Commercial Bank Portfolio Behavior and Endogenous Uncertainty

Abstract

This paper demonstrates how Bayesian information may be analyzed as a variable input in determining an optimal bank portfolio and investigates the impact of information in a way that is statistically satisfactory. A portfolio model is developed, and the impact of information is analyzed. Information is treated as an economic input that is used up to the point where its predicted marginal benefit is exactly equal to its marginal cost, and, from there, the optimal demand for information is derived. A comparative-static analysis demonstrates that the reaction of optimal portfolio holdings to interest rate changes under variable uncertainty is dramatically different from portfolio behavior when uncertainty is exogenous. Finally, the elasticity of reserves with respect to scale is examined under the assumption of variable uncertainty.* Associate Professor of Finance, Division of Finance, University of Oklahoma, Norman, Oklahoma. I would like to thank two anonymous referees for substantive comments, which led to a significant improvement in this paper. 1104The Journal of Finance increased, decreased, or remained the same. In addition, B and M had information reduce the variance of reserve losses in a fashion prescribed by an arbitrarily chosen mathematical function. This approach must be refined since the specification of how the mean and the variance of a random variable change with changes in information must be done in a fashion that is statistically satisfactory.' This paper seeks to endogenize Bayesian information in a conventional bank portfolio model of the type employed by Baltensperger and Milde. The Bayesian approach to the information demand decision allows the decision maker to revise the mean and the variance of reserve losses in a statistically meaningful way. In particular, a prior probability density function is updated by the acquisition of information, and the new probability density function, the posterior, will then yield a certain mean and variance. Therefore, the Bayesian approach will allow information to convince the bank that the mean of reserve losses has increased, decreased, or remained unchanged. In addition, it becomes clear that the modification of the variance by additional information is determined by the distinction between the prior and posterior variance and not by some ad hoc mathematical function. This paper will be divided into six sections. In Section I, I outline the portfolio model that will be used and discuss the role of information in revising the expected profit to the bank. In Section II, I derive and discuss the bank's optimal demand for financial assets. In Section III, I determine the prior expectation of the posterior expected profit so that the anticipated impact of information can be evaluated. Then I derive the optimal demand for information. The comparative-static behavior of the optimal level of information and financial holdings is examined in Section IV. In Section V, I examine the elasticity of bank reserves with respect to scale under the assumption of variabl...

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