We develop a model of banks' asset value dynamics in a centrally cleared market with endogenous trading interactions. We show that banks have a unique equilibrium allocation of funds between their trading capitals and operating assets when they adjust trading positions to hedge against excess risk from their business operations. We analyze the resulting asset value processes and show that asset value concentration has the inherent tendency to increase. Our analysis points to a trade off between diversity in banks' asset values and diversification in banks' asset holdings. We investigate the impact of policies aimed at controlling asset value concentration as well as the effect of capital injections on market collateral demand.