A Model for Selecting Commercial Bank Government Security Portfolios - Wolf, Charles R. (The Review of Economics and Statistics, 1969)
T HE object of this paper is to formulate a normative model for selecting a bank's Government security portfolio. Two major problems arise in constructing a model of bank portfolio selection. First, the model must handle uncertainty. This includes not only uncertain future events but also the decision maker's preferences for the outcomes associated with these events. Second, it must recognize the intertemporal or multi-period character of the decision making process. This means that a decision made in one period will influence subsequent decisions and hence, that subsequent decisions must be considered in arriving at the present one. The present paper applies Bayesian and sequential decision theory to handle both the expectationally stochastic and the dynamic aspects of this important decision problem simultaneously and consistently. No previous model of commercial bank portfolio selection handles either or both problems satisfactorily. Porter's model of bank asset selection recognizes uncertainty by treating future cash flows and security prices as random variables, but it is only one period in length. Moreover, it does not consider the decision maker's preferences.' Since the objective function is linear, the model produces a portfolio diversified between securities and loans only through the selection of distribution functions describing the random variables. These transform the function into a nonlinear one upon integration. Cheng's model of bank security portfolio selection is, in effect, a one period formulation also.2 It incorporates uncertainty and the decision maker's preferences through Markowitz's efficient portfolio concept.3 An efficient portfolio is one which maximizes expected return for a given variance of return (or minimizes the variance of return for a given expected return). As Tobin points out, however, this criterion assumes, quite restrictively, that either the variable return is normally distributed or that the decision maker has a quadratic utility function.4 Cheng also makes the highly unrealistic assumption that securities are held to maturity. Multi-period bank portfolio selection models are all based on the assumption that future events are known with certainty. One such model formulated by Chambers and Charnes attempts to reflect the risk inherent in different portfolio configurations by including the Federal Reserve's capital adequacy formula as a constraint.5 Used in the supervision of banks, the capital adequacy formula allocates a bank's capital to designated asset categories on a fractional basis. The values of the fractions are designed to measure the percent by which the different asset categories would decline in market value if they had to be liquidated quickly.6 The choice of these values is somewhat arbitrary. Moreover, the formula itself implicitly assumes a particular preference structure and a certain probabilistic occurrence of future events. Neither assumption is likely to represent accurately either the decision maker's preferences or expectations.7