# MOODY'S-KMV CREDIT MONITOR AND MOODY'S-KMV PORTFOLIO MANAGER

As with other models, we follow the structure of Section 51.1 for presenting the model. Moody's-KMV Portfolio Manager is considered as the most comprehensive portfolio model and provides all necessary outputs for calculating a credit VaR^{[1]}.

## Conceptual Framework

Moody's-KMV Portfolio Manager is an implementation of the structural default model. Default is triggered when asset value falls below a threshold matching the default probability assigned to each facility. When there is no default, the final credit state is modeled as the distance to default, or the distance between asset value simulated at horizon and the default point. The default point is the debt value projected as of horizon.

TABLE 51.1 **Vendors' models basic techniques for generating loss distributions**

## Credit Events and Credit State at Horizon

Moody's-KMV Portfolio Manager operates in full valuation mode, since it assigns a random distance to default to each facility. The distance to default is a metric mapped to default probabilities. Hence, the model simulates all credit states feasible at horizon. The model allows using book values, and it operates then under default mode only, since it simulates only default and non-default states at horizon.

## Risk Factors and Dependence Structure

The underlying "first level" risk factors, from which the credit events derive, are the asset values of firms. The unobservable asset values are modeled under the default option model. The asset values depend on common "second level" risk factors for generating dependencies. The "second level" factors influence asset returns from statistical fits. Statistical fits provide also the characteristics of the error terms. This is the case for all firms included in Moody's-KMV Credit Monitor universe, and the data is delivered with the model.

The correlations between modeled asset values are derived from a multifactor model, using orthogonal factors such as regions, or industry indices, obtained using principal component analysis. Orthogonal factors facilitate the calculation of asset value correlations since they derive directly from the coefficients of the multifactor model.

Frequently, the universe of bank portfolios does not include such firms, and there is no modeling available of factor influences. This requires providing an estimate of the fraction of specific variance resulting from the error term (or, alternatively, of the variance from all common factors, which is general risk). In such a case, the specific risk becomes a control parameter of the model. The higher is the specific risk, the lower is the correlation effect and, conversely, increasing the systematic risk generates a higher correlation. The final loss distribution is very sensitive to the correlation effect, so that the control values used for systematic risk are important.

Moody's-KMV Portfolio Manager allows defining the ratio of systematic risk to total risk. The ratio of general risk to total risk is the *R2* of the multifactor regression model. Stressing this *R2* is equivalent to increasing the general risk and, therefore, the correlations. The "R-square" of the regression - measuring general risk - is the output of the multifactor model linking assets returns to factors. When inputting directly the default probability, this "R-square" is necessary since it defines the relative weights of specific versus general risk. It becomes an input rather than an output of the multifactor model in the KMV universe. When no fit is available, for private firms for example, it is necessary to specify the *R2* using for instance the average over all firms, which is the range of 20% to 30% for listed companies in the main stock exchanges. The "R-Square" can be used as a stress variable. For example, country risk creates a "contagion" effects on firms, increasing the correlation between defaults. A contagion scenario within a country would reflect in a higher than usual value of the "R-Square."

- [1] This presentation is derived from publications on Moody's-KMV Portfolio Manager and from Kealhofer in [45] and [46].