This paper is concerned with evaluating value at risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Maganelli (2004) are based on such variables. In this paper we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker & Xiao, 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series.

The departure from the traditional concern with the central tendency is in line with the increasing recognition that an assessment of the degree of uncertainty surrounding a point forecast is indispensable (Clements 2004). We propose an econometric model to estimate the conditional density without relying on assumptions about the parametric form of the conditional distribution of the target variable. The methodology is applied to the U.S. unemployment rate and the survey of professional forecasts. Specification tests based on Koenker and Xiao (2002) and Gaglianone et al. (2011) indicate that our approach correctly approximates the true conditional density.

a b s t r a c tThis paper investigates macro stress testing of system-wide credit risk with special focus on the tails of the credit risk distributions conditional on adverse macroeconomic scenarios. These tails determine the ex-post solvency probabilities derived from the scenarios. This paper estimates the macro-credit risk link by the traditional Wilson (1997a,b) model as well as by an alternative proposed quantile regression (QR) method (Koenker and Xiao, 2002), in which the relative importance of the macro variables can vary along the credit risk distribution, conceptually incorporating uncertainty in default correlations. Stress-testing exercises on the Brazilian household sector at the one-quarter horizon indicate that unemployment rate distress produces the most harmful effect, whereas distressed inflation and distressed interest rate show higher impacts at longer periods. Determining which of the two stress-testing approaches perceives the scenarios more severely depends on the type of comparison employed. The QR approach is revealed more conservative based on a suggested comparison of vertical distances between the tails of the conditional and unconditional credit risk cumulative distributions.

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