  Conditional forecasts of risk measures play an important role in internal
risk management of financial institutions as well as in regulatory capital
calculations. In order to assess forecasting performance of a risk measurement
procedure, risk measure forecasts are compared to the realized financial losses
over a period of time and a statistical test of correctness of the procedure is
conducted. This process is known as backtesting. Such traditional backtests are
concerned with assessing some optimality property of a set of risk measure
estimates. However, they are not suited to compare different risk estimation
procedures. We investigate the proposal of comparative backtests, which are
better suited for method comparisons on the basis of forecasting accuracy, but
necessitate an elicitable risk measure. We argue that supplementing traditional
backtests with comparative backtests will enhance the existing trading book
regulatory framework for banks by providing the correct incentive for accuracy
of risk measure forecasts. In addition, the comparative backtesting framework
could be used by banks internally as well as by researchers to guide selection
of forecasting methods. The discussion focuses on three risk measures,
Value-at-Risk, expected shortfall and expectiles, and is supported by a
simulation study and data analysis.
