writer’s counterparty risk. That being said, Arora et al. (2012) find that the negative relation between CDS spreads and CDS writer credit quality is economically very small because of risk mitigation techniques, such as overcollateralization and bilateral netting.
- Historical recovery rates (as reported by Moody’s for instance) are, by definition, calculated on a sample of defaulting firms. The market-implied recoveries are extracted from a sample of firms underlying a CDS contract. The difference in the two populations of firms could generate a bias in the comparison of recoveries.6
- Most importantly, market-implied recoveries are risk-neutral expectations of random recovery rates. By contrast, historical recoveries are calculated once the default event has materialized. In some studies, the historical recovery rates are computed at the resolution of financial distress and they can be viewed as the realizations of random recovery. In other studies, the historical recovery rates are computed using 30-day post default bond prices. Such historical recovery rates are still expectations about ultimate recovery, but they are conditionally calculated on default having occurred.

## 4. Factor Analysis

#### 4.1. Descriptive Statistics

#### 4.2. Linear Regression Results

^{2}typically ranging between 40% and 60%. Table 7 indicates that their explanatory power is much lower when applied to market-implied recovery rates. Macroeconomic variables keep playing an important role, which confirms the pro-cyclical behavior of recovery rates. GDP growth rate stands as the macroeconomic variable that passes the multicollinearity test while keeping a high significance level. Among the firm specific variables, only leverage significantly contributes across all specifications. A possible interpretation is that the market mostly relies on a long-term financial analysis to estimate forward-looking recovery rates. Thus, financial indicators, such as liquidity or profit margin, which may affect immediate recovery, lose their explanatory power when it comes to assessing the consequences of default in a distant future. By contrast, leverage is a financial decision that impacts investment and operating policies in the long run. Similar to the findings regarding historical recovery rates, the relation between firm size and market-implied recovery rates is ambiguous.

#### 4.3. Tobit Regression Results

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1 | The aggregation is performed through a recursive algorithm. See Das and Hanouna (2009) for details. |

2 | The denominator is the expected present value of all the premiums to be paid. The numerator is the expected present value of the compensation for the loss given default. |

3 | All CDS are U.S. dollar denominated and senior unsecured single-name contracts. |

4 | Before September 2010, the data was provided by CMA via Datastream. After that date, the data is provided by Thomson Reuters. The data is combined from the two providers by using the function “SPLC” of Datastream. |

5 | For instance, empirical studies on U.S. bankruptcy filings (Bris et al. 2006; Denis and Rodgers 2007) report that firms in financial distress spend between two and three years on average under bankruptcy. |

6 | When regressing historical recovery rates, Jankowitsch et al. (2014) find a positive and significant coefficient for CDS availability. |

7 | Altman and Kalotay (2014) propose a mixture of normals to model the bimodal distribution of historical recovery rates. Siao et al. (2016) opt for a quantile-based regression. |

8 | Since CDS in the sample are written on the same type of bonds (senior unsecured), the factor analysis precludes those variables that are specific to the debt contract such as coupon, seniority, or collateral. |

**Figure 1.**Histograms for the level and the slope of market-implied recovery rates. Panel (

**a**) shows the distribution of the level (10-year recovery rate). Panel (

**b**) shows the distribution of the slope (10-year rate minus five-year rate). The sample contains 16,062 quarterly observations and it spans the January 2005–June 2014 period.

**Figure 2.**Time series of market-implied recovery rate level and slope. The level (slope) is shown in the top (bottom) curves. The solid line represents the median, the two dashed lines represent the first and third quartiles.

**Figure 3.**Distribution of historical recovery rates. Data is obtained from Moody’s credit reports and spans the 2005–2017 period.

**Table 1.**Review of the determinants of historical recovery rates. For each identified determinant, the table lists some studies documenting a significant relation with historical recovery rates. The next column indicates whether that relation is positive or negative. The method refers to linear regression (LR), probit regression (PR), logistic quantile regression (LQ), support vector regression (SVR), or regression trees (RT).

