Ruey-Ching Hwang

Predicting bankruptcy using the discrete-time semiparametric hazard model

The usual bankruptcy prediction models are based on single-period data from firms. These models ignore the fact that the characteristics of firms change through time, and thus they may suffer from a loss of predictive power. In recent years, a discrete-time parametric hazard model has been proposed for bankruptcy prediction using panel data from firms. This model has been demonstrated by many examples to be more powerful than the traditional models. In this paper, we propose an extension of this approach allowing for a more flexible choice of hazard function. The new method does not require the assumption of a parametric model for the hazard function. In addition, it also provides a tool for checking the adequacy of the parametric model, if necessary. We use real panel datasets to illustrate the proposed method. The empirical results confirm that the new model compares favorably with the well-known discrete-time parametric hazard model.

Predicting recovery rates using logistic quantile regression with bounded outcomes

Logistic quantile regression (LQR) is used for studying recovery rates. It is developed using monotone transformations. Using Moody’s Ultimate Recovery Database, we show that the recovery rates in different partitions of the estimation sample have different distributions, and thus for predicting recovery rates, an error-minimizing quantile point over each of those partitions is determined for LQR. Using an expanding rolling window approach, the empirical results confirm that LQR with the error-minimizing quantile point has better and more robust out-of-sample performance than its competing alternatives, in the sense of yielding more accurate predicted recovery rates. Thus, LQR is a useful alternative for studying recovery rates.

Forecasting credit ratings with the varying-coefficient model

The dynamic ordered varying-coefficient probit model (DOVPM) is proposed as a model for studying credit ratings. It is constructed by replacing the constant coefficients of firm-specific predictors in the dynamic ordered probit model (DOPM) of Blume, Lim and MacKinlay (1998) with the smooth functions of macroeconomic variables. Thus, the proposed model allows the effects of firm-specific predictors on credit risk to change with macroeconomic dynamics as investigated by Pesaran, Schuermann, Treutler and Weiner in 2006. The unknown coefficient functions in DOVPM are estimated using a local maximum likelihood method. Real data examples for studying credit ratings are used to illustrate the proposed model. Our empirical results show that macroeconomic dynamics significantly affect the sensitivities of firm-specific predictors on credit ratings, and there are nonlinear relationships between them. Comparing the out-of-sample performance of DOPM and DOVPM using an expanding rolling window approach, our empirical results confirm that the advantages of DOVPM over DOPM are twofold. First, the out-of-sample firm-by-firm rating probabilities predicted by DOVPM are more accurate and robust. Second, the out-of-sample total error rates of the prediction rule based on DOVPM are not only of smaller magnitudes but also of lower volatility. Thus, the proposed DOVPM is a useful alternative for credit rating forecasting.

On estimation and prediction for temporally correlated longitudinal data

Abstract In this paper, from a Bayesian point of view, we consider estimation of parameters and prediction of future values for the longitudinal model proposed by Diggle (1988. Biometrics 44, 959–971). This model, called the repeated measures linear model, incorporates group mean, variability among individuals, serial correlation within an individual, and measurement error. Two different priors are employed by the Bayesian approach, one is the noninformative prior and the other is composed of inverse gamma distributions. Given the noninformative prior, it is shown that the resulting approximate estimates of the regression coefficients are the same as those derived by the restricted maximum likelihood estimation. Markov chain Monte Carlo methods are also used to obtain more accurate Bayesian inference for parameters as well as prediction of future values. For parameter estimation and prediction of future values, the advantages of the Bayesian approach over the maximum likelihood method and the restricted maximum likelihood method are demonstrated by both real and simulated data.

DOUBLE SMOOTHING ESTIMATION OF THE MULTIVARIATE REGRESSION FUNCTION IN NONPARAMETRIC REGRESSION

ABSTRACT In the case of the random design nonparametric regression, the double smoothing technique is applied to estimate the multivariate regression function. The proposed estimator has desirable properties in both the finite sample and the asymptotic cases. In the finite sample case, it has bounded conditional (and unconditional) bias and variance. On the other hand, in the asymptotic case, it has the same mean square error as the local linear estimator in Fan (Design-Adaptive Nonparametric Regression. Journal of the American Statistical Association 1992, 87, 998–1004; Local Linear Regression Smoothers and Their Minimax Efficiencies. Annals of Statistics 1993, 21, 196–216). Simulation studies demonstrate that the proposed estimator is better than the local linear estimator, because it has a smaller sample mean integrated square error and gives smoother estimates.

