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Accounting-based expected loss given default and debt contract design

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Abstract

We investigate an unexplored channel—loss given default (LGD)—through which accounting information can shape the design of debt contracts. Using a sample of defaulted bonds, we find that borrower accounting information available at contract initiation possesses significant power for predicting realized LGD at the subsequent default date. We then use this model to construct an accounting-based measure of expected LGD at the contracting date for a large sample of bond issuances. We find that this measure is positively associated with issuance date interest spread and covenant use, and document that these relations are not artifacts of an association between LGD and probability of default. We then show that accounting-based expected LGD has a stronger association with issuance date spread when the borrower’s underlying accounting is more conservative and when the accounting-based LGD predictors are more persistent. Our results increase our understanding of both the informational role and contracting role of accounting information.

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Notes

  1. In other words, loss given default is the amount that lenders cannot recover from $1 of debt, which implies that loss given default is one minus the recovery rate on a debt instrument. As an example, consider a lender that invests $100 in a firm which defaults and is liquidated as a consequence. If the lender receives $20 out of the liquidation proceeds, the lender has loss given default of 80%.

  2. Our results do not imply that lenders use the same accounting predictors (or even a related deterministic model of predicted loss given default) to estimate and price loss given default. Rather, our results simply suggest that lenders price debt in a way that is consistent with their use of accounting information as captured by our analyses.

  3. See Altman (2008) for a survey of this emerging literature.

  4. The largest rating agencies have only recently started issuing independent loss given default ratings for debt instruments. These ratings are not available for many firms and were not available to lenders for most of the years in the sample. In addition, some of these ratings are available only after the contract has been designed. As Gupton (2005) discusses, a primary goal of Moody’s LossCalc v2 model is to help lenders to assess loss given default for bank regulatory provisioning purposes required by the Basel accord.

  5. Unrelated to whether debt contracts are viewed through a complete or incomplete contracting framework (e.g., Aghion and Bolton 1992; Hart and Moore 1994; Christensen et al. 2016), lenders always have the need to estimate probability of default and loss given default at the contracting date.

  6. Consistent with terminology used in practice, we use the term “straight” bond to refer to a bond that has no special features (e.g., is non-callable, non-convertible). In practice, these are also referred to as “plain vanilla” bonds.

  7. We follow Moody’s definition of default, which includes three categories of credit events. The first is a missed or delayed disbursement of interest and/or principal. The second includes filing for bankruptcy, legal receivership, and other legal blocks to the timely payment of interest and/or principal (perhaps by regulators). The third is a distressed exchange, which occurs when (i) the issuer offers bondholders a new security or package of securities that amounts to a diminished financial obligation (such as preferred or common stock, or debt with a lower coupon or par amount, lower seniority, or longer maturity), or (ii) the exchange had the apparent purpose of helping the borrower avoid default. The definition of a default is intended to capture events that change the relationship between the bondholder and bond issuer from the relationship which was originally contracted, and which subjects the bondholder to an economic loss. Technical defaults (covenant violations, etc.) are not included in Moody’s definition of default.

  8. Because the dependent variable, LGD, is between zero and one, OLS estimated coefficients may be biased. We also considered a fractional response model (Papke and Wooldridge 1996). Because this method yields similar results (untabulated) to the OLS results, we present OLS results for simplicity of calculation and interpretation.

  9. Less than 5% of observations in our broad bond sample are also included in the default sample. If we remove these overlapping observations from the bond sample, our inferences are unchanged.

  10. In untabulated analyses, we find identical inferences to our main analyses when we estimate a system of equations using seemingly unrelated regression where each bond term (i.e., Spread, FaceAmt, Maturity, CovIndex) is used as a dependent variable in the Eq. (3) structure.

  11. Our inferences remain unchanged if we instead cluster by year of bond issuance.

  12. We note that by including both net worth and assets in the regression, we are implicitly including leverage (i.e., the difference between assets and net worth).

  13. Shleifer and Vishny (1992) analytically show that when more similar assets are dumped into the market during liquidation, prices are depressed.

  14. We acknowledge that it is possible to conceive of stories that suggest opposing predictions. For example, rather than providing monitoring benefits (which would reduce LGD), short-term debt could indicate financial instability, which may translate into higher LGD. Either way, we are more concerned with whether the variables are useful for predicting LGD than with their particular directional associations.

  15. In this fixed-effects-only model, the reported intercept simply captures the constant effect of one industry that is necessarily omitted during model estimation.

