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We consider how the introduction of centralized netting in financial networks affects total netted exposures between counterparties. In some cases there is a trade-off: centralized netting increases the expectation of net exposures, but reduces the variance. We show that the set of networks for which expected net exposures decreases is a strict subset of those for which the variance decreases, so the trade-off can only be in one direction. For some network structures, introducing centralized netting is never beneficial to dealers unless sufficient weight is placed on reductions in variance. This may explain why, in the absence of regulation, traders in a derivatives network do not develop central clearing. Our results can be used to estimate margin requirements and counterparty risk in financial networks. We also provide techniques to evaluate the robustness of our results to behavioral responses to the introduction of centralized netting.