Credit Risk & Scoring Models

Question 1

What is the formula for future losses on a single credit?

Answer 1

L_i = D * EAD * LGD

L = Future loss on single credit, D = Default, EAD = Exposure at default, LGD = Loss given default(1- RR)

Question 2

What are the 2 main criteria to distinguish “good” vs “bad” companies

Answer 2

1. Interest expenses over turnover (the higher the worse)
2. Unauthorised overdrafts over total credit exposure (the higher the worse)

Question 3

What is the formula for the synthetic score that distinguishes good from bad companies?

Answer 3

D(x) = γ_IET * x_IET + γ_OE * x_OE

Where x is the ratio value and gamma is the weight

Question 4

How to choose weights (gamma) for calculating the synthetic score for bakning ratings?

Answer 4

We choose gamma that maximizes the distance between good companies and bad companies through the formula
(|γ’x₁-γ’x₂)/σ_D
or
γ=Σ^-1 * (x₁-x₂)

Question 5

How to use scores to classify companies into good and bad?

Answer 5

Take a point alpha, which is inbetween two cetnroids and classify as godd a company if its score is higher than alpha, bad if its score is lower than alhpa.
Alpha = (D₁ + D₂)/2

Question 6

What is the Altman Z score?

Answer 6

z_i = 1.2 * x_i,1 + 1.4 * x_i,2 + 3.3 * x_i,3 + 0.6 * x_i,4 + 1.0 * x_i,5

x1 = working capital/total assets
x2 = retained profits/total assets
x3 = earnings before interest and tax/total assets
x4 = mkt value of assets/book value of long-tem debts
x5 = turnover/total assets
The greater the z score of a company, the better its quality, cut-off point at 1.81

Question 7

What is more costly in risk management, being assigned to the “good” company while being “bad”, or being assigned to the “bad” company while being “good”?

Answer 7

A “bad” company being assigned as “good” is a much bigger problem as the losses tend to be much higher

Question 8

What is the summary of how to use discriminant analysis for credit score calculation?

Answer 8

1. Customers are divided into two (or more) groups that are supposed to have different means.
2. Such groups are described based on past data, so that new data can be assigned to one of them.
3. DA is a descriptive tool: no model for the process leading to default is present
4. The assumption of an equal variance/covariance matrix across groups is not totally realistic, although it helps keeping things simple
5. Probability estimates require “multi-normality”, which is seldom supported by empirical data

Question 9

How is the linear probabilistic model used for calculating the probability of default (PD)?

Answer 9

• Variables that lead to the default of a company, and theri weights, are identified with a simple linear regression.
  1. Sample selection: sample formed by large number of companies is selected and divided into two groups, identified by a binary state variable (dummy) y, which only takes value 0 or 1
  2. Selection of independent variables. For each company i, m significant vaiables (xi1, xi, … xij, … xim) are recorded: economic/financinal indicators, measured prior to default
  3. Estimating coefficients: OLS
  y_i = alpha + Σβ_jx_i,j + ε_i
  4. Estimate probability of default: model used to estimate PD of new companies applying for bank loans