  16. For the sake of brevity, we do not discuss the results of the control variable estimates for any of the estimations in this study except in cases where these results are important to the purposes of this paper. However, we note that these estimates are generally consistent with prior literature.

  17. The separate addition of each of the five accounting predictors that comprise PredLGD_Acct to the regression as a control variable does not change the inferences described above. We note that adding all of the accounting predictors to the regression together is not feasible because of full multicollinearity, as PredLGD_Acct is a linear combination of the five accounting predictors.

  18. As indicated in Table 1, consistent with prior studies, BSMProb is close to zero for more than 75% of our observations. Accordingly, we alternatively define high default probability based on a split at the 75th percentile (rather than at the median, as reported), and our inferences remain. Specifically, the coefficient estimate on PredLGD_Acct in the low (high) group is 1.14 (3.69), where both estimates are individually statistically significant and the difference is significant at the 5% level.

  19. Subsequently reported inferences are unchanged if we instead estimate the Eq. (5) default prediction model using OLS and then construct PredPD_Acct using the linear coefficient estimates.

  20. For example, Glover (2016) shows that estimation of the cost of bankruptcy using a sample of bankrupt firms can be biased because of self-selection.

  21. Note that our sample size is reduced to 762 observations because of data requirements associated with estimating Eq. (7) in firm-specific time series.

References

  • Acharya, V., S. Bharath, and A. Srinivasan. 2007. Does industry-wide distress affect defaulted firms? Evidence from creditor recoveries. Journal of Financial Economics 85: 787–821.

    Article  Google Scholar 

  • Aghion, P., and P. Bolton. 1992. An incomplete contracts approach to financial contracting. Review of Economic Studies 59: 473–494.

    Article  Google Scholar 

  • Altman, E. 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23: 589–609.

    Article  Google Scholar 

  • Altman, E. 2008. Default recovery rates and LGD in credit risk modeling and practice: An updated review of the literature and empirical evidence. In Advances in Credit Risk Modelling and Corporate Bankruptcy Prediction (Quantitative Methods for Applied Economics and Business Research, ed. S. Jones and D. Hensher, 175–206. Cambridge: Cambridge University Press.

    Google Scholar 

  • Amiram, D., A. Kalay, and G. Sadka. 2017. Industry characteristics, risk premiums, and debt pricing. The Accounting Review 92: 1–27.

    Article  Google Scholar 

  • Basu, S. 1997. The conservatism principle and the asymmetric timeliness of earnings. Journal of Accounting and Economics 24: 3–37.

    Article  Google Scholar 

  • Beatty, A., J. Weber, and J. Yu. 2008. Conservatism and debt. Journal of Accounting and Economics 45: 154–174.

    Article  Google Scholar 

  • Beaver, W. 1966. Financial ratios as predictors of failure. Journal of Accounting Research 4: 71–111.

    Article  Google Scholar 

  • Beaver, W., M. Correia, and M. McNichols. 2012. Do differences in financial reporting attributes impair the predictive ability of financial ratios for bankruptcy? Review of Accounting Studies 17: 969–1010.

    Article  Google Scholar 

  • Benmelech, E., M. Garmaise, and T. Moskowitz. 2005. Do liquidation values affect financial contracts? Evidence from commercial loan contracts and zoning regulation. Quarterly Journal of Economics 120: 1121–1154.

    Google Scholar 

  • Brown, S., W. Goetzmann, and A. Kumar. 1998. The Dow Theory: William Peter Hamilton’s track record reconsidered. The Journal of Finance 53: 1311–1333.

    Article  Google Scholar 

  • Campbell, J., J. Hilscher, and J. Szilagyi. 2008. In search of distress risk. Journal of Finance 63: 2899–2939.

    Article  Google Scholar 

  • Carrizosa, R., and S. Ryan. 2013. Conservatism, covenants, and recovery rates. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2197513. Accessed February 9, 2023.

  • Chava, S., and R. Jarrow. 2004. Bankruptcy prediction with industry effects. Review of Finance 8: 537–569.

    Article  Google Scholar 

  • Christensen, H., and V. Nikolaev. 2012. Capital versus performance covenants in debt contracts. Journal of Accounting Research 50: 75–116.

    Article  Google Scholar 

  • Christensen, H., V. Nikolaev, and R. Wittenberg-Moerman. 2016. Accounting information in financial contracting: The incomplete contract theory perspective. Journal of Accounting Research 54: 397–435.

    Article  Google Scholar 

  • Donovan, J., R. Frankel, and X. Martin. 2015. Accounting conservatism and creditor recovery rate. The Accounting Review 90: 2267–2303.

