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In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test to detect when tail dependence is truly high-dimensional and bivariate simplifications would produce misleading results. This occurs when a significant portion of the multivariate dependence structure in the tails is of higher dimension than two. Our test statistic is based on a decomposition of the stable tail dependence function, which is standard in extreme value theory for describing multivariate tail dependence. The asymptotic properties of the test are provided and a bootstrap based finite sample version of the test is suggested. A simulation study documents the good performance of the test for standard sample sizes. In an application to international government bonds, we detect a high tailrisk and low return situation during the last decade which can essentially be attributed to increased higherorder tail risk. We also illustrate the empirical consequences from ignoring higher-dimensional tail risk., address = Amsterdam and Rotterdam, author = Carsten Bormann and Melanie Schienle and Julia Schaumburg, copyright = http://www.econstor.eu/dspace/Nutzungsbedingungen, keywords = C12; C19; 330; decomposition of tail dependence; multivariate extreme values; stable tail dependence function; subsample bootstrap; tail correlation, language = eng, number = 14-024/III, publisher = Tinbergen Institute, title = A Test for the Portion of Bivariate Dependence in Multivariate Tail Risk, type = Tinbergen Institute Discussion Paper, url = https://hdl.handle.net/10419/98883, year = 2014