When CDS insurance on disjoint loss tranches of an index of credit-risky assets is offered, insurance on the whole basket can be aquired by entering into one insurance contract for each and every tranche. Alternatively, one may buy such insurance more directly in terms of entering into a so-called portfolio index CDS contract. In economic terms the two investments appear to be equivalent (except for small technical differences), and hence should come at a similar price. If this is not the case, one may sell the more expensive of the two investments and buy the cheaper in order to log in a seemingly risk-free gain. This investment strategy is known as “tranche round trip” in the marketplace. However, we point out that if the standardized running coupons of the tranche contracts differ, the two investment strategies might be far from being equivalent. In particular, the former depends both on the idiosyncratic default probabilities of the credit-risky assets and the dependence structure between the assets, while the latter index CDS contract is completely unaffected by the dependence structure.