A Basic Asymptotic Test for Value-at-Risk Subadditivity

An asymptotic hypothesis test for value-at-risk subadditivity is introduced and studied. The test is derived based on an equivalent formulation of the value-at-risk subadditivity inequality in terms of the distribution of the underlying risks’ sum. Its size is considered mathematically, and its power and p-value are studied empirically for different dependence structures, strength of dependence, marginal distributions, sample sizes, number of risks and value-at-risk confidence levels.