Evaluating the Probability of Failure of a Banking Firm
We develop a dynamic model in which the probability of failure of an infinitely lived financial intermediary (bank) is determined endogenously as a function of observable state and policy variables. The bank takes into account the effect of the optimal policy (the interest on deposits, dividend payouts, risky investments) on the probability of failure, which in turn affects the bank's ability to extract deposits. With the aid of simulations we study the effect of variables such as bank size, the riskiness of the bank's investment opportunities, and reserve requirements on the bank's optimal policy and on its probability of failure. A major finding is that small banks choose policies that render them more risky than large banks. As the risks are correctly priced by depositors, rates offered by small banks incorporate substantial risk premia. Another interesting finding is that a tighter reserve requirement induces banks of all sizes to take fewer risks.
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