Determinant | Examples of Studies | Effect | Method |
---|---|---|---|

Panel A: Debt contract-specific variables | |||

Coupon rate | Chava et al. (2011) | + | PR |

Collateral | Frye (2000) | + | LR |

Qi and Zhao (2011) | + | RT | |

Seniority | Varma and Cantor (2005) | + | LR |

Acharya et al. (2007) | + | LR | |

Siao et al. (2016) | + | LQ | |

Rating | Jankowitsch et al. (2014) | + | LR |

Panel B: Firm-specific variables | |||

Size | Acharya et al. (2007); Chava et al. (2011) | +/− | LR, PR |

Market-to-book | Chava et al. (2011) | − | PR |

Asset tangibility | Varma and Cantor (2005) | + | LR |

Chava et al. (2011) | + | PR | |

Liquidity | Varma and Cantor (2005) | + | LR |

Profit margin | Acharya et al. (2007) | + | LR |

Leverage | Varma and Cantor (2005) | − | LR |

Default event severity | Franks and Torous (1994); Altman and Karlin (2009) | − | LR |

Panel C: Industry-specific variables | |||

Industry dummies | Acharya et al. (2007); Chava et al. (2011) | +/− | LR, PR |

Industry sales growth dummy | Acharya et al. (2007) | + | PR |

Industry stock return dummy | Acharya et al. (2007) | + | PR |

Industry default rate | Jankowitsch et al. (2014) | − | LR |

Panel D: Macroeconomic variables | |||

Default rate | Frye (2000); Altman et al. (2005) | − | LR |

GDP growth | Altman et al. (2005); Chava et al. (2011) | + | LR, PR |

Fed fund rate | Jankowitsch et al. (2014) | + | LR |

Stock index return | Nazemi et al. (2018) | + | SVR, RT |

Corporate bond spread | Nazemi et al. (2018) | − | SVR, RT |

Unemployment rate | Nazemi et al. (2018) | − | SVR, RT |

**Table 2.**Fitting the credit default swap (CDS) term structure. The table reports the calibration results on monthly term structures of CDS spreads. The root mean squared errors (RMSE) and the relative root mean squared errors (RRMSE) are expressed in basis points and in percentage points, respectively. The initial sample contains 52,021 firm-month observations. The restricted sample is obtained by excluding the 5% of observations with the worst fit.

Statistic | Initial Sample | Restricted Sample | ||
---|---|---|---|---|

RMSE | RRMSE | RMSE | RRMSE | |

Mean | 23 | 10.23 | 9 | 7.19 |

Median | 3 | 4.76 | 2 | 4.44 |

Standard deviation | 222 | 17.12 | 17 | 7.58 |

Maximum | 9389 | 440.08 | 93 | 39.34 |

95% percentile | 93 | 39.34 | 51 | 24.59 |

Variable | Description |
---|---|

Size | Logarithm of total assets. |

Asset tangibility | Property, plant and equipment/total assets. |

Liquidity | (Cash plus short-term investments)/total assets. |

Profit margin | EBITDA/sales. |

Leverage | Long-term debt/total assets. |

Rating | Dummy = 1 if issuer is investment grade. |

Industry stress | Dummy = 1 if quarterly industry index return is below −30%. |

GDP growth | Seasonally adjusted, quarterly growth rate of U.S. GDP. |

Unemployment | Seasonally adjusted, quarterly U.S. unemployment rate. |

Stock index | S&P500 index adjusted, quarterly return. |

Default rate | Quarterly default rate reported by Moody’s and S&P. |

NAICS | Industry | GICS Stock Index | Ticker |
---|---|---|---|

11 | Agriculture, forestry and fishing | Agriculture | S5AGRI |

21 | Minerals and gases | Energy | SPN |

22 | Utilities | Utilities | S5UTIL |

23 | Construction | Construction and engineering | S5CSTEX |

31 | Food manufacturing | Food and beverage | SPSIFBUP |

32 | Wood and concrete manufacturing | Materials | S5MATR |

33 | Metal manufacturing | Metal and mining | SPSIMM |

42 | Wholesale trade | Retail | SPSIRE |

44 | Retail trade | Retail | SPSIRE |

45 | Sporting goods and book stores | Retail | SPSIRE |

48 | Transportation and warehousing | Transportation | SPSITN |

49 | Postal service | Transportation | SPSITN |

51 | Information and newspaper | Media and entertainment | S5MEDA |

52 | Finance and insurance | Financials | SPF |

53 | Real estate, rental and leasing | Real estate | S5RLST |

54 | Professional and technical services | Commercial and professional services | S5COMS |

