Combination of linear discriminant analysis and expert opinion for the construction of credit rating models: The case of SMEs

Abstract

The construction of an internal rating model is the main task for the bank in the framework of the IRB-foundation approach the fact that it is necessary to determine the probability of default by rating class. As a result, several statistical approaches can be used, such as logistic regression and linear discriminant analysis to express the relationship between the default and the financial, managerial and organizational characteristics of the enterprise. In this paper, we will propose a new approach to combine the linear discriminant analysis and the expert opinion by using the Bayesian approach. Indeed, we will build a rating model based on linear discriminant analysis and we will use the bayesian logic to determine the posterior probability of default by rating class. The reliability of experts’ estimates depends on the information collection process. As a result, we have defined an information collection approach that allows to reduce the imprecision of the estimates by using the Delphi method. The empirical study uses a portfolio of SMEs from a Moroccan bank. This permitted the construction of the statistical rating model and the associated Bayesian models; and to compare the capital requirement determined by these models.

Keywords:

• linear discriminant analysis
• Bayesian approach
• Probability of default (PD)
• IRB foundation
• Unexpected loss (UL)

JEL classification:

• C11
• C13
• C51
• G21
• G32

PUBLIC INTEREST STATEMENT

Customer rating is an important tool for determining credit pricing. Indeed, the bank must construct a model capable of determining the real profile of the customer. This article proposes a approach to the conception of a rating model that integrates the quantitative and qualitative data of the company can be of great utility for professionals, student credit risk researchers and academics.

It also meets the need for a portfolio manager by combining their opinion with statistical estimation.

The method we have proposed to combine statistical estimation and expert opinion can be used in other risk management areas such as operational and market risk.

Notes

1. The correlation formula for companies and banks is $R=0,12\left(\frac{1-e^{-50PD}}{1-e^{-50}}\right)+0,24\left(1-\frac{1-e^{-50PD}}{1-e^{-50}}\right)$. For exposures to SMEs this formula is adjusted to take into account the size of the entity: 0,04 x (1—(S—5)/45)). S is expressed as total annual sales in millions of euros with values of S falling in the range of equal to or less than €50 million or greater than or equal to €5 million. Reported sales of less than €5 million will be treated as if they were equivalent to €5 million. Paragraph 273 of the Basel Committee on Banking Supervision[7].

2. In the case of two groups, Bartlett’s approximation of the lambda distribution is chi-squared with p degrees of freedom $-\left(n-1+\left(p+2\right)/2\right)ln\left(\mathrm{\Lambda }\right)\text{~}{\chi }_p^2$.

3. Bank Al Maghrib’s circular 8/G/2010 considers that SMEs are characterised by a turnover (Sales) that varies between MAD 10 and 175 million $MAD$. The $SMEs$ whose turnover is less than 10 million $MAD$are treated as equivalent to this amount.

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Mohamed Habachi

Mohamed Habachi PhD in management science, banking experience of 20 years.

Specialized in Risk Management and Audit.

Two articles published in the field of operational risk and credit risk

Saâd Benbachir

Saâd Benbachir PhD, Studies and Researches in Management Sciences Laboratoy

Director of the Strategic Studies in Law, Economics and Management Center.

31 articles published in market risk, stochastic volatility, operational risk and credit risk.