Motivated by the nice characterization of copulas A for which d∞(A, At) is maximal as established independently by Nelsen  and Klement & Mesiar , we study maximum asymmetry with respect to the conditioning-based metric D1 going back to Trutschnig . Despite the fact that D1(A, At) is generally not straightforward to calculate, it is possible to provide both, a characterization and a handy representation of all copulas A maximizing D1(A, At). This representation is then used to prove the existence of copulas with full support maximizing D1(A, At). A comparison of D1- and d∞-asymmetry including some surprising examples rounds off the paper.
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