3.1 Investors/Depositors
Investors can either invest in illiquid securities (shares of the bank) or liquid
assets (deposits). They know that a limited-liablity bank has the incentive to
reduce portfolio quality at the expense of depositors (see Jensen and Meckling
(1976)). They would anticipate this behavior and demand higher deposit
rates. The breakeven return for the bank rises. The bank would, thus,
have higher incentive to decrease quality, thereby, increasing the expected
pay-off. In the worst case, the market for deposits would break down. The
bank could also try to credibly commit itself to a specified quality level
in order to lower its deposit rates. However, agency costs would accrue.
The existence of a regulator-supervisor simplifies this interaction. He forces
the limited-liability bank to take the depositors’ losses into account which
accrue in case of bankruptcy. Investors are assumed to be indifferent between
illiquid equity offering an expected rate of return of re and liquid deposits.
Depositors demand a fixed deposit rate, which I normalize to zero. As in case
of bankruptcy, depositors receive less than the amount initially deposited in
the bank, the expected rate of return on deposits is less than one. To capture
the preference of investors for liquidity most simply, I assume that re > 1.
3.2 Companies
Companies need funding from the bank to finance their investment projects.
I assume that banks are the only source of companies’ funding and have all
the bargaining power in negotiating financing with the companies. Banks
can, thus, capture as profit all the expected surplus from the loans.
3.3 Banks
At the start of the model, just prior to t0 , the bank has one outstanding
share and has no outstanding deposits. The bank’s only asset is access to
a segment of risky loans on the retail and interbank market with an innate
quality of q0. The objective of the bank is to maximize the value of its initial
equity share, its initial wealth. At t0, provided it has complied with the rules
established by the regulator, the bank can raise funds in the form of outside
equity E (a fraction z of the bank’s equity) and retail and interbank deposits
D.
The banks will then invest the proceeds L = E+D in loans to companies.
The portfolio size L is given by the market and is, thus, not subject to
neither the bank’s nor the regulator’s decision. The innate quality of the
risky projects is q0 with q0 ∈ [q,q] and the average rate of return on all