Financial Modeling Applications and Data Envelopment Applications: Volume 13

This chapter presents the portfolio optimization problem formulated as a multi-criteria mixed integer program. Weighting and lexicographic approach are proposed. The portfolio selection problem considered is based on a single-period model of investment. An extension of the Markowitz portfolio optimization model is considered, in which the variance has been replaced with the Value-at-Risk (VaR). The VaR is a quantile of the return distribution function. In the classical Markowitz approach, future returns are random variables controlled by such parameters as the portfolio efficiency, which is measured by the expectation, whereas risk is calculated by the standard deviation. As a result, the classical problem is formulated as a quadratic program with continuous variables and some side constraints. The objective of the problem considered in this chapter is to allocate wealth on different securities to maximize the weighted difference of the portfolio expected return and the threshold of the probability that the return is less than a required level. The auxiliary objectives are minimization of risk probability of portfolio loss and minimization of the number of security types in portfolio. The four types of decision variables are introduced in the model: a continuous wealth allocation variable that represents the percentage of wealth allocated to each asset, a continuous variable that prevents the probability that return of investment is not less than required level, a binary selection variable that prevents the choice of portfolios whose VaR is below the minimized threshold, and a binary selection variable that represents choice of stocks in which capital should be invested. The results of some computational experiments with the mixed integer programming approach modeled on a real data from the Warsaw Stock Exchange are reported.

Without short-sales constraints, mean-variance (MV) and power-utility portfolios generated from historical data are often characterized by extreme expected returns, standard deviations, and weights. The result is usually attributed to estimation error. I argue that modeling error, that is, modeling the portfolio problem with just a budget constraint, plays a more fundamental role in determining the extreme solutions and that a more complete analysis of MV problems should include realistic constraints, estimates of the means based on predictive variables, and specific values of investors’ risk tolerances. Empirical evidence shows that investors who utilize MV analysis without imposing short-sales constraints, without employing estimates of the means based on predictive variables, and without specifying their risk tolerance miss out on remarkably remunerative investment opportunities.

The Black and Litterman model (1992) for estimating asset returns is widely used in industry and has been widely studied in the academic and professional literature. Black and Litterman offer a way to incorporate investor's views into asset-pricing. This chapter provides a description of the Black and Litterman model. The model is analyzed using fuzzy goal programming approach using appropriate membership functions. We consider a real world financial example to implement our approach.

In view of the failure of high-profile companies such as Circuit City and Linens n Things, Financial distress or bankruptcy prediction of retail and other firms has generated much interest recently. Recent economic conditions have led to predictions of a wave of retail bankruptcies (e.g., McCracken and O’Connell, 2009). This research develops and tests a model for the prediction of bankruptcy of retail firms. We use accounting variables such as inventories, liabilities, receivables, net income (loss), and revenue. Some guiding discriminate rule is given, and a few factors were identified as measures of a profitable company.

Bond investing requires decision-making on multiple levels. Some criteria are qualitative, some are quantitative, and there may be conflicting objectives such as avoidance of credit risk versus need for income. Since managers of endowment funds must allocate their assets based on numerous dimensions, a multi-criteria decision model can help to evaluate competing criteria. We describe the Analytical Hierarchy Process (AHP), which allows investors to integrate multiple decision criteria, and apply the model to the sector allocation problem faced by managers of endowment portfolios. The AHP gives rise to a flexible model for bond investors for a range of economic scenarios, risk profiles, and time horizons.

This chapter evaluates the operational efficiency of major airports in the United States. The airport is defined as a major point of contact in the aviation industry, and on-time operations is regarded as a core service factor. We develop a bounded data envelopment analysis (DEA) model that evaluates the punctuality of airports and proposes a three-stage approach that analyzes not only current operations performance but also efficiency changes over time. We classify airports into several classes according to Federal Aviation Authority (FAA) definitions and compare their class efficiencies through decomposed efficiency scores. We find significant differences in efficiency scores between classifications.

With increased crude oil prices, railroad is emerging as a cheaper alternative to trucks and other less fuel efficient modes of transportation. As a result, with increase in crude oil price, while other modes of transportation have suffered economic slump, railroad industry is thriving with every company reporting an increase in revenue and profits. In this study, we analyze the performance of seven North American Class I freight railroads. In this chapter, we illustrate the use of data envelopment analysis (DEA), an operations research technique, to analyze the financial performance of the U.S. railroad industry by benchmarking a set of financial ratios of a firm against its peers. DEA clearly brings out the firms that are operating more efficiently in comparison with other firms in the industry and points out the areas in which poorly performing firms need to improve.

