In two previous articles [11] and [12] a family of normative models of the individual's economic decision problem under risk was presented. At the same time, certain implications of these models with respect to individual behavior were deduced for a class of utility functions. This paper will show that these models also give rise to an induced theory of the formation and operation of firms under risk for the same class of utility functions.

The relationship between return on assets and their riskiness is one of the liveliest topics in financial literature. In his 1952 landmark article, Markowitz developed a mathematical model that captured this key financial concept. defined risk as the variance of the rate of return of a portfolio. Later, Sharpe hypothesized a positive linear relationship between expected rate of return on an asset and the risk premium associated with that asset. Subsequently, Sharpe tested this hypothesis empirically and found support for his theory. Although portfolio theory specifies the two parameters of this model as ex ante return and risk, Sharpe used ex post data for testing the risk-return relationship. designated the ex post mean rate of return obtained on an an asset as a proxy for expected return and the standard deviation of ex post annual rates of return as a surrogate for risk.

Considerable attention has been given in recent years to studies of the cost of capital and investor preferences for dividends, but empirical analysis of the various theoretical propositions has been complicated by numerous difficulties associated with estimating the parameters in question. In many of the empirical studies, ordinary least squares has been the statistical method applied because, under certain assumptions, ordinary least squares produces unbiased estimates with a minimum of variance. However, the validity of one of the assumptions, namely, that all independent variables contain no measurement error, has been questioned by numerous writers. More specifically, it has been argued that investors tend to ignore temporary or random disturbances in current reported earnings. Thus, values of current earnings that are actually observed for the statistical study may be different from those values which ideally would be observed; i.e., they may contain measurement error, the size of which is reflected by the difference between the current reported earnings and the values on which investors presumably base their decisions. For example, in such least squares regressions as price on dividends and retained earnings, the impact of the measurement error is considered to fall mainly on the retained earnings, since dividends are thought to be relatively stable.

This paper describes the development and testing of a model of bank portfolio selection that considers variability of both income and gross asset levels as the risks involved in banking. In particular, the model is formulated as maximizing expected profit subject to risk constraints on wealth losses and the availability of liquid assets. The parameters for these constraints include the covariance matrices of rates of return on bank assets and deposit changes. Included in the latter category are fluctuations in business loans which are treated as negative deposits because, due to deposit feedbacks and the like, these can reasonably be considered exogenous to the short-run portfolio decision. Basically, the model is an extension of Markowitz's work [11] to incorporate problems associated with portfolios that include assets having imperfect markets and liabilities that are not completely under the control of the economic unit. As such, it is applicable (with minor institutional modifications) to the entire spectrum of financial intermediaries.

Researchers and political analysts concerned with the inter-regional flow of mortgage funds have often pointed to the existence of yield differentials as prima facie evidence of misallocation of capital and national resources. Limited information and myopic lending horizons, with market imperfections reinforced by state laws and institutional segmentation, have been postulated. They are regarded as responsible for costly “frictions” in the export of capitalto the fast-growing, generally low-income, states, particularly those of the South. Both federal and state legislative action, intensified private arbitrage, and better secondary market facilities and instruments are then urged to improve inter-regional financial mediation to reduce or eliminate the yield differentials.

Recently, Lusztig and Schwab [5] drew attention to a problem which occurs when applying linear programming methods to portfolio selection where capital is rationed over several investment periods. The problem is to determine the relevant discount rate with which to calculate the net present values of the objective function when this same rate is dependent upon the optimal solution to the linear program. Lusztig and Schwab suggested a neat procedure by which it was claimed that one could overcome this difficulty and which also does not rely upon the measurement of subjective utility as did the Baumol and Quandt approach [2]. It was decided to test the Lusztig and Schwab model (afterwards called the L-S procedure for brevity) on a hypothetical problem, and doing so resulted in two conclusions:

(a) The L–S procedure, as described, is incomplete but with small modification may be useful; however,

(b) concentration upon the discount rate problem in isolation from other capital budgeting problems may well be a pointless exercise.

In our earlier note, we drew attention to the problem of interdependency between the opportunity cost used as a discount rate in determining the net present values of the objective function and the optimal solution of a linear program. In expanding on our article, Lockett and Tompkins (L and T) rightly point to the need for an appropriate definition of opportunity costs.

Recently, several researchers, including Evans, Archer [1], Latané, and Young [2], have performed empirical analyses of the relationship between the number of securities in a portfolio and the reduction in portfolio dispersion. In this note, an exact mathematical relationship between these two factors is presented.

This paper proposes a model that a dealer or investor may employ in determining

• The potential investment value of a debt instrument,

• The potential gains in net after-tax yield which result from swaps, and

• The trade-off, effective, after-tax yield on a municipal vs a taxable corporate bond of the same quality or rating.