    Article  Google Scholar 

  • Dyreng, S., R. Vashishtha, and J. Weber. 2017. Direct evidence on the informational properties of earnings in loan contracts. Journal of Accounting Research 55: 371–406.

    Article  Google Scholar 

  • Easton, P., M. McAnally, G. Sommers, and X. Zhang. 2018. Financial Statement Analysis & Valuation (fifth edition). Cambridge Business Publishers.

  • Elgers, P. 1980. Accounting-based risk predictors: A re-examination. The Accounting Review 55: 389–408.

    Google Scholar 

  • Francis, J., R. LaFond, P. Olsson, and K. Schipper. 2004. Costs of equity and earnings attributes. The Accounting Review 79: 967–1010.

    Article  Google Scholar 

  • Glover, B. 2016. The expected cost of default. Journal of Financial Economics 119: 284–299.

    Article  Google Scholar 

  • Gupton, G. 2005. Advancing loss given default prediction models: How the quiet have quickened. Economic Notes 34: 185–230.

    Article  Google Scholar 

  • Gupton, G., and R, Stein. 2005. LossCalc V2: Dynamic prediction of LGD. Moody’s Investors Service 3:31–44.

  • Hart, O., and J. Moore. 1994. A theory of debt based on the inalienability of human capital. Quarterly Journal of Economics 109: 841–879.

    Article  Google Scholar 

  • Hillegeist, S., A. Keating, D. Cram, and K. Lundstedt. 2004. Assessing the probability of bankruptcy. Review of Accounting Studies 9: 5–34.

    Article  Google Scholar 

  • Murfin, J. 2012. The supply-side determinants of loan contract strictness. Journal of Finance 67: 1565–1601.

    Article  Google Scholar 

  • Nikolaev, V. 2010. Debt covenants and accounting conservatism. Journal of Accounting Research 48: 51–89.

    Article  Google Scholar 

  • Ohlson, J. 1980. Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research 18: 109–131.

    Article  Google Scholar 

  • Papke, L., and J. Wooldridge. 1996. Econometric methods for fractional response variables with an application to 401 (k) plan participation rates. Journal of Applied Econometrics 11: 619–632.

    Article  Google Scholar 

  • Roberts, M., and A. Sufi. 2009. Financial contracting: A survey of empirical research and future directions. Annual Review of Financial Economics 1: 207–226.

    Article  Google Scholar 

  • Shleifer, A., and R. Vishny. 1992. Liquidation values and debt capacity: A market equilibrium approach. Journal of Finance 47: 1343–1366.

    Article  Google Scholar 

  • Shumway, T. 2001. Forecasting bankruptcy more accurately: A simple hazard model. Journal of Business 74: 101–124.

    Article  Google Scholar 

  • Standard and Poor's. 2013. A Guide to the U.S. Loan Market. https://www.lcdcomps.com/lcd/na/2012/09/07/2013%20Guide%20To%20The%20US%20Loan%20Market.pdf. Accessed February 9, 2023.

  • Tirole, J. 2006. The Theory of Corporate Finance. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Varma, P., and R. Cantor. 2005. Determinants of recovery rates on defaulted bonds and loans for North American corporate issuers: 1983–2003. Journal of Fixed Income 14: 29–44.

    Article  Google Scholar 

  • Watts, R. 2003. Conservatism in accounting part I: Explanations and implications. Accounting Horizons 17: 207–221.

    Article  Google Scholar 

  • Zhang, J. 2008. The contracting benefits of accounting conservatism to lenders and borrowers. Journal of Accounting and Economics 45: 27–54.

    Article  Google Scholar 

  • Zmijewski, M. 1984. Methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research 22: 59–82.

