Aggregation Level in Stress-Testing Models

Abstract

We explore the question of optimal aggregation level for stress testing models when the stress test is specified in terms of aggregate macroeconomic variables, but the underlying performance data are available at a loan level. Using standard model performance measures, we ask whether it is better to formulate models at a disaggregated level (“bottom up”) and then aggregate the predictions in order to obtain portfolio loss values or is it better to work directly with aggregated models (“top down”) for portfolio loss forecasts. We study this question for a large portfolio of home equity lines of credit. We conduct model comparisons of loan-level default probability models, county-level models, aggregate portfolio-level models, and hybrid approaches based on portfolio segments such as debt-to-income (DTI) ratios, loan-to-value (LTV) ratios, and FICO risk scores. For each of these aggregation levels we choose the model that fits the data best in terms of in-sample and out-of-sample performance. We then compare winning models across all approaches. We document two main results. First, all the models considered here are capable of fitting our data when given the benefit of using the whole sample period for estimation. Second, in out-of-sample exercises, loan-level models have large forecast errors and underpredict default probability. Average out-of-sample performance is best for portfolio and county-level models. However, for portfolio level, small perturbations in model specification may result in large forecast errors, while county-level models tend to be very robust. We conclude that aggregation level is an important factor to be considered in the stress-testing model design.