Roman L. Weil

Duration Forty Years Later

The risk inherent in the price fluctuations of bonds has many dimensions. These include default risk, inflation risk, and call risk. The most important single source of risk, particularly for government and high-grade corporate bonds, is basis-risk price fluctuations caused by shifts in interest rates. For a given shift in the yield curve, and holding other factors unchanged, longer term-to-maturity bonds generally suffer greater price changes than shorter maturity bonds. This characterization is not exact because high coupon bonds are less volatile than low coupon bonds. Intuition says that this is to be expected because, other things being equal, high coupon bonds have a greater percentage of their value due to the interim coupons and, hence, have a shorter “effective†maturity. Duration may be interpreted as an attempt to quantify this qualitative statement through the use of a single, numerical measure intended to be used in place of maturity.

Disentangling Interrelated Effects of Regulatory Changes on Shareholder Wealth: The Case of Motor Carrier Deregulation

IN this paper we measure share price effects of several interrelated regulatory changes associated with the partial deregulation of interstate trucking. Three focal points of this investigation are (1) the Motor Carrier Act of 1980 and earlier Interstate Commerce Commission (ICC) actions, which made truck operating rights easier to secure, hence less valuable;1 (2) the Financial Accounting Standards Boards (FASB) subsequent issuance of Statement of Financial Accounting Standards No. 44 (SFAS No. 44), which required the immediate write-off of unamortized operating rights;2 and (3) the 1981 Economic Recovery Tax Act (ERTA), which allowed a tax deduction for the unamortized tax basis of the rights.

Technical Note—“Linear” Programming with Absolute-Value Functionals

Consider the problem Ax = b; max z = ∑cj|xj|. This problem cannot, in general, be solved with the simplex method. The problem has a simplex-method solution (with unrestricted basis entry) only if cj are nonpositive (nonnegative for minimizing problems).

Accumulating Damages in Litigation: The Roles of Uncertainty and Interest Rates

THE analysis presented here concentrates on one aspect of the problem of computing damage compensation: the accumulation of the dollar amount of the damages from the date of harm to the payment date. In attempting to compensate the plaintiff for the passage of time between damage and settlement, we must consider both the deferral of consumption and the resolution of uncertainty which occur during that interval. The bearing of risk and the market values of various risky claims figure prominently in the calculation of the proper interest rate. Uncertainty plays a key role in the analysis. In particular, three critical questions can be raised: (1) Will the defendant have sufficient funds to pay the accumulated amages when the suit is finally settled? (2) If the damage consisted of deprivation of a business opportunity, what was the ex ante probability distribution of outcomes, and which particular outcome oc-

Analysis of Reserve and Regular Bottlings: Why Pay for a Difference Only the Critics Claim to Notice?

I report my tests of the hypothesis that wine consumers cannot distinguish the difference between regular and reserve bottlings of otherwise-similar wines. My results suggest that only about one purchaser in five should even consider buying the reserve bottling of a wine, rather than the regular. But since I cannot tell you how to distinguish that one person out of five, we can all aspire to drinking the reserve. I have more than 800 observations of wine drinkers’ who engaged in the following experiment. The drinker faces 3 glasses of wine, two of which contain identical wines [either the regular or the reserve] and the third contains a different wine [the other one]. I record whether the drinker can distinguish wines whether he can tell the singleton from the doubleton and, if the drinker can distinguish, which wine he prefers. I find that just over 40 per cent of the drinkers distinguish correctly, whereas one-third could if the process were random. Of those 40 percent who can distinguish, 52 percent prefer the more expensive, reserve wine, where as half would if the process were random. For this data set, 52 percent does not differ significantly from the expectedif-random half. I have recorded the sex of the testers and I can find that men can distinguish the wines better than random, but women cannot. The differences are so small, even though significant, however, that the Exact F test detects no significant difference between the ability of men and women in these tests. The results span tests of wines from Bordeaux, Burgundy, the Rhone, Spain, New Zealand, Italy, California [both red and white], Oregon, and Australia; the tests include still and sparkling wines. 1 Also, V. Duane Rath Professor of Accounting, Graduate School of Business, University of Chicago, 1101 East 58 Street, Chicago IL 60637; 773.702.7261; fa x 206.202.2114; roman.weil@gsb.uchicago.edu. I prepared this paper for the 9 Oenometrics Meeting of the Vineyard Data Quantification Society, Budapest, May 22-24, 2003, whose attendees provide my final data set. Some past attendees asked why is an accountant doing such work. I respond as follows. First, note that accounting is an intellectual discipline even though you probably think of it as bookkeeping and tax reporting. Accounting records in aggregating numbers information about complex transactions. Then, it attempts to enable users of that information to deduce from the numbers the underlying reality and how to use the data in decision making. Similarly, wine ratings record in aggregating numbers useful information about complex sensory experience. This paper attempts to help the user decide how to use the reported data in making decisions. Shannon Harwick assisted in the compilation of the data for this research and in the writing of this paper. Neither he nor I can distinguish better than random. M.L. Marais helped us with choosing suitable tests for the sex test. He can.