    Article  Google Scholar 

Download references

Acknowledgements

Dan is grateful to his dissertation committee members, Robert Bushman (co-chair), Wayne Landsman (co-chair), Jeff Abarbanell, John Graham, Mark Lang, and Doug Shackelford for continuous support and advice. The authors would also like to thank Razi Avram, Ryan Ball, Mary Barth, Dinara Bayazitova, Anne Beatty, Nittai Bergman, Anne Beyer, Dirk Black, Alexander Bleck, Jesse Blocher, John Core, Elicia Cowins, Peter Demerjian, Scott Dyreng, Mary Margaret Frank, Koresh Galil, Joseph Gerakos, Wayne Guay, Trevor Harris, Ron Kasznik, Alon Kalay, Sharon Katz, Yaniv Konchitchki, Andrei Kovrijnykh, Eva Labro, Roby Lehavy, Christian Leuz, Lynn Li, Katie McDermott, Maureen McNichols, Mark Maffett, Steve Monahan, Valeri Nikolaev, Bugra Ozel, Ken Peasnell, Manju Puri, Shiva Rajgopal, Dick Rendleman, Gil Sadka, Richard Sansing, Cathy Shakespeare, Abbie Smith, David Smith, Steve Stubben, Phil Stocken, Florin Vasvari, Rodrigo Verdi, Joe Weber, Chris Williams, Regina Wittenberg-Moerman, and Tzachi Zach for helpful comments and discussions. We are also thankful to a managing director at Morgan Stanley who shared his knowledge on debt markets and distressed debt investing. We appreciate comments and suggestions from workshop participants at the University of Chicago, Columbia University, Dartmouth College, Duke University, Emory University, University of Michigan, MIT, New York University, University of North Carolina at Chapel-Hill, North Carolina State University, The Ohio State University, University of Pennsylvania, Tel-Aviv University, Stanford University, and the University of Virginia.

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Appendix

Appendix

Variable definitions

ATO i,t

Firm i’s year t asset turnover, calculated as sales (Compustat sale) divided by average total assets

BSMProb i,m

Firm i’s estimated default probability at the end of month m using the Black–Scholes-Merton option pricing model modified for dividends, closely following the methodology outlined in Hillegeist et al. (2004). Estimation requires initial estimates of market value of assets (VA), asset volatility (SIGA), dividend rate (DIVRATE), and risk-free rate (R). We compute VA as total liabilities plus market value of equity in month m. We compute SIGA as firm i’s stock price volatility using one year of daily stock returns ending in month m, multiplied by the equity-to-asset value ratio. DIVRATE requires annual Compustat data for common and preferred dividends, which we set to zero if missing. We set the risk-free rate to the one-year T-bill rate for month m. Finally, we set the time horizon to one year

CovIndex i,b

A count of the number of covenants attached to firm i’s bond b, as categorized and identified by the Mergent bond issue file

Debt i,t

Firm i’s total debt at the end of year t, calculated as long-term debt (Compustat dltt) plus debt in current liabilities (Compustat dlc)

DebtToEquity i,t

Firm i’s debt-to-equity ratio at the end of year t, calculated as total debt divided by common equity (Compustat (dltt + dlc)/ceq)

Default i,t

An indicator variable that equals one if firm i defaults in year t and zero otherwise

FaceAmt i,b

The par value of firm i’s bond b in millions, calculated as Mergent OFFERING_AMT divided by 1,000

HighConserv i,t

An indicator variable that equals one if firm i’s year t accounting conservatism is above the sample median and zero otherwise. We measure firm i’s year t conservatism as the coefficient ratio (β3 + β1)/β1 in the following firm-specific time-series regression (using at least five but no more than ten years of firm i’s data, ending in year t): Earni,t = β0 + β1Reti,t + β2DRreti,t + β3DRet*Reti,t + εi,t (Basu 1997), where Earn is earnings before extraordinary items scaled by beginning-of-year market value of equity, Ret is 12-month return ending three months after the fiscal year-end, and DRet is an indicator that equals one if Ret < 0

HighPersist i,t

An indicator variable that equals one if the average decile rank persistence of firm i’s year t LnNetWorth, ROA, IntanRatio, ShortDebtRatio, and LnTotalAssets is above the sample median and zero otherwise. We first measure firm i’s year t persistence of each variable (Var) with the coefficient from the following firm-specific time-series regression (using at least five but no more than ten years of firm i’s data, ending in year t): Vari,t = β0 + β1Vari,t-1. We next rank each variable’s persistence into firm-year sample deciles, then average those decile ranks for each firm year. Finally, we split the average decile ranks at the sample median

IndAvgLGD i,b

The average LGD of all defaulted bonds in firm i’s Fama–French 17 industry occurring prior to firm i’s bond b default

IntanRatio i,t

The percentage of firm i’s assets in year t that are intangible, calculated as intangible assets (Compustat intan) divided by total assets (Compustat at)

Leverage i,t

Firm i’s leverage in year t, calculated as total liabilities (Compustat lt) divided by total assets (Compustat at)

LiabToEquity i,t

Firm i’s liabilities-to-equity ratio at the end of year t, calculated as total liabilities divided by common equity (Compustat lt/ceq)

LGD i,b,d

Realized loss on firm i’s defaulted bond b on date d, calculated as one minus the realized recovery rate, using data from Moody’s DRS. Recovery rate is calculated as the market price of the bond 30 days after default divided by the face value of the bond

