Methodological comparison between DEA (data envelopment analysis) and DEA–DA (discriminant analysis) from the perspective of bankruptcy assessment

This study compares DEA (data envelopment analysis) with DEA–DA (discriminant analysis) in terms of bankruptcy assessment. Recently, many DEA researchers propose a use of DEA as a quick-and-easy tool to assess corporate bankruptcy. Meanwhile, other DEA researchers discuss a use of DEA–DA for bankruptcy-based financial analysis. The two groups are very different from the conventional use of DEA because we have long applied DEA to the measurement of operational performance, or productivity analysis. The two research groups open up a new application area (bankruptcy-based financial assessment) for DEA. This study discusses methodological strengths and weaknesses of DEA and DEA–DA from the perspective of corporate failure. The proposed comparative analysis has the three main criteria: (a) how to handle negative data in financial variables, (b) how to handle data imbalance between default and non-default firms, and (c) how to identify a failure process over time. This study finds that DEA is a managerial tool for the initial assessment of corporate failure and DEA is useful for busy corporate leaders and financial managers. In contrast, DEA–DA is useful for researchers and individuals who are interested in the detailed assessment of bankruptcy and its failure process in a time horizon.     

Data envelopment analysis for environmental assessment: Comparison between public and private ownership in petroleum industry

Environmental assessment recently becomes a major policy issue in the world. This study discusses how to apply Data Envelopment Analysis (DEA) for environmental assessment. An important feature of the DEA environmental assessment is that it needs to classify outputs into desirable (good) and undesirable (bad) outputs because private and public entities often produce not only desirable outputs but also undesirable outputs as a result of their production activities. This study proposes the three types of unification for DEA environmental assessment by using non-radial DEA models. The first unification considers both an increase and a decrease in the input vector along with a decrease in the direction vector of undesirable outputs. This type of unification measures “unified efficiency”. The second unification considers a decrease in an input vector along with a decrease in the vector of undesirable outputs. This type of unification is referred to as “natural disposability” and measures “unified efficiency under natural disposability”. The third unification considers an increase in an input vector but a decrease in the vector of undesirable outputs. This type of unification is referred to as “managerial disposability” and measures “unified efficiency under managerial disposability”. All the unifications increase the vector of desirable outputs. To document their practical implications, this study has applied the proposed approach to compare the performance of national oil firms with that of international oil firms. This study identifies two important findings on the petroleum industry. One of the two findings is that national oil companies under public ownership outperform international oil companies under private ownership in terms of unified (operational and environmental) efficiency and unified efficiency under natural disposability. However, the performance of international oil companies exhibits an increasing trend in unified efficiency. The other finding is that national oil companies need to satisfy the environmental standard of its own country while international oil companies need to satisfy the international standard that is more restricted than the national standards. As a consequence, international oil companies outperform national oil companies in terms of unified efficiency under managerial disposability.     

E-DEA: Enhanced data envelopment analysis

Data envelopment analysis (DEA) has enjoyed a wide range of acceptance by researchers and practitioners alike as an instrument of performance analysis and management since its introduction in 1978. Many formulations and thousands of applications of DEA have been reported in a considerable variety of academic and professional journals all around the world. Almost all of the formulations and applications have basically centered at the concept of “relative self-evaluation”, whether they are single or multi-stage applications. This paper suggests a framework for enhancing the theory of DEA through employing the concept of “relative cross-evaluation” in a multi-stage application context. Managerial situations are described where such enhanced-DEA (E-DEA) formulations had actually been used and could also be potentially most meaningful and useful.     

Risky asset allocation and consumption rule in the presence of background risk and insurance markets

This study examines joint decisions regarding risky asset allocation and consumption rate for a representative agent in the presence of background risk and insurance markets. Contrary to the conclusion of the “mutual fund separation theorem”, we show that the optimal risky asset mix will reflect an agent’s risk attitude as long as background risk is not independent of investment risk. This result can, however, be used to solve the “riskyasset allocation puzzle”. We also unveil that optimal insurance to shift background risk is determined through establishing a hedging portfolio against investment risk and is an arrangement maintaining the balance between growth and volatility of expected consumption. Because the optimal insurance we obtain generally leads to a smoother consumption path, it may plausibly explain the “equity premium puzzle” in the financial literature.     

Identifying distress among banks prior to a major crisis using non-oriented super-SBM

We illustrate how data envelopment analysis (DEA) can be used as a forward-looking method to flag bank holding companies (BHCs) likely to become distressed. Various financial performance models are tested in the period leading up to the recent global financial crisis. Results generally support DEA’s discriminatory and predictive power, suggesting that it can identify distressed banks up to 2 years in advance. Robustness tests reveal that DEA has a stable efficient frontier and its discriminatory and predictive powers prevail even after data perturbations. DEA can be used as a preliminary off-site screening tool by regulators, by business managers to ascertain their standing among competitors, and by investors. Attention by regulators can be further directed at potentially distressed banks as some of them would be candidates for closer monitoring. In conclusion, DEA may be useful in making economic decisions because there is an identifiable link between inefficiency and financial distress. To the best of our knowledge, application of DEA to predict financial distress among BHCs prior to a major crisis has not been published.     

