Bank's Portfolio Management under Uncertainty

By Samanta, Subarna K.; Mohamad-Zadeh, Ali H. | American Economist, Fall 1992 | Go to article overview

Bank's Portfolio Management under Uncertainty


Samanta, Subarna K., Mohamad-Zadeh, Ali H., American Economist


I. Introduction

Optimal bank-management is a continuous struggle of maintaining a balance between liquidity, profitability and risk. Banks need liquidity because such a large portion of their liabilities are payable on demand but typically an asset more liquid the less it yields. Thus, the decision to choose one combination of assets over another, given the liability size and capital accounts of a bank, would have a direct and significant effect on bank profitability, liquidity and risk.

The pioneering works of Markowitz (1952) and Tobin (1958, 1965) on the theory of portfolio selection have developed into analysis of several distinct areas.(1) One such area has been the theory of banking firm, where banks have been analyzed in a microeconomic firm-theoretical context. In such studies the authors, utilizing the neo-classical theory of the firm, have defined inputs, outputs and appropriate resource cost constraints of a typical profit maximizing bank and derived the optimal resource allocations under perfect or imperfect market conditions under certainty (Klein 1971, Pringle 1973, 1974, Tobin 1982) or uncertainty (Elysiani 1983). An alternative approach treats banks as rational investors or portfolio holders, and therefore, a portfolio choice framework has been employed for analyzing bank behavior (Aigner 1971, Hester and Pierce 1975). The Markowitz-Tobin model of portfolio selection has also been directly applied to financial institutions. Among these works Hart and Jaffer's study (1974) is notable. They, unlike others, have taken into account certain regulatory and institutional characteristics of financial institutions in their model. Although, the modeling of portfolio management is fairly well formulated, these models provide little practical applicability for a commercial bank operating under uncertain environment in the context of new developments in the financial markets such as wide use of federal funds market, repurchase agreement for maintaining the optimal reserve position and the deregulation of the existing deposit rate. The development of the federal fund opportunity and the evolving deregulations of financial markets have sparked interest in the economic implications of portfolio selections of the commercial banks in previously regulated and limited markets. Since the current literature lacks the analysis of optimal decision rules for a commercial bank under such new phenomena, this paper is an attempt to provide such rules, which can be used by other economic agents as well. Specifically, we intend to investigate the optimal asset management policies and examine the impact of the federal funds market and deposit rate deregulation.

The layout of the paper is as follows: Section two explains the model with relevant assumptions. In section three we obtain some comparative static results relating to the optimal decision rules by the bank and provide some economic explanations. Section four explains the impact of the deregulations on the deposit rate and also set up a more general model involving stochastic deposit loss as well as loss in the return from the loans extended by the bank. Concluding remarks are included in section five.

II. The Model

In this paper we examine the optimal strategic (asset and liability management) decision rules derived from the maximization of the expected utility from the net income of the bank. We first identify the important variables of the model given the relevant assumptions. An expected utility functions will be developed and optimal decision rules yielding expected utility maximizing portfolio will be derived.

It is assumed, for simplicity, that the bank has only one type of deposit, namely demand deposit. The type of assets that will be considered here are reserves, government securities and loans. The level of net worth (or equity capital) may be ignored (or included) since it is assumed to be constant in our analysis.

In addition, we assume that the level of demand deposit (or reserve) fluctuates over time due to unforeseen deposits or withdrawals by the public (or depositors). …

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