“Computation of the Efficient Boundary in the E-S Portfolio Selection Model” William W. Hogan and James M. Warren Volume VII, No. 4, September 1972

The interdependence of loan cost and tangible bank activity is an aspect of the cost of bank debt that has not been treated in the literature. Understanding this interdependence is important for banks in pricing their services, especially as banks adopt more flexible pricing policies. This understanding is crucial for a firm in establishing the true cost of bank borrowing, in comparing bank borrowing with other sources of funds, and in evaluating the firm's banks. It is also important for understanding the firm-bank relationship in general and the cost of capital in particular.

A number of recent articles have explored the reasons underlying observed differences in deposit variability among commercial banks. The variability of deposits at individual banks is of interest to bank management, the Federal Reserve, and the general public for several reasons:

1. Deposit variability is frequently included as an important determinant of portfolio strategy. The more volatile a bank's deposits are, the more liquid its mix of assets will be.

In this paper, the models utilized in earlier studies were applied to a larger sample with greater size and geographic dispersion. For those functions that account for the largest proportions of direct operating cost and employment, the scale coefficients increased from 1965 to 1968 so that they were not significantly different from unity. For activities requiring more skilled human resources than the “factory” operations of the typical bank, there were significant economies of scale of magnitudes similar to those in the 1965 Northeast sample. A test of overall scale economies assuming proportional expansion of all facilities showed a decrease in scale economies since 1965.

This paper is a selective review of the received theory of financial institutions with some suggestions regarding future research on this topic. The major emphasis is placed on the positive economic theory of these firms. Financial institutions are considered to be firms that supply financial securities and contracts held as assets by other sectors of the economy and that use the proceeds of these sales to finance the purchase of financial securities and contracts which are the liabilities of other economic units. The theory discussed here is stripped of much of the regulatory and legal framework surrounding financial institutions. The primary reason for so limiting the scope of this paper is a conviction that a reasonably complete model of a simple financial institution is a necessary precursor to useful models of the positive economic behavior of financial institutions in any specific legal, regulatory, and operational framework. While recognizing that no tractable model of a financial institution is likely to be so general as to avoid the problem of model specificity, I take the view that many of the questions asked in the literature would be better answered in less specific models, i.e., in models capable of explaining additional important aspects of the behavior of the financial institution in question.

A belief frequently expressed by observers of the stock market is that groups of institutions tend to trade in the same way at the same time. Two expressions of this belief follow:

Frequently reference is made to the ‘impact’ of institutional investors on the stock market. Apparently it is worrisome to the observers of the markets to find that we tend to buy and sell somewhat in unison.

Most insurance companies are involved in reinsurance activities. For the majority, reinsurance means laying-off portions of the risk that they have assumed in the primary insurance market. A few other companies assume these laid-off risks. Our concern is with the former companies; that is, those seeking to cede a portion of their risk.

In this paper a recursive programming model is constructed and optimized so that a mix of bank assets may be selected. The purpose is to link optimization over time with a commercial bank asset management model.

This paper has considered the sequence of optimal credit expansion decisions of a bank operating under the legal structure imposed by the Federal Reserve System. Two alternative structures are considered, one relating to the pre-September 1968 period and the other to the currently enforced one. Using dynamic programming techniques, a closed-form equation for the optimal credit expansion decision has been derived in each case. The optimal level of credit expansion has been shown to be a nonlinear function of the prevailing interest rate, the parameters of the distribution of reserve losses, and several parameters set by Federal Reserve policy. The presence of uncertainty in the model has been shown to have an indefinite effect; however, several policy parameters may be chosen so as either to restrict or to encourage expansion to levels below or above the simple certainty prediction. These results are intuitively in accord with those of general inventory studies.