Anchor points in DEA

Anchor points play an important role in DEA theory and application. They define the transition from the efficient frontier to the “free-disposability” portion of the boundary. Our objective is to use the geometrical properties of anchor points to design and test an algorithm for their identification. We focus on the variable returns to scale production possibility set; our results do not depend on any particular DEA LP formulation, primal/dual form or orientation. Tests on real and artificial data lead to unexpected insights into their role in the geometry of the DEA production possibility set.     

Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market

We propose a way of using DEA cross-efficiency evaluation in portfolio selection. While cross efficiency is an approach developed for peer evaluation, we improve its use in portfolio selection. In addition to (average) cross-efficiency scores, we suggest to examine the variations of cross-efficiencies, and to incorporate two statistics of cross-efficiencies into the mean-variance formulation of portfolio selection. Two benefits are attained by our proposed approach. One is selection of portfolios well-diversified in terms of their performance on multiple evaluation criteria, and the other is alleviation of the so-called “ganging together” phenomenon of DEA cross-efficiency evaluation in portfolio selection. We apply the proposed approach to stock portfolio selection in the Korean stock market, and demonstrate that the proposed approach can be a promising tool for stock portfolio selection by showing that the selected portfolio yields higher risk-adjusted returns than other benchmark portfolios for a 9-year sample period from 2002 to 2011.     

Theory of integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, introducing new axioms of “natural disposability” and “natural divisibility”. We derive a DEA production possibility set that satisfies the minimum extrapolation principle under our refined set of axioms. We also present a mixed integer linear programming formula for computing efficiency scores. An empirical application to Iranian university departments illustrates the approach.     

Unoriented two-stage DEA: The case of the oscillating intermediate products

Data envelopment analysis (DEA) allows us to evaluate the relative efficiency of each of a set of decision-making units (DMUs). However, the methodology does not permit us to identify specific sources of inefficiency because DEA views the DMU as a “black box” that consumes a mix of inputs and produces a mix of outputs. Thus, DEA does not provide a DMU manager with insight regarding the internal source of the organization’s inefficiency.     

Portfolio insurance: Gap risk under conditional multiples

The research on financial portfolio optimization has been originally developed by Markowitz (1952). It has been further extended in many directions, among them the portfolio insurance theory introduced by Leland and Rubinstein (1976) for the “Option Based Portfolio Insurance” (OBPI) and Perold (1986) for the “Constant Proportion Portfolio Insurance” method (CPPI). The recent financial crisis has dramatically emphasized the interest of such portfolio strategies. This paper examines the CPPI method when the multiple is allowed to vary over time. To control the risk of such portfolio management, a quantile approach is introduced together with expected shortfall criteria. In this framework, we provide explicit upper bounds on the multiple as function of past asset returns and volatilities. These values can be statistically estimated from financial data, using for example ARCH type models. We show how the multiple can be chosen in order to satisfy the guarantee condition, at a given level of probability and for various financial market conditions.     

Stepwise selection of variables in data envelopment analysis: Procedures and managerial perspectives

One of the most important steps in the application of modeling using data envelopment analysis (DEA) is the choice of input and output variables. In this paper, we develop a formal procedure for a “stepwise” approach to variable selection that involves sequentially maximizing (or minimizing) the average change in the efficiencies as variables are added or dropped from the analysis. After developing the stepwise procedure, applications from classic DEA studies are presented and the new managerial insights gained from the stepwise procedure are discussed. We discuss how this easy to understand and intuitively sound method yields useful managerial results and assists in identifying DEA models that include variables with the largest impact on the DEA results.     

Diversification-consistent data envelopment analysis with general deviation measures

We propose new efficiency tests which are based on traditional DEA models and take into account portfolio diversification. The goal is to identify the investment opportunities that perform well without specifying our attitude to risk. We use general deviation measures as the inputs and return measures as the outputs. We discuss the choice of the set of investment opportunities including portfolios with limited number of assets. We compare the optimal values (efficiency scores) of all proposed tests leading to the relations between the sets of efficient opportunities. Strength of the tests is then discussed. We test the efficiency of 25 world financial indices using new DEA models with CVaR deviation measures.     

Brazilian exchange rate complexity: Financial crisis effects

With the financial market globalization, foreign investments became vital for the economies, mainly in emerging countries. In the last decades, Brazilian exchange rates appeared as a good indicator to measure either investors’ confidence or risk aversion. Here, some events of global or national financial crisis are analyzed, trying to understand how they influenced the “dollar-real” rate evolution. The theoretical tool to be used is the López-Mancini-Calbet (LMC) complexity measure that, applied to real exchange rate data, has shown good fitness between critical events and measured patterns.     

