A New Approach to Backtesting and Risk Model Selection

Backtesting risk measures represents a challenge and complex methods are often required. In this paper, we propose a new framework for backtesting that can be applied to every law invariant risk measures. We base our approach on the formalization of the concept of level of coverage associated with the risk model as defined in the original Basel Accord. Thus, we propose two simple hypothesis tests based only on results of probability theory without requiring any approximation or simulation. In addition, within this new framework, we introduce a methodology for selecting the best performing risk model among all the existing alternatives. This proposal adds value to the current state of the art, since, using the traditional loss function approach, any comparison among forecasting outcomes of different risk models appeared to be meaningless. A series of simulation studies show that our hypothesis tests provide similar size and power to the classical binomial tests of value at risk and well-known tests of expected shortfall. A final experiment on real data allows determining the best risk measure procedures among the value at risk, expected shortfall, expectiles and lambda value at risk in different time windows over more than 40 years of daily data