This talk summarizes recent joint work with Tobias Fissler on the use of multivariate loss functions in forecast evaluation. Statistical functionals (e.g., mean, variance, quantiles) for which such multivariate loss functions exist are termed multi-objective elicitable. We discuss two applications.

First, we show that many systemic risk measures (such as CoVaR) are not elicitable in the usual sense, i.e., no suitable univariate loss functions exist. However, bivariate (multi-objective) loss functions exist that allow for meaningful comparisons of systemic risk forecasts. Second, we demonstrate that while copula forecasts can be evaluated jointly with the marginals using standard methods, this does not allow practitioners to distinguish between the quality of the copula component only. Yet, by using suitable bivariate loss functions, such an attribution becomes feasible.