Predicting issuer credit ratings using generalized estimating equations

The dynamic ordered probit model (DOPM) with autocorrelation structure is proposed as a model for credit risk forecasting. It is more appropriate than the DOPM with independence structure, because correlations among repeated credit ratings have been observed by Altman and Kao [J. Financ. Anal., 1992, 48, 64–75] and Parnes [Financ. Res. Lett., 2007, 4, 217–226]. The unknown parameters in the proposed model are estimated by a generalized estimating equations (GEE) approach (Lipsitz et al. [Statist. Med., 1994, 13, 1149–1163]). The GEE approach has been applied in many applications to analyse correlated repeated data due to its less-stringent distributional assumptions and robustness properties. Real data examples are used to illustrate the proposed model. The empirical results confirm that the proposed model compares favorably to the usual DOPM with independence structure, in the sense that the out-of-sample total error rate produced by the former is not only of smaller magnitude, but also of lower volatility. Thus the proposed model is a useful alternative for credit risk forecasting.

A logistic regression point of view toward loss given default distribution estimation

We propose a new procedure to estimate the loss given default (LGD) distribution. Owing to the complicated shape of the LGD distribution, using a smooth density function as a driver to estimate it may result in a decline in model fit. To overcome this problem, we first apply the logistic regression to estimate the LGD cumulative distribution function. Then, we convert the result into the LGD distribution estimate. To implement the newly proposed estimation procedure, we collect a sample of 5269 defaulted debts from Moody’s Default and Recovery Database. A performance study is performed using 2000 pairs of in-sample and out-of-sample data-sets with different sizes that are randomly selected from the entire sample. Our results show that the newly proposed procedure has better and more robust performance than its alternatives, in the sense of yielding more accurate in-sample and out-of-sample LGD distribution estimates. Thus, it is useful for studying the LGD distribution.

Forecasting forward defaults: a simple hazard model with competing risks

A forward default prediction method based on the discrete-time competing risk hazard model (DCRHM) is proposed. The proposed model is developed from the discrete-time hazard model (DHM) by replacing the binary response data in DHM with the multinomial response data, and thus allowing the firms exiting public markets for different causes to have different effects on forward default prediction. We show that DCRHM is a reliable and efficient model for forward default prediction through maximum likelihood analysis. We use actual panel data-sets to illustrate the proposed methodology. Using an expanding rolling window approach, our empirical results statistically confirm that DCRHM has better and more robust out-of-sample performance than DHM, in the sense of yielding more accurate predicted number of forward defaults. Thus, DCRHM is a useful alternative for studying forward default losses on portfolios.

Forecasting Credit Ratings by the Pairwise Classifier

Multiclass classification models are important to the prediction of credit ratings. In this paper, we propose a pairwise classifier to predict credit ratings. Our basic approach is to first convert the multiclass classification problem into multiple two-class classification problems, and then the final prediction rule is obtained by aggregating the results from multiple two-class predictions. We present some empirical results to show that such pairwise classifier significantly improves the prediction accuracy rates from 65% to 75%.

A NEW VERSION OF THE LOCAL CONSTANT M-SMOOTHER

ABSTRACT In the case of the equally spaced fixed design nonparametric regression, the local constant M-smoother (LCM) in Chu, Glad, Godtliebsen, and Marron [1] has the interesting property of jump-preserving. However, it suffers from the problem of boundary effects. To correct for such adverse effects on the LCM, Rue, Chu, Godtliebsen, and Marron [2] apply the local linear fit to the “inside” of the kernel function, and propose the local linear M-smoother (LLM). Unfortunately, the LLM is more sensitive to random fluctuations, since an extra tuning parameter is included. To avoid such a practical drawback to the LLM, we propose a new version of the LCM by applying the local linear fit to the “outside” of the kernel function. Our proposed estimator employs both the same tuning parameter associated with the ordinary LCM and the same weights assigned to the observations by the local linear smoother in Fan 3-4. It has the same asymptotic mean square error as the LLM. In practice, it can be calculated by using the fast computation algorithm designed for the ordinary LCM by Chu et al. [1], and does not suffer from the drawback to the LLM. More importantly, our results obtained for the new version of the LCM in the one-dimensional case can be extended directly to the multidimensional case. Simulation studies demonstrate that the asymptotic effects hold for reasonable sample sizes.