Constant and variable returns to scale DEA models for socially responsible investment funds

In order to evaluate the performance of socially responsible investment (SRI) funds, we propose some models which use data envelopment analysis (DEA) and can be computed in all phases of the business cycle. These models focus on the most crucial elements of an investment in mutual funds.     

Data envelopment analysis of mutual funds based on second-order stochastic dominance

Although data envelopment analysis (DEA) has been extensively used to assess the performance of mutual funds (MF), most of the approaches overestimate the risk associated to the endogenous benchmark portfolio. This is because in the conventional DEA technology the risk of the target portfolio is computed as a linear combination of the risk of the assessed MF. This neglects the important effects of portfolio diversification. Other approaches based on mean–variance or mean–variance–skewness are non-linear. We propose to combine DEA with stochastic dominance criteria. Thus, in this paper, six distinct DEA-like linear programming (LP) models are proposed for computing relative efficiency scores consistent (in the sense of necessity) with second-order stochastic dominance (SSD). The aim is that, being SSD efficient, the obtained target portfolio should be an optimal benchmark for any rational risk-averse investor. The proposed models are compared with several related approaches from the literature.     

Contrarian investment strategy with data envelopment analysis concept

One of the typical issues in financial literature is that the market tends to be overly pessimistic about value stocks, many of which are past losers. Therefore, over-reactions might capture by measuring earnings surprise vary with past return levels. In this paper, we propose a new index for an effective investment strategy to capture the return-reversal effect using both Data Envelopment Analysis (DEA) and Inverted DEA in order to consider the above characteristics of the market. Our investment strategy using the new index exhibits better performance than the naive return-reversal strategy that only uses past returns or earnings surprise. In addition, the correlations between our new index and commonly used value indices are insignificant, and the value indices cannot represent the over-valued (under-valued) situations perfectly. Hence, considering both proposed and value indices like book-to-price one, we could select value stocks more effectively than by using only one of these indices.     

Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach

This research theoretically explores the measurement of returns to scale (RTS), using a non-radial DEA (data envelopment analysis) model. A range-adjusted measure (RAM) is used as a representative of such non-radial models. Historically, a type of RTS has been discussed within an analytical framework of radial models. The radial-based RTS measurement is replaced by the non-radial RAM/RTS measurement in this study. When discussing the non-radial RAM/RTS measurement, this study finds a problem of multiple projections that cannot be found in the radial measurement. In this research, a new linear programming approach is proposed to identify all efficient DMUs (decision making units) on a reference set. The important feature of the proposed approach is that it can deal with a simultaneous occurrence of (a) multiple reference sets, (b) multiple supporting hyperplanes and (c) multiple projections. All of the three difficulties are handled by the proposed RAM/RTS measurement. In particular, we discuss both when the three different types of multiple solutions occur on the RAM/RTS measurement and how to deal with such difficulties. Our research results make it possible to measure not only the type of RTS but also the magnitude of RTS in the RAM measurement.     

Measuring returns to scale in DEA models when the firm is regulated

In the standard framework of data envelopment analysis (DEA) models, the returns to scale are fully characterized using the multiplier on the convexity constraint of inefficient decision making units (DMU) using the projection of the input–output vector on the frontier. In this note, we investigate how the returns to scale measurements in DEA models are affected by the presence of regulatory constraints. These additional constraints change the role played by the convexity constraint. In order to avoid biased estimation of the returns to scale, we show that the interaction between the regulatory and the convexity constraints has to be taken into account.     

An investigation on the sensitivity and stability radius of returns to scale and efficiency in data envelopment analysis

An issue which has received widespread attention in rapidly growing field of DEA is the sensitivity of the results of analysis to perturbations in the data.     

Resampling DEA estimates of investment fund performance

Data envelopment analysis (DEA) is attractive for comparing investment funds because it handles different characteristics of fund distribution and gives a way to rank funds. There is substantial literature applying DEA to funds, based on the time series of funds’ returns. This article looks at the issue of uncertainty in the resulting DEA efficiency estimates, investigating consistency and bias. It uses the bootstrap to develop stochastic DEA models for funds, derive confidence intervals and develop techniques to compare and rank funds and represent the ranking. It investigates how to deal with autocorrelation in the time series and considers models that deal with correlation in the funds’ returns.     

