We design and analyze a model for aggregate performance measures of US residential mortgages based on publicly available information. The objective is to implement a top down stress testing framework at the macro level that can be compared with bottom up stress testing approaches that model loan performance at the loan level. We consider a class of simple auto-regressive time series models similar to those used by US banking supervisors under the Capital and Loss Assessment under Stress Scenarios (CLASS, Hirtle 2014).
First, we identify suitable aggregate performance measures of mortgage credit risk together with a set of macroeconomic variables. All data are publicly available for automatic download. Second, we implement a set of functions that explore and visualize the data including tests for stationarity and cointegration. Third, we address the diﬃcult problem of creating parsimonious and robust models for which practitioners can develop their own intuition. While the selection of a small number (1-3) of macro factors is often based on expert judgment, here we aim to implement data driven selection methods that can help experts in variable selection and model design. Fourth, we backtest the suite of models by calibrating against pre-crisis data and explore the stability of model selection and model parameters. Fifth, we highlight the suitability of Bayesian statistical methods to better capture model and forecast uncertainty.
The use of time series models for top down stress testing of bank performance data has received much attention from central banks and supervisors to investigate macro prudential stability. Recent contributions in the US include Hirtle (2014) and Kapinos (2014) and further references therein. The footnote of Kapinos (2014) cites a number of country studies conducted by central bank staﬀ across Europe. Some central banks have published explicit models for residential mortgages or secured household loans, however, each selecting a diﬀerent set of macroeconomic variables (e.g. the RAMSI model of the Bank of England, Burrows et al. 2012). For US data and the modeling of net charge-oﬀs of residential mortgages, Hirtle 2014 consider the annual change in house prices as sole explanatory variable. They use commercial property price changes for commercial real estate loans and model all other loan asset classes with the annual change in unemployment. Other researchers have used more than one macrovariable. For instance, Bermingham(2011)model Irish mortgage performance using household net worth, unemployment and the mortgage debt service payment whereas the RAMSI model of the Bank of England uses income gearing, undrawn equity and the unemployment rate to model the probability of default for secured loans to households (Burrows 2012). Other macro variables used to model aggregate mortgage default are the loan to value ratio of ﬁrst time buyers (Whitley 2005 in the UK), short term interest rates, GDP and the mortgage interest rate spread over a long term government bond yield (Alves 2012 in Portugal), or the growth of mortgage lending (Blanco 2012 in Spain). A pre-crisis analysis of aggregate US mortgage delinquencies by the IMF (GFSR 2008-2) used a residential property price index and a measure for lending conditions. We conclude from this brief overview that there is little consensus on how to design a top downstress testing model for residential mortgages. Diﬀerent stress tests focus on diﬀerent economic scenarios warranting diﬀerent model speciﬁcations and the availability of suitable macro variables diﬀer by country. For example, the loan to value ratio for ﬁrst time buyers is a common measure of credit availability in the UK, but is not available in many other European countries. From a statistical perspective it is unlikely that the diﬀerent model speciﬁcations suggested in the stress testing literature would perform equally well. In the following, we aim at establishing a framework for model selection and back testing that quantiﬁes the statistical performance of diﬀerent models, helps with model selection and validates the model based on out-of-sample predictive performance over a multi-year time horizon.