Input/output selection in DEA under expert information,with application to financial markets

Data envelopment analysis (DEA), as generally used, assumes precise knowledge regarding which variables are inputs and outputs; however, in many applications, there exists only partial knowledge. This paper presents a new methodology for selecting input/output variables endogenously to the DEA model in the presence of partial (or expert’s) knowledge by employing a reward variable observed exogenous to the operation of the DMUs. The reward is an allocation of a limited resource by an external agency, e.g. capital allocation by a market, based on the perceived internal managerial efficiencies. We present an iterative two-stage optimization model which addresses the benefit of possibly violating the expert information to determine an optimal internal performance evaluation of the DMUs for maximizing its correlation with the reward metric. Theoretical properties of the model are analyzed and statistical significance tests are developed for the marginal value of expert violation. The methodology is applied in Fundamental Analysis of publicly-traded firms, using quarterly financial data, to determine an optimized DEA-based fundamental strength indicator. More than 800 firms covering all major sectors of the US stock market are used in the empirical evaluation of the model. The firms so-screened by the model are used within out-of-sample mean-variance long-portfolio allocation to demonstrate the superiority of the methodology as an investment decision tool.     

Financial sustainability and poverty outreach within a network of village banks in Cameroon: A multi-DEA approach

Microfinance institutions face a double bottom-line. They perform financial tasks by giving microcredits to their customers and support projects aiming at reducing poverty. In doing so, they have to be financially self-sufficient and to target poor people excluded from the traditional financial systems. However, a trade-off may exist between financial sustainability and poverty outreach for these institutions. By using a multi-DEA approach, this paper shows that even if a trade-off exists for 15% of the MC² (Mutuelles Communautaires de Croissance) in Cameroon, there is no trade-off for 46% of them. In order to increase, without trade-off, financial and social performance of inefficient MC², a benchmarking approach combing DEA and performance indicators has been developed. DEA is used for identifying best-practices and setting benchmarking goals. Performance indicators are used for characterizing areas needing improvements and following the evolution of MC² toward their goals, i.e., for implementing benchmarking. Complementarity of both approaches provides a tool box for improving financial and social efficiency and reducing the trade-off between financial sustainability and poverty outreach of microfinance institutions.     

Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments

Demand fluctuations that cause variations in output levels will affect a firm’s technical inefficiency. To assess this demand effect, a demand-truncated production function is developed and an “effectiveness” measure is proposed. Often a firm can adjust some input resources influencing the output level in an attempt to match demand. We propose a short-run capacity planning method, termed proactive data envelopment analysis, which quantifies the effectiveness of a firm’s production system under demand uncertainty. Using a stochastic programming DEA approach, we improve upon short-run capacity expansion planning models by accounting for the decreasing marginal benefit of inputs and estimating the expected value of effectiveness, given demand. The law of diminishing marginal returns is an important property of production function; however, constant marginal productivity is usually assumed for capacity expansion problems resulting in biased capacity estimates. Applying the proposed model in an empirical study of convenience stores in Japan demonstrates the actionable advice the model provides about the levels of variable inputs in uncertain demand environments. We conclude that the method is most suitable for characterizing production systems with perishable goods or service systems that cannot store inventories.     

A dual simplex-based method for determination of the right and left returns to scale in DEA

This study reviews the concept of the “right” and the “left” returns to scale (RTS) in data envelopment analysis (DEA), and a dual simplex-based method, for determining these two notions in RTS, is proposed, which has computational advantages as compared to the customary method.     

An epsilon-based measure of efficiency in DEA – A third pole of technical efficiency

In DEA, we have two measures of technical efficiency with different characteristics: radial and non-radial. In this paper we compile them into a composite model called “epsilon-based measure (EBM).” For this purpose we introduce two parameters which connect radial and non-radial models. These two parameters are obtained from the newly defined affinity index between inputs or outputs along with principal component analysis on the affinity matrix. Thus, EBM takes into account diversity of input/output data and their relative importance for measuring technical efficiency.     

Financial statement analysis: A data envelopment analysis approach

Ratio analysis is a commonly used analytical tool for verifying the performance of a firm. While ratios are easy to compute, which in part explains their wide appeal, their interpretation is problematic, especially when two or more ratios provide conflicting signals. Indeed, ratio analysis is often criticized on the grounds of subjectivity, that is the analyst must pick and choose ratios in order to assess the overall performance of a firm.In this paper we demonstrate that Data Envelopment Analysis (DEA) can augment the traditional ratio analysis. DEA can provide a consistent and reliable measure of managerial or operational efficiency of a firm. We test the null hypothesis that there is no relationship between DEA and traditional accounting ratios as measures of performance of a firm. Our results reject the null hypothesis indicating that DEA can provide information to analysts that is additional to that provided by traditional ratio analysis. We also apply DEA to the oil and gas industry to demonstrate how financial analysts can employ DEA as a complement to ratio analysis.     

Chapter 13 Satisficing DEA models under chance constraints

DEA (Data Envelopment Analysis) models and concepts are formulated here in terms of the P-Models of Chance Constrained Programming, which are then modified to contact the satisficing concepts of H.A. Simon. Satisficing is thereby added as a third category to the efficiency/inefficiency dichotomies that have heretofore prevailed in DEA. Formulations include cases in which inputs and outputs are stochastic, as well as cases in which only the outputs are stochastic. Attention is also devoted to situations in which variations in inputs and outputs are related through a common random variable. Extensions include new developments in goal programming with deterministic equivalents for the corresponding satisficing models under chance constraints.