Effects of Economic Interactions on Credit Risk

We study a credit risk model which captures effects of economic interactions on a firm's default probability. Economic interactions are represented as a functionally defined graph, and the existence of both cooperative, and competitive, business relations is taken into account. We provide an analytic solution of the model in a limit where the number of business relations of each company is large, but the overall fraction of the economy with which a given company interacts may be small. While the effects of economic interactions are relatively weak in typical (most probable) scenarios, they are pronounced in situations of economic stress, and thus lead to a substantial fattening of the tails of loss distributions in large loan portfolios. This manifests itself in a pronounced enhancement of the Value at Risk computed for interacting economies in comparison with their non-interacting counterparts.Comment: 24 pages, 6 figure

QCD Corrections to Hadronic Z and tau Decays

We present a brief (mainly bibliographical) report on recently performed calculations of terms of order O(\alpha_s^4 n_f^2) and O(\alpha_s^4 n_f^2 m_q^2) for hadronic Z and \tau decay rates. A few details about the analytical evaluation of the masters integrals appearing in the course of calculations are presented.Comment: revised version (some references corrected); 3 pages, talk given at International Europhysics Conference on High Energy Physics, Aachen, Germany, 17-23 July 200

Costs and efficiencies of model meat packing plants in the Tennessee Valley

The overall objective of this study was to generate short and long range planning data for combined beef and pork packing plants in the Tennessee Valley. The effects of prices received by packers for meat products and variations in plant utilization rates were also considered . The general approach involved application of an economic engineering or synthetic cost analysis. Four kinds of plant operations (beef slaughter, beef boning, hog slaughter, and hog cutting and boning) were described so that each could be considered as an autonomous plant. Each operation had its own total cost function and was constructed in three different sizes. Complete plants that handled both beef and pork were formed by summing total cost functions for the four operating stages, and plant capacities depended on the particular combinations of different sized operating stages. A series of least cost specialized slaughter and boning operations was determined for five different levels of slaughter animal availability: (l) 100 percent utilization of capacity; (2) seasonal utilization of capacity (88.13 percent for beef and 94.15 percent of capacity for hogs); (3) 80 percent; (4) 70 percent; and (5) 60 percent utilization of capacity. Each of the model combined operations was examined under both full shift, eight-hour day operating schedules and a half shift schedule involving two four-hour shifts of slaughtering, boning, and/or cutting, respectively. Slaughter animal and processed product prices were used to estimate net revenues and the dollar value of total sales for the dual species plants at the five rates of plant utilization indicated above under both full and half shift operating schedules. Data for the model plants were used in a feasibility test that estimated ability of the plants to repay initial aggregate investment costs over a ten year period. Average total unit costs ranged from $8.15 to$13,07 in specialized beef slaughter and boning operations, and from $1.9H to$3.60 in the specialized hog slaughter, cutting, and boning operations at full capacity. The net values per head processed in the model operations (gross value minus slaughter animal cost minus processed animal delivery cost minus annual plant operating cost) were relatively low in relation to the gross value for both cattle and hogs. The net values ranged from -$0.60 to$H.32 per head of beef and from -$0.36 to$1.30 per hog in the specialized model operations at full capacity. As these low margins per head change from one period to another, there will be proportional changes in annual net revenue to the plant (net revenue = net value per head times the number of head processed in a given operation) for the time period involved. In absolute terms, however, changes in annual net revenue can be quite large. The specialized hog slaughter, cutting, and boning operations had higher estimated rates of return on annual operating costs than both the specialized beef slaughter and boning operations and the plants that slaughtered both species. Plants handling both beef and pork, however, would be able to offset decreases in net revenue from one species with possible higher returns from operations with the other species. Plant operation at less than full capacity in all model operations reduced estimated returns as well as the ability to repay initial aggregate investment costs over a ten year period, The model plants on full shift operating schedules had lower total unit costs and higher rates of return on annual operating costs than plants operating on half, shift schedules at all levels of utilization of.capacity. And, in all cases, the largest plants had the lowest unit costs, the highest annual net revenues, and the greatest ability to repay initial investment costs over a limited planning horizon