56 | Administrative and support services | Consumer services | S5HOTR |

62 | Health care | Health care | S5HLTH |

72 | Food services | Restaurants | S5REST |

81 | Other non-public services | Consumer services | S5HOTR |

Variable | Mean | Std Dev | Min | Q1 | Q2 | Q3 | Max |
---|---|---|---|---|---|---|---|

Size | 9.5283 | 1.3598 | 4.7791 | 8.5894 | 9.3755 | 10.2807 | 14.8302 |

Asset tangibility | 0.3120 | 0.2461 | 0.0000 | 0.1009 | 0.2534 | 0.5050 | 0.9530 |

Liquidity | 0.1619 | 0.2233 | 0.0000 | 0.0336 | 0.0877 | 0.1975 | 3.4089 |

Profit margin | 0.2015 | 0.3369 | −7.7214 | 0.1043 | 0.1735 | 0.2771 | 24.1566 |

Leverage | 0.2767 | 0.1973 | 0.0000 | 0.1445 | 0.2428 | 0.3714 | 2.3640 |

GDP growth | 0.0177 | 0.0267 | −0.0840 | 0.0050 | 0.0225 | 0.0360 | 0.0540 |

Unemployment | 0.0688 | 0.0187 | 0.0440 | 0.0500 | 0.0655 | 0.0880 | 0.1000 |

Stock index | 0.0153 | 0.0688 | −0.2356 | −0.0207 | 0.0335 | 0.0605 | 0.1314 |

Default rate | 0.0042 | 0.0039 | 0.0008 | 0.0020 | 0.0022 | 0.0047 | 0.0174 |

Industry | Count | Industry | Count |
---|---|---|---|

Agriculture | 1 (0.2%) | Professional services | 149 (30.0%) |

Minerals and gases | 80 (16.1%) | Health care | 9 (1.8%) |

Manufacturing | 186 (37.4%) | Food services | 9 (1.8%) |

Transportation and trade | 62 (12.5%) | Other non-public services | 1 (0.2%) |

**Table 7.**Regression results for the level of market-implied recovery rates. Robust standard errors are reported in parentheses. Variables preceded by “L_” are lagged by one quarter. Statistical significance at the 10%, 5%, and 1% level is indicated by superscript *, ** and ***, respectively.

Variable | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Intercept | 0.5762 *** | 0.5762 *** | 0.4369 *** | 0.3977 *** | 0.3850 *** |

