There is substantial evidence that new banks and rapidly growing banks are risk prone. We study this problem by designing a relationship-lending model in which a bank operates as a financial intermediary and centralised monitor. In the absence of deposit insurance, the bank's limited liability option creates an incentive problem between the bank and its depositors, the likely outcome of which is a reduction in the amounts of resources allocated to monitoring its borrowers. Hence, the bank must signal its safety to depositors by maintaining the equity ratio held. The optimal equity ratio is dynamic, ie new banks need relatively more equity than established banks, which enjoy profitable old lending relationships - charter value - that reduce the incentive problem. However, if an established bank grows rapidly, its share of old relationships also decreases and the bank will have to raise its equity ratio. With deposit insurance, regulators should set higher equity requirements for new banks and rapidly growing banks than for those in a more established position. The results of the model can be extended to more general inter-firm control of credit institutions.