Forecasting is an important tool used to plan and evaluate business operations. Regression analysis is one of the most commonly used forecasting techniques for this purpose. Often forecasts are produced based on a set of comparable units such as individuals, groups, departments, or companies that perform similar activities. We apply a methodology that includes a new independent variable, the comparable unit's data envelopment analysis (DEA) relative efficiency, into the regression analysis. In this chapter, we apply this methodology to compare the performance of commercial banks over a 10-year time period.

A great deal of uncertainty accompanies predictions of the potential effects of global climate change on the coastal hazards associated with severe storms. One way to obviate the effects of this uncertainty on the design of policies is to understand the manner in which populations are currently vulnerable to these types of hazards. In this chapter, we develop a method for constructing a relative composite measure of vulnerability using data envelopment analysis (DEA). Through the application of this index, and one constructed using a weighted average, to four costal towns along Boston's North Shore, we demonstrate their potential usefulness to policy formulation and implementation. The DEA composite index is shown to complement the information provided by the weighted average and helps overcome some of its shortcomings such as assigning importance weights and masking of the influence of one or a subset of vulnerability attributes. Acknowledging the spatial implications of floodplain protection and mitigation efforts, the indices are constructed and analyzed at a number of different geographic scales.

DEA is a favored method to investigate the efficiency of institutions that provide educational services. We measure the efficiency of German universities especially from the students’ perspective. Since 1998, the Centrum für Hochschulentwicklung (CHE) evaluates German universities annually. The CHE ranking consists of three ranking groups for different indicators, but they do not create a hierarchy of the universities. Thus, a differentiation of the universities ranked in the same group is not possible. Based on the CHE data set, especially the surveys among students, we evaluate teaching performance from the students’ point of view using data envelopment analysis (DEA). DEA enables us to identify departments that – in the students’ perspective – are efficient in the sense that they provide high quality of education. As a method for performance evaluation, we apply a DEA bootstrap approach. By the use of this approach, we incorporate stochastic influences in the data and derive confidence intervals for the efficiency. Based on data generated by the bootstrap procedure, we are able to identify stochastic efficient departments. These universities serve as a benchmark to improve teaching performance.

Globalization speeds up competition among nations in various sectors. In terms of multinational and transnational phenomena, countries are seen as inescapable from competition, thus the linking of the term global with “competitiveness.” The research described here explores the relationship between the competitiveness of a country and its implications for human development. For this purpose, using data envelopment analysis (DEA) and cluster analysis, 44 selected countries were evaluated. An output-oriented super-efficiency model where global competitiveness indicators are taken as input variables with human development indicators as output variables is utilized. Then cluster analysis depending on the competitiveness and human development indicators is conducted by using self-organizing maps to specify the development levels of the countries. Both analyses are repeated for years between 2005 and 2007. Finally, the relationship between the super efficiency scores and the development levels is analyzed.

Many urban areas of the United States have experienced urban sprawl in the past 60 years. Severe out-migration of relatively wealthier families to ex-urban counties has left relatively poorer families behind. When combined with the recent national conversation about school improvement, this migration has caused significant stress on urban school districts, as indicated by population demographics, revenues, and school performance.

This chapter looks at 22 public school districts in Saint Louis County, Missouri. It first reviews the decision environment for those districts and constructs a relative wealth variable from environmental factors. Then, using data envelopment analysis (DEA), it compares rich districts and poor districts, and attempts to classify the relative efficiencies of those districts. Three DEA models are considered: the baseline CCR-O (Model 1), a CAT-O-C model (Model 2), and a revised CCR-O (Model 3). Using computer software, DEA-Solver, these three model results are compared and analyzed to study the effects of each district's relative wealth on the model results.

The study concludes that adding a relative wealth variable produces more robust model results and suggests that school district decisions may be improved by including a relative wealth variable in their decision-making processes.

An appropriate assessment of sustainability in venture business is an important managerial and investment decision making. Data envelopment analysis (DEA) is utilized for sustainability assessment for venture business firms’ performance. Venture business firms are primary decision-making units (DMUs). Required information for this study is collected from Korea Listed Companies Association (KLCA) database. The proposed DEA model incorporates multiple inputs and outputs to assess the relative operational efficiency of the DMUs, identifying the best performance group among the peer venture business firms. The proposed model provides decision-makers with more accurate information for strategic insights to make better investment decisions in the competitive business environment.

Data envelopment analysis (DEA) is used to determine the relative efficiency of the top-ranked gynecology departments in the United States as designated by the U.S. News & World Report ranking. DEA is a linear programming base procedure used to determine the relative efficiency of operating units that have similar characteristics. Efficiency scores are calculated by comparing two different input sets to the performance of each gynecological department. Ranking based on DEA more completely and accurately represents gynecological departments. Further, DEA makes it possible to fairly compare specific departments. The new ranking coupled with the efficiency score accrued by each hospital will motivate and guide hospital administrators to improve the performance of hospital gynecology departments by better utilizing expensive resources.