Ratings Assignment Methodologies (II)

This is the second part of the article on Rating Assignment Methodologies. The first part, as well as other articles of this series can be accessed using the following these links:

• The Credit Decision
• Classifications and Key Concepts of Credit Risk (I)
• Classifications and Key Concepts of Credit Risk (II)
• Rating Assignment Methodologies (I)

We start by presenting structural and reduced form approaches to predict defaults.

The structural approach entails building a model that estimates the formal relationships linking relevant model variables. 

An example is the Merton model that assumes a default occurs when a company’s structure is no longer worthwhile. The default probability and the distance to default can be calculated using relevant financial variables, such as interest rates, maturity, debt face value, the underlying value of the asset, and the assets volatility and applying the Black-Scholes-Merton formula:

Where:

F = debt face value 

VA = firm asset value (market value of equity and net debt) 

 μ = expected return in the risky world 

T = time to maturity remaining 

 σA= standard deviation of asset values

The model is extremely sensitive to market movements and variables, such as asset value, volatility, and the underlying debt itself, which are difficult and complicated to value. 

This distance to default (DtD) represents a threshold beyond which a firm will enter financial distress and subsequently default. The DtD using the Merton approach, assuming remaining time to maturity of one year (T = 1) is:

The Merton model presents several challenges:

• Asset values and volatilities are not observed.
• The structure of the underlying debt is typically complex given for example differing maturities and covenants.
• It requires continuous recalibration.
• It only applies to liquid, publicly traded firms.
• Tends to fall short of fully reflecting the dependence between credit risk, the business and credit cycles given its high sensitivity to market movements.

Moving to the reduced form approaches, these use the most statistically suitable variables without taking into consideration their relationships. There are statistical-based models and numerical-based models inside this category. 

The first example of reduce form method is the Linear discriminant analysis (LDA), due to its dependency on exogenous variable selection, the default composition and definition. The method is used to develop scoring models and to provide accept/reject decisions.

The variables are chosen based on their estimated contribution to the likelihood of default, come from an extensive pool of qualitative features and the main goal is to choose the coefficients that minimize the overlap between performing and nonperforming counterparts. The weights of each feature to the overall score are represented by Altman’s Z-score and the output of the LDA is the classification of the counterparts into performing or non-performing.

A Z-score is assigned to each firm at some moment prior to default based on the selected features and Z cut-off point is used to differentiate the groups.

The process of fitting empirical data into a statistical model is called calibration.

LDA calibration involves quantifying the probability of default by using statistical-based outputs of ratings systems and accounting for differences between the default rate of the samples and the overall population. In practice, the calibration will depend on the objective of the model:

? In the case the aim is only to accept or reject credit applications, it involves adjusting the Z-score cut-off to take into consideration differences between the sample and population default rates. 

? In the case the aim is to categorise borrowers into different ratings classes, it will include a cut-off adjustment and a potential rescaling of Z-score.

Altman (1968) proposed the following LDA model for corporates: 

Z = 1.21x1 + 1.40x2 + 3.30x3 + 0.6x4 + 0.999x5

where: 

x1 = working capital / total assets 

x2 = accrued capital reserves / total assets 

x3 = EBIT / total assets 

x4 = equity market value / face value of term debt 

x5 = sales / total assets

The higher the Z-score, the more likely it is that a firm will be classified in the group of performing counterparts. The discriminant threshold of this model considered to be Z = 2.675.

Another example of LDA is the RiskCalc model developed by Moody’s, that considers variables that as financial leverage, growth, liquidity, debt coverage, profitability, size, and assets.

In the next article, we will explore the logistic regression, cluster and cash flow analysis and also some heuristic methods.