We propose a theory of financial intermediaries operating in markets influenced by investor sentiment. In our model, banks make loans, securitize these loans, trade in them, or hold cash. They can also borrow money, using their security holdings as collateral. We embed such banks in a stylized financial market, in which securitized loans may be mispriced, and investigate how banks allocate limited capital among the various activities, as well as how they choose their capital structure. Banks maximize profits, and there are no conflicts of interest between bank shareholders and creditors. The theory explains the cyclical behavior of credit and investment, but also accounts for the fundamental instability of banks operating in financial markets, especially when banks use leverage.