Forecasting expected and unexpected losses

BIS Working Papers  |  No 913  | 
21 December 2020



To align banks' loss-absorbing resources with actual risks, new regulation features forward-looking elements. Namely, recently adopted provisioning standards seek to align the amount of assets that banks write down with the level of expected future losses (EL), which may vary over time. In parallel, capital requirements are set to generate resources for time-varying unexpected losses (UL), or the extent to which EL may be exceeded in extreme scenarios.

Even though EL and UL are complementary aspects of the same loss distribution, the literature has studied them separately. It has been largely pessimistic about the feasibility of reliable forecasts that flag turning points of EL in advance. And existing UL forecasts are only indirect, stemming from early warning indictors of banking crises.


We extend the model behind the Basel III requirements for credit risk in order to study forecasts of a loss distribution that transitions between boom and bust phases. While improved forecasts of the phase-switching risk factor should lead to adjustments to both EL and UL forecasts, the degree of diversification in the portfolio determines whether these adjustments should be in the same or opposite directions. In addition, forecasting either EL or UL carries information about the other aspect of the loss distribution.

This leads us to develop an empirical framework for forecasting EL and UL jointly and in real time ("out of sample"). On the basis of variables from the loss-rate literature and traditional financial-cycle indicators, we forecast the mean and variance of loan-portfolio losses over individual quarters, up to three years in the future. Then we develop and apply a methodology for aggregating these forecasts across quarters in order to construct EL and UL over the portfolio's lifetime. To the best of our knowledge, we propose the first real-time UL forecasts. Finally, we assess alternative results that stem from different forecast variables and econometric specifications.


We apply our methodology to US data on quarterly loan-loss rates from 1985 to 2019, confirming that there are benefits from forecasting EL and UL jointly. We find that financial-cycle indicators – notably the debt service-to-income ratio and the deviation of the credit-to-GDP ratio from its real-time trend – deliver reliable forecasts, as they signal turning points up to three years in advance. Given this long lead, provisions and capital that reflect such forecasts would help reduce the procyclicality of banks' loss-absorbing resources.


Extending a standard credit-risk model illustrates that a single factor can drive both expected losses and the extent to which they may be exceeded in extreme scenarios, ie "unexpected losses." This leads us to develop a framework for forecasting these losses jointly. In an application to quarterly US data on loan charge-offs from 1985 to 2019, we find that financial-cycle indicators – notably, the debt service ratio and credit-to-GDP gap – deliver reliable real-time forecasts, signalling turning points up to three years in advance. Provisions and capital that reflect such forecasts would help reduce the procyclicality of banks' loss-absorbing resources.

JEL Codes: G17, G21, G28

Keywords: loss rate forecasts, cyclical turning points, expected loss provisioning, bank capital