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Characterise three families of default prediction: judgmental approaches, empirical models and financial (structural) models.

FRM® Part II · Credit Risk Measurement and Management · Introduction to Credit Risk Modeling and Assessment · FRM2.CR.5.d

The idea

Default prediction approaches fall into three families. Judgmental approaches rely on the experience of credit officers and expert systems, such as the five Cs of credit. They cope with small samples and private firms but are subjective and can differ between analysts. Empirical models are statistical: discriminant analysis such as the Altman Z-score, or logit and probit models, are fitted to historical data on defaulting and surviving firms, with accounting ratios as inputs. They are objective but backward looking and only as good as the sample, and in-sample fit overstates out-of-sample accuracy. Financial or structural models, with Merton as the classic, derive default from the firm's asset value, volatility and liabilities, using market data, so they need traded equity. Exam questions turn on matching an approach to the data available and naming its main limitation.

Formulas

Probability from a logistic regression

p = 1 ÷ (1 + e^(−z))

z
the fitted linear score, the log-odds b₀ + b₁ × X₁ + …

z is the score built from accounting ratios; convert it to a probability before use. A positive coefficient on leverage raises PD.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which of the following is an example of a judgmental approach to default prediction?

  1. A logit model fitted on historical defaults and accounting ratiosWhy not: This is an empirical (statistical) model, estimated from data rather than from expert judgment.
  2. The Altman Z-scoreWhy not: The Z-score is a discriminant-analysis model, which is an empirical approach.
  3. An option-pricing model using equity value and volatilityWhy not: This describes a financial (structural) model such as Merton.
  4. A credit officer's assessment based on the five Cs of credit - correct

Judgmental approaches rely on expert experience and structured checklists such as the five Cs (character, capacity, capital, collateral, conditions).

A harder one

An empirical model uses Z = 1.2 X1 + 1.4 X2 + 3.3 X3 + 0.6 X4 + 1.0 X5. Zones: Z below 1.81 is distress, between 1.81 and 2.99 is grey, above 2.99 is safe. A firm has X1 = 0.10, X2 = 0.15, X3 = 0.08, X4 = 0.90 and X5 = 1.10. Its score and zone are:

  1. Z = 1.13, distress zoneWhy not: Leaves out the X5 term (1.0 x 1.10) when summing the weighted ratios.
  2. Z = 2.23, grey zone - correct
  3. Z = 28.37, safe zoneWhy not: Enters EBIT / assets as 8 (a percentage) while the other ratios are decimals, inflating the profitability term.
  4. Z = 2.05, grey zoneWhy not: Applies a weight of 1.0 instead of 3.3 to X3, mis-weighting the profitability term.

Z = 1.2(0.10) + 1.4(0.15) + 3.3(0.08) + 0.6(0.90) + 1.0(1.10) = 0.120 + 0.210 + 0.264 + 0.540 + 1.100 = 2.234, which lies between 1.81 and 2.99: grey zone.

The hardest tier

A logit model gives PD = 1 / (1 + exp(-S)), with S = -3.0 + 4.0 x (debt / assets) - 0.5 x (interest cover). For a firm with debt / assets of 0.65 and interest cover of 2.5, the estimated PD is closest to:

  1. 83.9%Why not: Reverses the sign in the exponent, giving the probability of not defaulting.
  2. 16.1% - correct
  3. 19.2%Why not: Reports the odds exp(S) as if it were a probability.
  4. 4.9%Why not: Applies the normal distribution (a probit link) to the score instead of the logistic function.

S = -3.0 + 4.0 x 0.65 - 0.5 x 2.5 = -1.65. PD = 1 / (1 + e^1.65) = 1 / 6.207 = 16.1%.

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