  Motivated by the Basel 3 regulations, recent studies have considered joint
forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring
functions can be used to evaluate forecast performance in this context.
However, little intuitive or empirical guidance is currently available, which
renders the choice of scoring function awkward in practice. We therefore
develop graphical checks (Murphy diagrams) of whether one forecast method
dominates another under a relevant class of scoring functions, and propose an
associated hypothesis test. We illustrate these tools with simulation examples
and an empirical analysis of S&P 500 and DAX returns.
