 2012 Royal Statistical Society 0964–1998/13/176635 J. R. Statist. Soc. A (2013) 176, Part 3, pp. 635–653 Measures of the economic value of probabilities of bankruptcy D. J. Johnstone and S. Jones, University of Sydney, Australia V. R. R. Jose Georgetown University, USA and M. Peat University of Sydney, Australia [Received April 2010. Final revision April 2012] Summary. Financial institutions and regulatory agencies direct much effort and expertise towards estimating probabilities of bankruptcy. By comparison, the techniques that are used to evaluate probability estimates have attracted little attention and remain somewhat ad hoc. The most common approach is to count misclassifications, based on an arbitrary classification threshold. Some use is made of conventional probability score functions, such as the Brier score (from meteorology) but these are not standard practice. Our purpose is to introduce a family of economic probability score functions designed to capture the utility obtained by a user, with a specified utility function, who uses the estimated probabilities to make hypothetical bets against a rival forecaster or model. The conceptual appeal of these score functions is that probability forecasts are evaluated neither in abstract, nor in isolation, but by whether they would hypo- thetically have ‘made money’ for a given user, with specified risk aversion, against comparable forecasts or market betting prices. Keywords: Baseline distribution; Economic forecast evaluation; Probability of bankruptcy; Scoring rules 1. Introduction Probability forecasting models applied to bankruptcy trace to Martin (1977) and Ohlson (1980). In recent years, driven partly by explicit modelling obligations imposed on banks by the Basel II accord, the bankruptcy forecasting literature has grown in both recognition and statistical sophistication. Note particularly the model forms that were introduced by Shumway (2001), Jones and Hensher (2004) and Duffie et al. (2007). Hillegeist et al. (2004) surveyed the literature and provided a thorough empirical comparison of the forecasting performance or informative- ness of the best established bankruptcy probability prediction models, including particularly Ohlson’s logistic regression model, discrete hazard models following Shumway (2001) and a form of the Black–Scholes–Merton (option-based) model, similar to the commercially well-known Moody’s ‘KMV’ proprietary model, e.g. Bharath and Shumway (2008). Address for correspondence: D. J. Johnstone, University of Sydney Business School, University of Sydney, Sydney, NSW 2006, Australia. E-mail: d.johnstone@econ.usyd.edu.au