The at-Risk approach: a new tool for stress tests and overlays

We present a general framework, called at-Risk (aR) modelling, that is particularly useful for both macroprudential and microprudential stress testing. The aR approach is based on a two-step semi-parametric estimation procedure that allows us to forecast the full conditional distribution of a variable as a function of a set of observed factors at a given horizon. These density forecasts can then be used to produce coherent forecasts for any risk measure, such as Value-at-Risk (VaR), expected shortfall, or downside entropy. The aR approach was originally introduced by Adrian et al. (Am Econ Rev 109(4):1263–1289, 2019) to reveal the vulnerability of economic growth to financial conditions. It is now widely used by international financial institutions to provide VaR-type forecasts for various macroeconomic variables, such as GDP growth (i.e., Growth-at-Risk or GaR) or inflation (i.e., Inflation-at-Risk or IaR). Our contribution in this paper is twofold. First, we provide a detailed overview of the aR-type models and discuss various extensions. We also propose an R package that can be used to automatically produce density forecasts and downside risk forecasts. Second, we discuss the potential uses of aR-type models in the specific context of internal or regulatory (IRB) bank stress tests as well as in the governance and monitoring of overlays (IFRS9). The at-Risk models can generate density forecasts of the risk parameter (i.e., PD or LGD) at any horizon, surpassing the mere point forecasts produced by traditional time series models. An aR models can be used in three ways: as a scenario generator for macroeconomic or sectoral risk factors, as a conditional stress model, or as a tool for integrating new risk factors into a PD model, thereby enhancing the rationale behind overlay decisions. Finally, we propose two empirical applications to illustrate these uses, with one application intended for use on a portfolio of retail credits.