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August 2010

Multiperiod Corporate Default Prediction - A Forward Intensity Approach

A working paper by Prof. Jin-Chuan Duan, (Risk Management Institute and Department of Finance, National University of Singapore), Jie Sun (Risk Management Institute, National University of Singapore) and Tao Wang (Department of Finance, National University of Singapore)

Prof. Jin-Chuan Duan together with his co-authors, Sun and Wang, recently finished their working paper titled "Multiperiod Corporate Default Prediction - A Forward Intensity Approach". In this paper, they proposed a forward intensity approach for the prediction of corporate defaults over different future periods. The model is also amenable to aggregation, which allows analysts to assess default behavior at the portfolio and/or economy level.

Understanding the term structures of default probabilities is critical to credit risk management, macro policy making and financial regulation. Firms may have totally different short-term and long-term credit risk profiles due to their debt structures, liquidity positions and other attributes. For example, firm A can present a smaller credit risk vis-á-vis firm B in next three months due to its healthy cash position, but at the same time be a bigger credit risk over next two years simply because of its dismal profit prospect. Major credit rating agencies usually provide both short-term and long-term corporate credit ratings. However, the terms are vaguely defined and not refined enough. The academic literature has also been lacking as far as the term structure of defaults is concerned.

In order to assess a company's credit risk for different time horizons, the paper develops a forward intensity model which takes into account both defaults/bankruptcies and other types of firm exits such as mergers and acquisitions. The model is an extension of the traditional Poisson intensity model which is built upon the instantaneous rate of event occurrence called instantaneous intensity. The time-series dynamics of the state variables in the traditional Poisson intensity model need to be specified for the purpose of multiperiod default prediction. As an example, modeling 1000 firms using two common risk factors and four firm-specific attributes will require the analyst to specify the joint dynamics for 4002 state variables, a formidable modeling challenge. The forward intensity approach by Duan, Sun and Wang, however, models the forward rate of event occurrence directly which avoids estimating the high-dimensional time-series dynamics of the state variables. The forward intensity approach can be implemented by maximum likelihood estimation. Particularly attractive is the fact that the likelihood function is decomposable to independent components, making it numerically easier in estimation.

The authors implemented the model based on a large sample of U.S. listed companies (both industrial and financial) covering more than 12,000 firms and over 1,000,000 firm-month observations for the period 1991 to 2009. They examined the effects of several frequently used macroeconomic factors and firm-specific attributes on companies' one-month forward default probabilities starting one month ahead to as long as thirty-six months ahead. They found that a firm's leverage, liquidity, profitability and volatility are four important attributes affecting its forward default probabilities for almost all the horizons considered in the paper. Interestingly, the empirical results suggested that large companies seem to be able to delay defaults, but cannot fully avoid defaults simply because of the size advantage. They also discovered that trends in most firm-specific attributes play an equally important role. For example, a firm with high leverage is more likely to default. If the high leverage is part of a growing trend, then it makes the firm even more susceptible to default.

The forward intensity model can be applied to study portfolio behavior. As reported in the paper, the predicted number of defaults is quite close to the actual numbers of defaults for the U.S. corporate sector over the intended period when the prediction period is one and three months. For longer prediction periods, the performance is not as good but is still able to reflect the overall default pattern over the past twenty years.

The paper also examines the prediction accuracy based on the commonly employed cumulative accuracy profile and accuracy ratio. The forward intensity approach is able to generate accurate predictions for short horizons. The accuracy ratios drop as the horizon increases but still remain reasonable. The results are robust to different out-of-sample tests.

The authors also used Lehman Brothers as an illustrative example to check whether the term structure of predicted default probabilities is informative. The analysis reveals that three months prior to Lehman Brother's filing of Chapter 11 bankruptcy, the model has already suggested a substantially raised term structure of default probabilities.

In summary, this paper offers a reduced-form model for predicting corporate defaults/bankruptcies over different prediction horizons. The model is able to provide accurate predictions and useful analysis for term structures of corporate default probabilities.

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Editor: Ivy Wang (rmiwy@nus.edu.sg)