مدیریت نقدینگی بهینه و سیاست نجات در صنعت بانکداری

We characterize the profit-maximizing reserves of a commercial bank, and the generated probability of a liquidity crisis, as a function of the penalty imposed by the Central Bank, the probability of depositors' liquidity needs, and the return on outside investment opportunities. We demonstrate that banks do not fully internalize the social cost associated with the bail-out policy if the liquidity needs of individuals are correlated, and that competitive interbank markets will induce banks to raise their reserves under reasonable conditions. The marginal benefits from an interbank market decrease as the correlation between the liquidity shocks of banks increases.

The literature on demand deposits has focused on liquidity crises generated by expectation-driven panics, but it has not offered any general method for calculating the probability of bank runs generated by a realization of liquidity needs by a large, but finite, number of depositors. Therefore, in this article we propose a method for calculating the probability of realizing a liquidity crisis and we characterize banks' optimal reserve ratio assuming that depositors face real liquidity needs as opposed to rumors or panics concerning a liquidity crisis. We determine the optimal response of a commercial bank to the interest rate (penalty rate) at which the Central Bank offers liquidity. We further delineate the socially optimal bail-out policy and show that the commercial bank does not fully internalize the social costs of a liquidity crisis. In particular, we establish that the socially optimal penalty rate is increasing in the correlation of the liquidity shocks facing depositors. Finally, we explore the implications of interbank markets. We prove that access to an interbank market will typically induce competing banks to raise their reserve holdings, as the interbank market offers an opportunity to benefit from potential liquidity needs of competing banks in a situation where the bank has excess reserves. However, the marginal benefits to banks from an interbank market are shown to decrease in response to an increase in the correlation between the liquidity shocks of banks. The existing banking literature views the depository institutions as “pools of liquidity” providing consumers with insurance against idiosyncratic liquidity shocks. In the influential model by Diamond and Dybvig (1983), banks provide liquidity to depositors who are, ex ante, uncertain about their intertemporal preferences with respect to consumption sequences. They demonstrate how deposit contracts offer insurance to consumers and how such contracts can support a Pareto efficient allocation of risk. However, as they show, there exists a second, inefficient Nash equilibrium where the interaction between pessimistic depositor expectations generates a liquidity crisis. Such liquidity crises confronting individual banks may trigger socially costly bank panics. Against this background, most countries apply explicit or implicit deposit insurance policies as a mechanism for the elimination of inefficient Nash equilibria driven by pessimistic expectations. Despite the indisputable insurance benefits, empirical observations as well as theoretical research convincingly demonstrate how federal deposit insurance will encourage banks to engage in excessive risk taking and to keep lower levels of liquid reserves than what would be socially optimal (cf. Cooper and Ross, 1998). Consequently, researchers have systematically investigated mechanisms other than deposit insurance as instruments for reducing the instability of the banking system. Bhattacharya et al. (1998) categorize those regulatory measures.1 In addition, all policy commitments relative to distressed financial institutions face a severe time-consistency problem as governments and Central Banks seem to have an incentive of bailing out distressed financial institutions with the intention of eliminating potential contagion problems (e.g. Chen, 1999). Freixas (1999) investigates such bail-out policies. A meaningful evaluation of all policy measures directed towards the banking industry rely on the knowledge of how ex-ante uncertain liquidity needs translate into probabilities of realizing liquidity crises and of how the characteristics of this transmission mechanism interacts with banks' optimal allocation of their portfolios between liquid low-yield assets and illiquid high-yield investments. In this paper we delineate the bank's optimal liquidity management and characterize how the profit-maximizing reserves adjust to the interest rate applied by the Central Bank for liquidity provision to a bank facing a liquidity crisis. In particular, the optimal reserves are found to be an increasing function of the correlation between the liquidity shocks facing individual depositors. As Holmström and Tirole (1998) show, the private sector cannot satisfy its own liquidity needs when aggregate uncertainty dominates the liquidity shocks. In our study we characterize the socially optimal interest rate (denoted penalty rate) to charge from banks facing a liquidity crisis. We find the socially optimal penalty rate to be an increasing function of the correlation between the liquidity shocks facing depositors. Thus, the private banking industry fails to fully internalize the full social costs of public liquidity provision. Our study is organized as follows. Section 2 presents our model and characterizes the bank's optimal liquidity management. In Section 3 we carry out a welfare analysis and delineate the socially optimal bail-out policy. In Section 4 we explore the effects of introducing an interbank market. Section 5 concludes.

This paper analyzes a banking industry with liquidity risks caused by depositors facing uncertain liquidity needs. We develop a method for calculating the profit-maximizing amount of reserves of a representative bank, and characterize the associated probability of a liquidity crisis. We show that the only information needed to predict the probability of a liquidity crisis is the cost of maintaining reserves and the penalty rate charged to a bank facing a run. Within the framework of our welfare analysis we delineated a characterization of the socially optimal penalty rate, which, by taking the optimal response of the banking industry into account, will determine the socially optimal fraction of reserves. Importantly, this socially optimal penalty rate was found to be an increasing function of the correlation between the liquidity shocks facing depositors. Indeed, as was established in our analysis, the private banking industry will have an incentive to adjust the reserves upwards when facing an increased correlation, but this incentive will for structural reasons be too weak from a social point of view. Namely, the banking industry does not fully internalize the increasing social costs associated with a need to raise additional liquidity in order to support a more extensive bail-out program. We further demonstrated that access to an interbank market will induce competing banks to raise their reserve holdings under reasonable conditions. However, the marginal benefits from an interbank market was shown to decrease as a function of the correlation between the liquidity shocks of banks. The expected profit of the bank (1) could be formulated in alternative ways. An example of a plausible reformulation of (1) would be: equation(28) View the MathML source where the interest on the principal withdrawn in period 1 would be paid at the end of period one. In such an alternative setting the probability of a bank run would be unchanged, but the optimal reserves must be scaled up with the coefficient (1+gd). However, the qualitative findings of our analysis are easily adapted to such an alteration.