(−0.0366) | (0.1025) | (0.1021) | (0.0209) | (0.0656) | |

Size | −0.0137 *** | −0.0137 | −0.0125 | - | 0.0077 ** |

(0.0021) | (0.0104) | (0.0104) | - | (0.0030) | |

Asset tangibility | 0.0286 | 0.0286 | 0.0254 | 0.0324 | 0.0210 |

(0.0589) | (0.0486) | (0.0486) | (0.0491) | (0.0174) | |

Liquidity | 0.0214 | 0.0214 | 0.0181 | 0.0258 | 0.0201 ** |

(0.0142) | (0.0186) | (0.0186) | (0.0189) | (0.0103) | |

Profit margin | 0.0032 | 0.0032 | 0.0031 | 0.0035 | 0.0037 |

(0.0070) | (0.0065) | (0.0067) | (0.0068) | (0.0034) | |

Leverage | −0.1214 ** | −0.1214 *** | −0.1220 *** | −0.1223 *** | −0.1202 *** |

(0.0449) | (0.0326) | (0.0326) | (0.0328) | (0.0140) | |

Rating | 0.0091 | 0.0091 | 0.0098 | 0.0085 | 0.0220 *** |

(0.0049) | (0.0067) | (0.0073) | (0.0074) | (0.0043) | |

Industry stress | 0.0046 | 0.0046 | −0.0068 | −0.0043 | 0.0039 |

(0.0058) | (0.0067) | (0.0064) | (0.0063) | (0.0062) | |

GDP growth | 0.1339 * | 0.1339 *** | - | 0.1497 *** | 0.1362 ** |

(0.0595) | (0.0485) | - | (0.0483) | (0.0621) | |

Unemployment | −0.8287 | −0.8287 *** | - | - | −0.7864 *** |

(0.6827) | (0.2794) | - | - | (0.2827) | |

Stock index | −0.0353 | −0.0353 * | - | −0.0304 * | −0.0356 |

(0.0208) | (0.0182) | - | (0.0184) | (0.0249) | |

Default rate | −3.5229 *** | −3.5229 *** | - | - | −3.4103 *** |

(0.6149) | (0.6956) | - | - | (0.6752) | |

L_ GDP growth | - | - | 0.1401 *** | - | - |

- | - | (0.0470) | - | - | |

L_ Unemployment | - | - | 1.2948 *** | - | - |

- | - | (0.2692) | - | - | |

L_ Stock index | - | - | −0.0183 | - | - |

- | - | (0.0161) | - | - | |

L_ Default rate | - | - | 3.7581 *** | - | - |

- | - | (0.4939) | - | - | |

Industry fixed effects | Yes | No | No | No | Yes |

Firm fixed effects | No | Yes | Yes | Yes | No |

R^{2} within | 0.1182 | 0.1182 | 0.1198 | 0.1142 | - |

R^{2} between | 0.0458 | 0.0458 | 0.0598 | 0.1567 | - |

R^{2} overall | 0.0928 | 0.0928 | 0.1013 | 0.1447 | - |

**Table 8.**Regression results for the slope of market-implied recovery rates. Robust standard errors are reported in parentheses. Variables preceded by “L_” are lagged by one quarter. Statistical significance at the 10%, 5% and 1% level is indicated by superscript *, ** and ***, respectively.

Variable | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Intercept | −0.1164 ** | −0.1164 ** | −0.0740 ** | −0.1980 *** | −0.1605 *** |

(0.0435) | (0.0585) | (0.0335) | (0.0116) | (0.0340) | |

Size | −0.0173 *** | −0.0173 *** | −0.0077 *** | −0.0077 *** | |

(0.0044) | (0.0059) | (0.0015) | (0.0016) | ||

Asset tangibility | 0.0721 ** | 0.0721 *** | 0.0404 *** | 0.1149 *** | 0.0392 *** |

(0.0240) | (0.0223) | (0.0089) | (0.0260) | (0.0090) | |

Liquidity | 0.0031 | 0.0031 | 0.0053 | 0.0140 | 0.0044 |

(0.0114) | (0.0129) | (0.0053) | (0.0124) | (0.0052) | |

Profit margin | −0.0111 * | −0.0111 ** | −0.0113 *** | −0.0122 ** | −0.0111 *** |