Data envelopment analysis with nonlinear virtual inputs and outputs

An underlying assumption in DEA is that the weights coupled with the ratio scales of the inputs and outputs imply linear value functions. In this paper, we present a general modeling approach to deal with outputs and/or inputs that are characterized by nonlinear value functions. To this end, we represent the nonlinear virtual outputs and/or inputs in a piece-wise linear fashion. We give the CCR model that can assess the efficiency of the units in the presence of nonlinear virtual inputs and outputs. Further, we extend the models with the assurance region approach to deal with concave output and convex input value functions. Actually, our formulations indicate a transformation of the original data set to an augmented data set where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. To underline the usefulness of such a new development, we revisit a previous work of one of the authors dealing with the assessment of the human development index on the light of DEA.     

Benefit-cost analysis using data envelopment analysis

Benefit-cost analysis is required by law and regulation throughout the federal government. Robert Dorfman (1996) declares ‘Three prominent shortcomings of benefit-cost analysis as currently practiced are (1) it does not identify the population segments that the proposed measure benefits or harms (2) it attempts to reduce all comparisons to a single dimension, generally dollars and cents and (3) it conceals the degree of inaccuracy or uncertainty in its estimates.’ The paper develops an approach for conducting benefit-cost analysis derived from data envelopment analysis (DEA) that overcomes each of Dorfman's objections. The models and methodology proposed give decision makers a tool for evaluating alternative policies and projects where there are multiple constituencies who may have conflicting perspectives. This method incorporates multiple incommensurate attributes while allowing for measures of uncertainty. An application is used to illustrate the method. This work was funded by grant N00014-99-1-0719 from the Office of Naval Research     

On a basic definition of returns to scale

A concept that has sparked considerable interest in DEA is that of returns to scale (RTS). One of the basic and useful definitions of RTS in DEA models is based upon the PPS. In this work, a discussion about the PPS-based definition of RTS is given, leading to a modified definition of RTS which is suitable in the presence of multiple supporting hyperplanes passing through the unit under assessment. The definition provided is a simplification of a definition given by Tone.     

Global variation of outputs with respect to the variation of inputs in performance analysis; generalized RTS

Returns to scale (RTS) is an important topic in performance analysis, which helps managers to make decisions about the expansion or contraction of the operation of the DMU under assessment. But the RTS classification of DMUs gives only partial information, because it is a local notion. In this paper we extend the concept of RTS and we seek the precise relation between the proportional variation of outputs and the proportional variation of inputs. An approach is provided, which is able to determine this relation based on the parametric analysis and perturbation in linear programming.     

Measurement of returns to scale using non-radial DEA models

There are some specific features of the non-radial data envelopment analysis (DEA) models which cause some problems for the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using Strong Complementary Slackness Conditions from optimization theory. However, our investigation and computational experiments show that such methods increase computational complexity significantly and may generate as optimal, solutions contradicting optimization theory. In this paper, we propose and substantiate a direct method for the returns to scale measurement in the non-radial DEA models. Our computational experiments documented that the proposed method works reliably and efficiently on the real-life data sets.     

Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks

Conventional data envelopment analysis (DEA) for measuring the efficiency of a set of decision making units (DMUs) requires the input/output data to be constant. In reality, however, many observations are stochastic in nature; consequently, the resulting efficiencies are stochastic as well. This paper discusses how to obtain the efficiency distribution of each DMU via a simulation technique. The case of Taiwan commercial banks shows that, firstly, the number of replications in simulation analysis has little effect on the estimation of efficiency means, yet 1000 replications are recommended to produce reliable efficiency means and 2000 replications for a good estimation of the efficiency distributions. Secondly, the conventional way of using average data to represent stochastic variables results in efficiency scores which are different from the mean efficiencies of the presumably true efficiency distributions estimated from simulation. Thirdly, the interval-data approach produces true efficiency intervals yet the intervals are too wide to provide valuable information. In conclusion, when multiple observations are available for each DMU, the stochastic-data approach produces more reliable and informative results than the average-data and interval-data approaches do.     

Two-stage financial risk tolerance assessment using data envelopment analysis

Typical questionnaires administered by financial advisors to assess financial risk tolerance mostly contain stereotypes of people, have seemingly unscientific scoring approaches and often treat risk as a one-dimensional concept. In this work, a mathematical tool was developed to assess relative risk tolerance using Data Envelopment Analysis (DEA). At its core, it is a novel questionnaire that characterizes risk by its four distinct elements: propensity, attitude, capacity, and knowledge. Over 180 individuals were surveyed and their responses were analyzed using the Slacks-based measure type of DEA efficiency model. Results show that the multidimensionality of risk must be considered for complete assessment of risk tolerance. This approach also provides insight into the relationship between risk, its elements and other variables. Specifically, the perception of risk varies by gender as men are generally less risk averse than women. In fact, risk attitude and knowledge scores are consistently lower for women, while there is no statistical difference in their risk capacity and propensity compared to men. The tool can also serve as a “risk calculator” for an appropriate and defensible method to meet legal compliance requirements, known as the “Know Your Client” rule, that exist for Canadian financial institutions and their advisors.     

