Negative Data in DEA: A Simple Proportional Distance Function Approach

The need to adapt Data Development Analysis (DEA) and other frontier models in the context of negative data has been a rather neglected issue in the literature. Silva Portela, Thanassoulis, and Simpson (2004) proposed a variation on the directional distance function, a very general distance function that is dual to the profit function, to accomodate eventual negative data. In this contribution, we suggest a simple varaiation on the proportional distance funtion that can do the same job.DEA, negative data, directional distance funtion

Portfolio Performance Gauging in Discrete Time Using a Luenberger Productivity Indicator

This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of portfolios with respect to the traditional Markowitz mean-variance efficient frontier, as well as the eventual shifts of this frontier over time. Based on the analysis of local changes relative to these mean-variance and higher moment (in casu, mean-variance-skewness) frontiers, this methodology allows to neatly separate between on the one hand performance changes due to portfolio strategies and on the other hand performance changes due to the market evolution. This methodology is empirically illustrated using a mimicking portfolio approach (Fama and French 1996; 1997) using US monthly data from January 1931 to August 2007.shortage function, mean-variance, mean-variance-skewness, efficient portfolios, Luenberger portfolio productivity indicator

Geometric Representation of the Mean-Variance-Skewness Portfolio Frontier Based upon the Shortage Function

The literature suggests that investors prefer portfolios based on mean, variance and skewness rather than portfolios based on mean-variance (MV) criteria solely. Furthermore, a small variety of methods have been proposed to determine mean-variance-skewness (MVS) optimal portfolios. Recently, the shortage function has been introduced as a measure of efficiency, allowing to characterize MVS optimalportfolios using non-parametric mathematical programming tools. While tracing the MV portfolio frontier has become trivial, the geometric representation of the MVS frontier is an open challenge. A hitherto unnoticed advantage of the shortage function is that it allows to geometrically represent the MVS portfolio frontier. The purpose of this contribution is to systematically develop geometric representations of the MVS portfolio frontier using the shortage function and related approaches.shortage function, efficient frontier, mean-variance-skewness efficiency

Optimal Capacity Utilization and Reallocation in a German Bank Branch Network: Exploring Some Strategic Scenarios

Quite a few studies have considered efficiency at the bank branch level by comparing mostly a single branch network, while an abundance of studies have focused on comparing banking institutions. However, to the best of our knowledge no study has ever assessed performance at the level of the branch bank network by looking for ways to reallocate resources such that overall performance improves. Here, we introduce the Johansen-Färe measure of plant capacity of the firm into a multi-output, frontier-based version of the short-run Johansen industry model. The first stage capacity model carefully checks for the impact of the convexity assumption on the estimated capacity utilization results. Policy scenarios considered for the short-run Johansen industry model vary in terms of their tolerance with respect to existing bank branch inefficiencies, the formulation of closure policies, the reallocation of labor in terms of integer units, etc. The application to a network of 142 bank branches of a German savings bank in the year 1998 measures their efficiency and capacity utilization and demonstrate that by this industry model approach one can improve the performance of the whole branch network.Bank Branch Network, Efficiency, Capacity, Reallocation

Visualizing surfaces in Euclidean 3-space with VisuMath

status: publishe

Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space

We examine curvature properties of twisted surfaces with null rotation axis in Minkowski 3-space. That is, we study surfaces that arise when a planar curve is subject to two synchronized rotations, possibly at different speeds, one in its supporting plane and one of this supporting plane about an axis in the plane. Moreover, at least one of the two rotation axes is a null axis. As is clear from its construction, a twisted surface generalizes the concept of a surface of revolution. We classify flat, constant Gaussian curvature, minimal and constant mean curvature twisted surfaces with a null rotation axis. Aside from pseudospheres, pseudohyperbolic spaces and cones, we encounter B-scrolls in these classifications. The appearance of B-scrolls in these classifications is of course the result of the rotation about a null axis. As for the cones in the classification of flat twisted surfaces, introducing proper coordinates, we prove that they are determined by so-called Clelia curves. With a Clelia curve we mean a curve that has linear dependent spherical coordinates.status: publishe

Cost functions are nonconvex in the outputs when the technology is nonconvex: convexification is not harmless

International audienceThis contribution focuses on testing the empirical impact of the convexity assumption in estimating costs using nonparametric specifications of technology and cost functions. Apart from reviewing the scant available evidence, the empirical results based on two publicly available data sets reveal the effect of the convexity axiom on cost function estimates: cost estimates based on convex technologies turn out to be on average between 21% and 38% lower than those computed on nonconvex technologies. These differences are statistically significant when comparing kernel densities and can be illustrated using sections of the cost function estimates along some output dimension. Finally, also the characterization of returns to scale and economies of scale using production and cost functions for individual units yields conflicting results for between 19% and 31% of individual observations. The theoretical known potential impact as well as these empirical results should make us reconsider convexity in empirical production analysis: clearly, convexity is not harmless

Negative Data in DEA: A Simple Proportional Distance Function Approach

The need to adapt Data Envelopment Analysis (DEA) and other frontier models in the context of negative data has been a rather neglected issue in the literature. A recent article in this journal proposed a variation on the directional distance function, a very general distance function that is dual to the profit function, to accommodate the occurrence of negative data. In this contribution, we define and recommend a generalised Farrell proportional distance function that can do the same job and that maintains a proportional interpretation under mild conditions. © 2011 Operational Research Society Ltd. All rights reserved.status: publishe

On flat tensor product surfaces

nrpages: 9status: publishe