Counterparty risk could hamper trade and worsen a financial crisis. A central clearing party (CCP) insures traders against counterparty default and thus benefits trade. Default of the CCP however becomes a new systemic risk. CCP risk management does not account for risks associated with crowded positions. This paper proposes a CCP exposure measure based on tail risk in trader portfolios. It identifies and measures crowded risk and assigns it to traders according to the polluter pays principle. CCP data show that crowded positions increase CCP exposure most (about one-third) on turbulent days, when exposure is high already.