The roots of matrix pencils (Ay=λBy): existence, calculations, and relations to game theory

Abstract : Given m x n matrices A and B, by a solution to the pencil system of A relative to B we mean a triple lambda not equal to 0, x not equal to 9, y not equal to 0, where lambda is (x), x is 1 x m and y is n x 1, such that both x(A-lambda B) = 0 and (A-lambda B) y = 0. A canonical form is derived from which it is easy to state conditions for existence of such solutions. By further decomposing the canonical form it is shown that ordinary elimination methods and eigenvalue routines may be used to find pencil solutions. Next the relationship between matrix pencils and matrix games is studied. Finally, the relationship between game theory and dual systems of linear homogeneous equations is developed for both the real and complex cases and applied to pencil systems. (Author)

The cyclical majority problem

The problem of the cyclical majority is presented and some new, simulated results for 3, 4, 5, … , 40 issues and 3, 5, 7, … , 37 judges are reported.

COMPUTATION OF EXPANSION RATES FOR THE GENERALIZED VON NEUMANN MODEL OF AN EXPANDING ECONOMY

Abstract : The first part of the paper is a theoretical study of v(B - alpha A) considered as a function of alpha, the expansion factor, where A and B are the input and output matrices of the model. Then a simple search algorithm is presented for computing the maximum and minimum expansion rates of the model. The algorithm uses the simplex method of linear programming as its basic subroutine. For a typical set of data, an expansion rate can be found to sufficient accuracy by solving 14 or fewer linear programming problems. With modern computers this is not a difficult task. The last part of the paper discusses the available data, in this case, input-output data, and gives the computational results found using it. Limitations of the data and conclusions drawn from it are discussed. The use of the model for economic planning and evaluation is considered.

Management science: a view from nonlinear programming

A brief history of integer and continuous nonlinear programming is presented as well as the current obstacles to practical use of these mathematical programming techniques. It is forecast that the useful contributions to nonlinear programming actually made in the next few years are more likely to be consolidations than theoretical breakthroughs. These contributions are likely to be the documentation of standard test problems, construction of user oriented software, and comparisons of currently known algorithms to demonstrate which techniques are best for specific problems.

SOLUTIONS TO THE DECOMPOSABLE VON NEUMANN MODEL

A method is shown for finding all solutions to the generalized von Neumann model formulated by Kemeny, Morgenstern, and Thompson. The method uses results from decomposing economic production systems to extend the algorithm of Hamburger, Thompson, and Weil. THIS ARTICLE shows how the results derived by Weil [5, 6] for decomposable production systems can be used to extend the results of Hamburger, Thompson, and Weil [1] for performing calculations on the generalized von Neumann model of an expanding economy formulated by Kemeny, Morgenstern, and Thompson [2]. A method is shown for finding all solutions to a generalized von Neumann model. The model represents an economy of m goods and n fixed-coefficient, constantreturns-to-scale processes for producing those goods. The set of processes form an m by n input matrix A and an m by n output matrix B. When the jth process is operated at unit intensity the amount ai of the ith good must be supplied at the beginning of the production period and the amount bij of the jth good is produced at the end of the period. The element xj, xj > 0, Ixj = 1, of the stochastic column vector x is the level at which the jth activity is operated. The element yi of the stochastic row vector y is the price of the ith good. Von Neumann required that