Goodness-of-Fit of Logistic Regression of the Default Rate on GDP Growth Rate and on CDX Indices

Abstract

Under the Basel II and Basel III agreements, the probability of default (PD) is a key parameter used in calculating expected credit loss (ECL), which is typically defined as: PD × Loss Given Default × Exposure at Default. In practice or in regulatory requirements, gross domestic product (GDP) has been adopted in the PD estimation model. Due to the problem of excessive fluctuation and highly volatile ECL estimation, models that produce satisfactory PD and thus ECL estimations in the context of existing risk management techniques are lacking. In this study, we explore the usage of the credit default swap index (CDX), a market’s expectation of future PD, as a predictor of the default rate (DR). By comparing the goodness-of-fit of logistic regression, several conclusions are drawn. Firstly, in general, GDP has considerable explanatory power for the default rate which is consistent with current models in practice. Secondly, although both GDP and CDX fit the DR well for rating B class, CDX has a significantly better fit of DR for ratings [A, Baa, Ba]. Thirdly, compared with low-rated companies, the relationship between the DR and GDP is relatively weak for rating A. This phenomenon implies that, in addition to using macroeconomic variables and firm-specific explanatory variables in the PD estimation model, high-rated companies exhibit a greater need to use market supplemental information, such as CDX, to capture the changes in the DR.

Impact of COVID-19 on the Robustness of the Probability of Default Estimation Model

“…In studying the fit performance of a PD model, Hu et al [31] concluded that high-rated companies exhibit a greater need to use market-traded information, such as the CDX, to capture changes in the DR. The similarities and differences between this paper and that of Hu et al [31] are as follows. A logistic regression model was used as the underlying PD model in both papers.…”

“…In addition, Moody's DR and the IMF's GDP datasets were used in both papers with different time periods. The paper from Hu et al [31] was motivated by observing the poorly fitted results of the PD model with GDP determinants, whereas this paper is motivated by observing the extreme mismatch between the behaviour of GDP and DR over 2020. The main criteria of model comparison used by Hu et al [31] were p values and AIC, whereas we primarily use Cook's distance and AIC increasing ratio (see Section 3.2).…”

“…The paper from Hu et al [31] was motivated by observing the poorly fitted results of the PD model with GDP determinants, whereas this paper is motivated by observing the extreme mismatch between the behaviour of GDP and DR over 2020. The main criteria of model comparison used by Hu et al [31] were p values and AIC, whereas we primarily use Cook's distance and AIC increasing ratio (see Section 3.2). The empirical results registered by Hu et al [31] related to goodnessof-fit, especially for the companies from higher rated classes, whereas we, mainly, have determined the impact on PD and, thus, ECL estimation through outlier observation.…”

“…The main criteria of model comparison used by Hu et al [31] were p values and AIC, whereas we primarily use Cook's distance and AIC increasing ratio (see Section 3.2). The empirical results registered by Hu et al [31] related to goodnessof-fit, especially for the companies from higher rated classes, whereas we, mainly, have determined the impact on PD and, thus, ECL estimation through outlier observation. In other words, the results of the PD model (with GDP determinant) revealed a serious lack of robustness in the 2020 data originating from COVID-19.…”