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I came across an example where a well-known weakness of a credit risk model was dealt with by augmenting some of the existing risk factors via increased factor loadings. This made the the model more conservative in terms of the required economic capital it recommended. What does that mean? Is it a matter of increasing the estimated coefficients by some arbitrary percentage or is there more to it? |
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"Factor loading" is a somewhat ambiguous phrase -- it could refer to the factors in a linear model (e.g. the beta in CAPM or extended linear stock models), the factors of principal component analysis, etc. If you could provide a reference to the exact example/paper it would be clearer. In credit, however, a likely interpretation is the loadings of different macroeconomic variables and firm-specific risk components within a Cox Framework model. The Cox Framework is a generalized stochastic analysis framework where the default trigger level of a particular credit/firm is uniformly distributed, and the countdown process is controlled by a strictly decreasing firm specific function such that the firm defaults once this countdown process falls below the trigger level. Increasing the "loadings" of the risk factors within the countdown process would increase the speed at which the countdown process decreases and therefore cause the firm to default more quickly/frequently in the model. This would be one way of making a Cox-based credit model more conservative. (How much more conservative, and how to build the firm-specific countdown process realistically in the first place can be more art than exact science). For more information, the Cox framework is treated in some detail in several credit textbooks. |
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In many popular copula models a factor driving a certain even (e.g. default) has the form $ Y_i = \sum_k a_{ik} X_k + b_i Z_i $ where $\lbrace X_k \rbrace, Z_i$ are independent random factors. Coefficients $a_{ik}$ and $b_i$ are commonly called "factor loadings". |
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