LnMVE i,t

The natural log of firm i’s market value of equity at the end of year t, where market value of equity is computed as the number of common shares outstanding (Compustat csho) times the closing price per share at the end of the year (Compustat prcc_f)

LnNetWorth i,t

Firm i’s net worth at the end of year t, calculated as (the natural log of) total assets (Compustat at) minus total debt, where total debt is computed as long-term debt (Compustat dltt) plus debt in current liabilities (Compustat dlc)

LnNetWorth2 i,t

Firm i’s net worth at the end of year t, calculated as (the natural log of) total assets (Compustat at) minus total liabilities (Compustat lt)

LnTotalAssets i,t

The natural log of firm i’s total assets in year t (Compustat at)

Maturity i,b

The years to maturity (at issuance) of firm i’s bond b, calculated as Mergent (MATURITY-OFFERING_DATE)/360

PredLGD_Acct i,t

Firm i’s year t accounting-based predicted loss given default, estimated in two steps. First, using a sample of defaulted bonds from Moody’s DRS, we regress realized loss given default on a set of five contracting-date accounting variables (LnNetWorth, ROA, IntanRatio, ShortDebtRatio, and LnTotalAssets), as in Eq. (1). Second, we apply the estimated coefficients to firm i’s year t accounting data, as in Eq. (2). When working with the Mergent bond issue sample, we use firm i’s most recent accounting data prior to the issuance of bond b

PredLGD_Ind i,t

Firm i’s industry-based predicted loss given default, estimated in two steps. First, using a sample of defaulted bonds from Moody’s DRS, we regress realized loss given default on a set of industry fixed effects based on the Fama–French 17-industry classifications. Second, using a broad sample of bond issues from Mergent FISD we apply the estimated coefficients to firm i’s most recent industry classification prior to the issuance of bond b

PredPD_Acct i,t

Firm i’s accounting-based predicted probability of default, estimated in two steps. First, using a sample of defaults from Moody’s DRS intersected with the Compustat annual file, we estimate a standard logit-based default hazard model using the same set of five accounting variables that we use to estimate PredLGD_Acct (LnNetWorth, ROA, IntanRatio, ShortDebtRatio, and LnTotalAssets), as in Eq. (4). Second, using a broad sample of bond issues from Mergent FISD, we apply the estimated coefficients to firm i’s most recent accounting data prior to the issuance of bond b, as in Eq. (5)

PriorityCov i,b

An indicator that equals one if firm i’s bond b includes a cross default or cross acceleration covenant and zero otherwise (Mergent Cross_default, Cross_acceleration)

ProfitMargin i,t

Firm i’s year t profit margin, calculated as net income divided by sales (Compustat ni/sale)

Q i,t

Firm i’s Tobin’s q ratio at the end of year t, computed as the sum of total liabilities (Compustat lt) and market value of equity, divided by total assets (Compustat at). Market value of equity is computed as the number of common shares outstanding (Compustat csho) times the closing price per share at the end of the year (Compustat prcc_f)

Rated i,b

An indicator variable that equals one if firm i has a long-term S&P credit rating in place within the most recent year prior to the issuance of firm i’s bond b and zero otherwise. We base this indicator on the Compustat variable splticrm (we consider splticrm = “SD” to be unrated)

RestrictPmtCov i,b

An indicator that equals one if firm i’s bond b includes a covenant that restricts the firm’s payments to shareholders (including dividends restrictions) and zero otherwise (Mergent Restricted_payments, Dividends_related_payments_sub, Dividends_related_payments_is)

ROA i,t

Firm i’s return on assets in year t, computed as firm i’s earnings before extraordinary items in year t (Compustat ib) divided by year t and t-1 average total assets (Compustat at)

ShortDebtRatio i,t

The proportion of short-term debt in firm i’s total liability structure in year t, computed as debt in current liabilities (Compustat dlc) divided by total liabilities (Compustat lt)

Spread i,b

The interest spread on firm i’s bond b, calculated as the bond offering yield to maturity (Mergent OFFERING_YIELD) minus the benchmark Treasury rate (i.e., the prevailing rate during the month of bond issue of a same-maturity Treasury bond; data obtained from the Federal Reserve)

TimesInterest i,t

Firm i’s year t times interest earned ratio, calculated as earnings before interest and taxes divided by interest expense (Compustat ebit/xint)

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Amiram, D., Owens, E. Accounting-based expected loss given default and debt contract design. Rev Account Stud (2023). https://doi.org/10.1007/s11142-023-09772-x

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