(0.0050) | (0.0049) | (0.0017) | (0.0056) | (0.0017) | |

Leverage | 0.0624 *** | 0.0624 *** | 0.0614 *** | 0.0972 *** | 0.0602 *** |

(0.0146) | (0.0203) | (0.0072) | (0.0208) | (0.0072) | |

Rating | −0.0181 *** | −0.0181 *** | −0.0198 *** | −0.0219 *** | −0.0194 *** |

(0.0040) | (0.0042) | (0.0022) | (0.0047) | (0.0022) | |

Industry stress | 0.0085 | 0.0085 ** | 0.0200 *** | 0.0246 *** | 0.0087 *** |

(0.0064) | (0.0038) | (0.0030) | 0.0036) | (0.0031) | |

GDP growth | 0.0143 | 0.0143 | - | −0.2603 *** | 0.0140 |

(0.0287) | (0.0264) | - | (0.0301) | (0.0316) | |

Unemployment | 1.0304 *** | 1.0304 *** | - | - | 1.0447 |

(0.2230) | (0.1548) | - | - | (0.1438) | |

Stock index | −0.0445 *** | −0.0445 *** | - | −0.0459 *** | −0.0444 *** |

(0.0109) | (0.0090) | - | (0.0113) | (0.0127) | |

Default rate | 2.0635 *** | 2.0635 *** | - | - | 2.1315 *** |

(0.4733) | (0.3694) | - | - | (0.3434) | |

L_ GDP growth | - | - | −0.1958 *** | - | - |

- | - | (0.0330) | - | - | |

L_ Unemployment | - | - | −0.4481 *** | - | - |

- | - | (0.1436) | - | - | |

L_ Stock index | - | - | 0.0327 *** | - | - |

- | - | (0.0127) | - | - | |

L_ Default rate | - | - | 0.8050 ** | - | - |

- | - | (0.3444) | - | - | |

Industry fixed effects | Yes | No | Yes | No | Yes |

Firm fixed effects | No | Yes | No | Yes | No |

R^{2} within | 0.2142 | 0.2142 | 0.2048 | 0.1543 | - |

R^{2} between | 0.0722 | 0.0722 | 0.1274 | 0.0601 | - |

R^{2} overall | 0.1377 | 0.1377 | 0.1848 | 0.0984 | - |

**Table 9.**Tobit regression results for the level of market-implied recovery rates. Robust standard errors are reported in parentheses. Variables preceded by “L_” are lagged by one quarter. Statistical significance at the 10%, 5% and 1% level is indicated by superscript *, ** and ***, respectively.

Variable | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Intercept | 0.3853 *** | 0.3775 *** | 0.2449 *** | 0.4329 *** |

(0.0710) | (0.0350) | (0.0709) | (0.0589) | |

Size | 0.0086 *** | 0.0077 ** | 0.0091 *** | - |

(0.0032) | (0.0032) | (0.0033) | - | |

Asset tangibility | 0.0129 | 0.0055 | 0.0105 | 0.0089 |

(0.0187) | (0.0166) | (0.0186) | (0.0189) | |

Liquidity | 0.0212 ** | 0.0206 * | 0.0182 * | 0.0188 * |

(0.0108) | (0.0109) | (0.0108) | (0.0108) | |

Profit margin | 0.0050 | 0.0049 | 0.0049 | 0.0058 |

(0.0036) | (0.0036) | (0.0036) | (0.0036) | |

Leverage | −0.1348 *** | −0.1386 *** | −0.1350 *** | −0.1406 *** |

(0.0150) | (0.0150) | (0.0150) | (0.0150) | |

Rating | 0.0221 *** | 0.0228 *** | 0.0227 *** | 0.0241 *** |

(0.0046) | (0.0046) | (0.0046) | (0.0045) | |

Industry stress | 0.0047 | 0.0051 | −0.0072 | −0.0049 |

(0.0065) | (0.0065) | (0.0061) | (0.0061) | |

GDP growth | 0.1268 * | 0.1264 * | - | 0.1414 ** |

(0.0656) | (0.0656) | - | (0.0656) | |

Unemployment | −0.9115 *** | −0.9145 *** | - | - |

(0.2998) | −0.2998 | - | - | |

Stock index | −0.0342 | −0.0342 | - | −0.0273 |

(0.0263) | (0.0263) | - | (0.0252) | |

Default rate | −3.4702 *** | −3.4672 *** | - | - |

(0.7143) | (0.7143) | - | - | |

L_ GDP growth | - | - | 0.1497 ** | - |

- | - | (0.0681) | - | |

L_ Unemployment | - | - | 1.2966 *** | - |

- | - | (0.2968) | - | |

L_ Stock index | - | - | −0.0192 | - |

- | - | (0.0262) | - | |

L_ Default rate | - | - | 3.9085 *** | - |

- | - | (0.7104) | - | |

Industry fixed effects | Yes | No | Yes | Yes |

Log-likelihood | 7047.49 | 7043.20 | 7058.31 | 7020.83 |

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

François, P.
The Determinants of Market-Implied Recovery Rates. *Risks* **2019**, *7*, 57.
https://doi.org/10.3390/risks7020057

**AMA Style**

François P.
The Determinants of Market-Implied Recovery Rates. *Risks*. 2019; 7(2):57.
https://doi.org/10.3390/risks7020057

**Chicago/Turabian Style**

François, Pascal.
2019. "The Determinants of Market-Implied Recovery Rates" *Risks* 7, no. 2: 57.
https://doi.org/10.3390/risks7020057