Knowledge that Transforms

This paper shows that the integer efficient frontier for capital budgeting problems can be computed using a modified Markowitz approach. It is shown that if the quadratic integer capital budgeting problem is reformulated as a parametric programming problem on the right-hand side of the return constraint, the problem indicated by Baum, Carlson, and Jucker [1] is eliminated. The traditional Markowitz approach is to formulate the problem as an objective function parametric programming problem. Baum, Carlson, and Jucker [1] show that the traditional approach cannot generally be applied to solve quadratic zero-one integer capital budgeting problems. They show that this approach may fail to identify some efficient points. The failure results from the objective function parametric programming approach. Even though the objective function and the right-hand side parametric programming approaches are equivalent in the continuous case, they may not be equivalent in the integer case.

The algorithm leading to a solution of the above question has been known at least since Kaplan's 1965 tutorial [5] on Sturm's theorem. The Sturm-Kaplan method has the power to count all zeros on the real axis between any two specified limits. A significant problem may arise, however, when one tries to generate the Sturmian functions which play a central part in the Sturm-Kaplan method. The rather arduous nature of the task derives from the necessity to perform several polynomial (synthetic) divisions. As the number of cash flows involved in the analysis increases, the time and effort required to determine the Sturmian functions increase as well.

The familiar two-parameter model for portfolio decisions, attributed to Markowitz [11], has individuals maximizing an objective function, ϕ [E(Y), V(Y)], of mean and variance of end-of-period wealth, subject to a constraint imposed by initial wealth. In the usual version there is an arbitrary number, n, of risky assets with stochastic end-of-period values (price plus dividend) represented by the vector X with exogenously given mean vector μ and nonsingular variance matrix σ. There is also one riskless asset, whose certain end-of-period value per dollar invested is p. Final wealth, as constrained by initial wealth, W, is given by Y = WP + a' (X – OP), where a and P are vectors of risky asset quantities and prices. Assuming ϕE > 0 (wealth preference), ϕV

Boquist, Racette, and Schlarbaum [3] and Livingston [6] show that a security systematic risk may be expressed as a function of its duration. These results have led to research examining the role of duration in explaining systematic risk, but Lanstein and Sharpe [5] indicate that Livingston's expression relies on the implicit assumption that extra-market covariances between securities are insignificant. Lanstein and Sharpe argue that such an assumption is unwarranted. They find a significant negative relationship between extra-market covariances and differences in duration between paired samples of common stock. Their paper suggests that duration may be associated with unsystematic risk and that any relation between duration and systematic risk is more complex than implied in [3] and [6].

Eric H. Sorensen, Clark A. Hawkins, On the Pricing of Preferred Stock, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 4, Proceedings of 16th Annual Conference of the Western Finance Association, June 18-20, 1981, Jackson Hole, Wyoming (Nov., 1981), pp. 515-528

Frank J. Fabozzi, Richard R. West, Negotiated Versus Competitive Underwritings of Public Utility Bonds: Just One More Time, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 3 (Sep., 1981), pp. 323-339

Robert M. Conroy, Robert L. Winkler, Informational Differences Between Limit and Market Orders for a Market Maker, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 5 (Dec., 1981), pp. 703-724

Earl D. Benson, David S. Kidwell, Timothy W. Koch, Robert J. Rogowski, Systematic Variation in Yield Spreads for Tax-Exempt General Obligation Bonds, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 5 (Dec., 1981), pp. 685-702

Edward Miller [5], expanding on the work of Williams [8], Smith [6], and Lintner [4], has proposed a direct relationship between a stock's “risk” and its “divergence of opinion.” Under conditions of uncertainty, potential investors in a stock arrive at different assessments of expected return. Thisvariation in expectations is characterized as the stock's divergence of opinion. Miller argues persuasively that at a point in time a stock's price does not reflect the expectations of all potential investors, but rather the expectations of only the most optimistic minority who are trading the issue. As long as this minority can absorb the entire supply of stock, an increase (decrease) in divergence of opinion-leaving the average expectation unchanged-will increase (decrease) the market clearing price.

The idea that various characteristics of financial contracts and institutions can be explained as a rational response to problems created by information asymmetries has received a great deal of attention recently. A central theme of the literature in this area is that while moral hazard may hamper the direct transfer of information between market participants, information may be conveyed indirectly through the actions of market participants. For example, the characteristics of the insurance contract purchased may convey information as to riskiness of the insured. Recognition of the possible effects of information asymmetries has provided valuable insights into the role of financial intermediaries and the characteristics of the contracts they offer. In this paper we apply this literature to an analysis of the market for bank loan commitments. Through our analysis we are able to explain the use of various payment options such as fees and compensating balance requirements associated with loan commitments. Extensions of our analysis into the pricing of other bank services are also explored.