Corporate Credit Risk Modelling and the Macroeconomy

thumbnail of SSRN-id630082 Original by K. Carling, T.Jacobson, J. Lindé, K. Roszbach, 2006 , 29 pages 

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Note: there is an older version dated 2004 which also mention Value at risk and Expected shortfall


  • This paper contributes to the field by presenting a duration model for the survival time until default of business-loan borrowers that includes both firm-specific and macroeconomic explanatory variables.
  • Swedish bank portfolio
  • Our model, by taking macro conditions into account, manages to capture the absolute level of default risk,
  • Benchmark models, conditioning only on rankings
  • The output gap, the yield curve and consumers’ expectations of future economic development have significant explanatory power for the default risk of firms.
  • Compared model with a frequently used model of firm default risk that conditions only on firm-specific information.
  • Make a reasonably accurate ranking of firms’ according to default risk,
  • Found evidence for the existence of duration dependence. Implies that a binary model specification is inappropriate
  • Idiosyncratic risk factors need to be complemented with information on survival time to obtain consistent default-risk estimates.
  • Found that the risk of default is markedly higher for short-term loans than for long-term credit.
  • This is in accordance with a common thought that banks are more inclined to extend short-term loans to firms with a more uncertain future,
  • Safer enterprises tend to have better access to loans with longer, fixed, maturities.

General stuff

  • Pioneering contribution from the 1960’s is Altman’s study of business default risk
    There are four groups of portfolio credit risk models.
    • ’structural’ and based on Merton’s [36] model of firm capital structure (bottom up model)
    • Econometric factor risk models, where default risk in ’homogeneous’ subgroups is determined by a macroeconomic index and a number of idiosyncratic factors (also bottom up model)
    • ’top-down’ actuarial models, like Credit Suisse’s CreditRisk+, that make no assumptions regarding causality
    • Carey use non-parametric methods.
  • Main sources of discrepancies in predictions are differences in distributional assumptions and functional forms.

Basic Model

  • The definition of variables are: TS = total sales; EBITDA = earnings before interest payments, taxes, depreciation and amortizations; TA = total assets; TL = total liabilities; I = inventories; Bank pay-remark = a dummy variable taking the value of 1 if the firm has a “non-performing loan” at a bank in the preceding four quarters; Legal pay-remark = a dummy variable taking the value of 1 if the firm has a payment remark due to one or more of the following events in the preceding four quarters; a bankruptcy petition, issuance of a court order to pay a debt, seizure of property.
  • Replaced missing data entries by the firm-specific mean of that variable over time.
  • Annual reports typically become available with a significant time lag,
  • To account for this, we have lagged all accounting data by 4 quarters in the estimations.
  • Adjust for reporting periods that did not coincide with the calendar year,
  • Annual balance sheet figures were calculated as weighted averages of the multiple period values.
  • In these cases, such ’deviations’ were accounted for by adjusting the ’four quarter lag’
  • Selected 17 ratios that were employed in frequently cited articles studying bankruptcy risk. See Altman, Frydman, Altman and Kao, Li, and Shumway , liquidity measures, two are leverage ratios, remainder are profitability ratios.
  • Three accounting ratios: earnings before interest, taxes, depreciation, and amortization (ebitda) over total assets (earnings ratio);
  • Total liabilities over total assets (debt ratio); and inventories over total sales (the inverse of inventory turnover).
  • Composite dummy of three events: a bankruptcy petition, the issuance of a court order – because of absence during the court hearing – to pay a debt, and the seizure of property.
  • ”Having a non-performing loan” with a bank, not necessarily with the current one.

Macroeconomic variables

  • Growth rate in real GDP,
  • The series for potential output is computed using an unobservable components method due to Apel and Jansson.
  • Swedish households’ expectations of the future macroeconomic development, with a lag of 2 quarters,
  • The output gap functions as an indicator of demand conditions.
  • Higher aggregate demand relative to production capacity can be expected to reduce default risk.
  • Estrella and Hardouvelis and Estrella and Mishkin suggests that the yield curve can be an important indicator of future real activity;
  • Positively sloping yield curve signals higher future economic activity
  • Expect that an increase in the spread between the short- and long-term interest rate is associated with decreasing default rates,
  • Expect that positive household expectations about increased future economic activity also reduce the default rate today.
  • The index of household expectations about the future stance of the macroeconomy is taken from the survey data produced by the Swedish National Institute for Economic Research.
  • Enter the series for the output gap and the household expectations with a lag of two quarters,
  • In credit risk modelling the default event is usually defined in terms of a specific time-period,
  • Duration dependence means that the time a borrower has managed to avoid default directly affects the risk of a default
  • In the absence of any duration dependence, there is no need for conditioning on the survival time of the borrower.
  • Shumway offers an investigation of the consequences of incorrectly assuming a constant default rate as implied by a binary model.
  • Business cycle affects are supposed to be captured by z(τ), which can include variables like the yield curve, z(τ), the output gap, inflation, household expectations, and the unemployment rate.
  • Environmental variables that do not vary over time are the duration dummies.

Duration model

  • A common way to impose additional structure on the model is to assume a multiplicative relationship between the variables and the hazard rate suggested by Cox
  • This model postulates a base-line hazard, (k), that is common to all loans and a multiplicative h0 (k), component that depends on both firm specific variables and common environmental variables.
  • Use Goodman-Kruskal’s as a pseudo R2 measure of fit
  • While firm size, the earnings ratio, and the inventory turnover have a significant impact on default risk, the leverage ratio is the financial ratio with by far the biggest impact on default risk