Lanstein and Sharpe (LS) attempt to explain residual covariances between stocks on the basis of duration considerations. The results, by admission are mixed. Rather than to focus on these per se, I would like to further the work by making some suggestions with respect to the formal model development and the empirical tests-on the basis that both could be made crisper and thereby increase the value of what already is a contribution.

The relationship between an investor's attitude toward risk and the shape of his preference functions has long been recognized in both the general portfolio problem and the mean-variance model. By contrast, the literature has largely ignored the connection between general measures of an investor's attitude toward risk and the shape of his mean-variance or mean-standard deviation indifference curves. Yet this relationship is significant. Through general measures of risk aversion, assumptions about an investor's behavior under uncertainty imply restrictions on indifference curves. Conversely, assumptions about indifference curves impose restrictions on an investor's behavior under uncertainty. The development of this relationship and its implications is the objective of this note.

My comment was requested by the Chairman to be directed especially toward Dr. Robert Holland's excellent and thoughtful account of the changes, past and prospective, springing from the development of bank holding companies in American banking markets.

The theory of efficient capital markets suggests that if the capital markets are efficient, security prices can be assumed at any time to “fully reflect” all available information. Various forms of the model have been subjected to extensive empirical testing. The results of these tests have been such that in reviewing the literature on the theory Fama [3] states, “ … the evidence in support of the efficient markets model is extensive, and (somewhat uniquely in economics) contradictory evidence is sparse.” Most of the research, however, has been addressed to the question of whether prices “fully reflect” particular subsets of available information. The validity of these results depends on the extent to which the information in the subset used for testing captures the information actually impounded in prices.

The theory of efficient capital markets indicates that the prices in an efficient market fully reflect all available information. In much of the literature on efficient markets the term fully reflect is made operational with the assumption that the conditions for market equilibrium can be expressed as expected returns. Fama suggests that most expected return theories can be expressed in the following manner:(1) where — adopting Fama's notation — E is the expected value operator; Pjt is the price of security j at time t; Pj, t+1 is its price at t+1; is the one-period percentage return (Pj, t+1|Pjt); φt is a general symbol to represent whatever set of information is assumed to be fully reflected in the price at time t; and the tildes indicate that Pj, t+1 and rj, t+1 are random variables at t.

In [2] Hakansson and Liu presented a multiperiod portfolio model in which there is an optimal myopic policy. In particular, at any decision point j and state m the optimal amount to invest in opportunity i, namely , may be found by maximizing(42a) subject to(42b) (42c) , where the expectation is taken with respect to the β's, and the p's and r are positive constants (r > 1). Assumptions are made in [2] which guarantee that (42) has a unique optimal solution and that the set of vijm which satisfies (42b and 42c) is a nonempty, compact, convex set for all j and m.

In many nonlinear programming applications the objective function has an inherent uncertainty that depends upon a set of random variables that have a known distribution. If one wishes to optimize the expectation of the objective, as suggested by the expected utility theorem, then as is shown here one can often solve such problems by modifying standard nonlinear programming algorithms. To illustrate what is involved, the details and justification for the application of the interior parametric sequential unconstrained maximization technique and the generalized programming method for the solution of such problems are given. Some related problems with stochastic constraints for which the solution method applies are mentioned and an example of a portfolio selection problem is given.

To assure that the commercial banking industry's performance serves the “convenience and needs” of the public, bank supervisory authorities have been vested with broad powers to alter the competitive environment in bank markets. While several criteria have been used to evaluate the effects of entry, merger, branching, and other changes in the allocation of bank resources, the results have been largely inconclusive. Since the regulatory authorities have pursued somewhat conflicting objectives in seeking a “failure-proof” system that is also “efficient, ” there may be no single criterion for evaluation of bank behavior that is wholly consistent with the behavior predicted by the neoclassical theory of the firm.

The classic 1955 paper of Lorie and Savage has stimulated the development of mathematical programming approaches to the analysis of capital budgeting problems. A problem that they considered has been succinctly stated as:given the net present value of a set of independent investment alternatives, and given the required outlays for the projects in each of two time periods, find the subset of projects which maximizes the total net present value of the accepted ones while simultaneously satisfying a constraint on the outlays in each of the two periods.

Christian T. L. Janssen, Comment: Deposit Insurance in the United States--Evaluation and Reform, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1613-1618