An additive model approach for estimating returns to scale in imprecise data envelopment analysis

In this paper, additive model is used to provide an alternative approach for estimating returns to scale in data envelopment analysis. The proposed model is developed in both stochastic and fuzzy data envelopment analysis. Deterministic (crisp) equivalents are obtained which correspond to the stochastic and fuzzy models. Numerical examples are, also, used to illustrate the proposed approaches.     

Improving weak efficiency frontiers in the fuzzy data envelopment analysis models

Evaluating the performance of activities or organization by common data envelopment analysis models requires crisp input/output data. However, the precise inputs and outputs of production processes cannot be always measured. Thus, the data envelopment analysis measurement containing fuzzy data, called “fuzzy data envelopment analysis”, has played an important role in the evaluation of efficiencies of real applications. This paper focuses on the fuzzy CCR model and proposes a new method for determining the lower bounds of fuzzy inputs and outputs. This improves the weak efficiency frontiers of the corresponding production possibility set. Also a numerical example illustrates the capability of the proposed method.     

The impossibility of convex constant returns-to-scale production technologies with exogenously fixed factors

The extensions to the variable (VRS) and the constant (CRS) returns-to-scale models developed by Banker and Morey are considered among the main approaches to the incorporation of exogenously fixed factors in models of data envelopment analysis (DEA). Recently, Syrjänen showed that the Banker and Morey CRS technology is not convex. Taking into account that its subset VRS technology is explicitly assumed convex, this observation leads to difficulties with explaining the fundamental production assumptions of the CRS extension. Motivated by the example of Syrjänen, the contribution of this paper is twofold. First, we show that the nonconvex Banker and Morey CRS technology is nevertheless a suitable reference technology for the assessment of scale efficiency. Second, we ask if a convex technology could be constructed that would “correct” the nonconvexity of the CRS technology of Banker and Morey. The answer to this is negative: one consequence of assuming both convexity and ray unboundness with fixed exogenous factors is that we can always “mix-and-match” discretionary and nondiscretionary factors taken from different units, arriving at totally unrealistic production plans. This demonstrates that generally there exists no meaningful convex CRS technology with exogenously fixed factors that can be used in its own right, apart from its use as a reference technology in the measurement of scale efficiency.     

Incorporating performance measures with target levels in data envelopment analysis

Data envelopment analysis (DEA) is a technique for evaluating relative efficiencies of peer decision making units (DMUs) which have multiple performance measures. These performance measures have to be classified as either inputs or outputs in DEA. DEA assumes that higher output levels and/or lower input levels indicate better performance. This study is motivated by the fact that there are performance measures (or factors) that cannot be classified as an input or output, because they have target levels with which all DMUs strive to achieve in order to attain the best practice, and any deviations from the target levels are not desirable and may indicate inefficiency. We show how such performance measures with target levels can be incorporated in DEA. We formulate a new production possibility set by extending the standard DEA production possibility set under variable returns-to-scale assumption based on a set of axiomatic properties postulated to suit the case of targeted factors. We develop three efficiency measures by extending the standard radial, slacks-based, and Nerlove–Luenberger measures. We illustrate the proposed model and efficiency measures by applying them to the efficiency evaluation of 36 US universities.     

Network data envelopment analysis: A review

Network data envelopment analysis (DEA) concerns using the DEA technique to measure the relative efficiency of a system, taking into account its internal structure. The results are more meaningful and informative than those obtained from the conventional black-box approach, where the operations of the component processes are ignored. This paper reviews studies on network DEA by examining the models used and the structures of the network system of the problem being studied. This review highlights some directions for future studies from the methodological point of view, and is inspirational for exploring new areas of application from the empirical point of view.     

Enhancement of equity portfolio performance using data envelopment analysis

This paper examines the applicability of data envelopment analysis (DEA) as a basis of selection criteria for equity portfolios. It is the first DEA application for constructing a combined equity investment strategy that aims to integrate the benefits of both value investing and momentum investing. The 3-quantile portfolios are composed of a comprehensive sample of Finnish non-financial stocks based on their DEA efficiency scores that are calculated using three variants of DEA models (the constant returns-to-scale, the super-efficiency, and the cross-efficiency models). The performance of portfolios is evaluated on the basis of the average return and several risk-adjusted performance metrics throughout the 1994–2010 sample period.