Zhongbao Zhou

A bargaining game model for efficiency decomposition in the centralized model of two-stage systems

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). The centralized model has been widely used to examine the efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Since there may exist some flexibility in decomposing the overall efficiency between the two stages when multiple optimal weights exist, we develop a Nash bargaining game model to obtain a fair efficiency decomposition for the two stages while keeping the overall efficiency unchanged under this circumstance. The minimal achievable efficiencies for the two stages are used as the breakdown point and the unique bargaining decomposition of the overall efficiency is obtained subsequently. The Nash bargaining game model is applied to evaluate the performance of 10 branches of China Construction Bank.

Short communication: Fuzzy data envelopment analysis models with assurance regions: A note

In a recent paper in this journal by Liu and Chuang [Liu, S. -T., & Chuang, M. (2009). Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries. Expert Systems with Applications, 36(2), 1105-1113]. Proposition 1 is proved for finding lower and upper bounds of the @a-cut of E~r. However, we find that the above proof omit the verification of constraints of assurance regions and the models (11) and (12) omit the constraints of DMUr, which makes it incredible. In this paper, we correct the models and proof of Proposition 1 in Liu and Chuang (2009). We also propose a generalized fuzzy data envelopment model with assurance regions, whose lower and upper bounds at given levels could be obtained similarly.

Further study of production possibility set and performance evaluation model in supply chain DEA

Performance evaluation is an importance issue in supply chain management. Yang et al. (Ann. Oper. Res. 38(6):195–211, 2011) defined two types of supply chain production possibility sets and proved the equivalence between them. Based on the sub-perfect CRS production possibility set, they proposed a supply chain DEA model to appraise the overall technical efficiency of supply chains. The relationship among efficiency scores of the proposed model, CCR models of system and subsystems are discussed. However, we find that the equivalence between the two types of supply chain production possibility sets is not correct. The proofs of their three theorems are all problematic. In this paper, we correct some results and give three new proofs.

Performance Evaluation of Portfolios with Margin Requirements

In financial markets, short sellers will be required to post margin to cover possible losses in case the prices of the risky assets go up. Only a few studies focus on the optimization and performance evaluation of portfolios in the presence of margin requirements. In this paper, we investigate the theoretical foundation of DEA (data envelopment analysis) approach to evaluate the performance of portfolios with margin requirements from a different perspective. Under the mean-variance framework, we construct the optimization model and portfolio possibility set on considering margin requirements. The convexity of the portfolio possibility set is proved and the concept of efficiency in classical economics is extended to the portfolio case. The DEA models are then developed to evaluate the performance of portfolios with margin requirements. Through the simulations carried out in the end, we show that, with adequate portfolios, DEA can be used as an effective tool in computing the efficiencies of portfolios with margin requirements for the performance evaluation purpose. This study can be viewed as a justification of DEA into performance evaluation of portfolios with margin requirements.

Game cross efficiency for systems with two-stage structures

Data envelopment analysis (DEA) is a nonparametric approach for measuring the relative efficiencies of peer decision-making units (DMUs). For systems with two-stage structures, where all the outputs from the first stage are the only inputs to the second stage, the centralized model, which is based on the concept of cooperative game theory, has been widely used to examine the efficiencies of such systems. We define the cross efficiencies of systems with two-stage structures. Since the centralized model may lead to multiple and unacceptable cross efficiencies and rankings of DMUs due to its high flexibility in choosing optimal weights on input and output factors, we develop a game model to obtain a unique cross efficiency measure, which is constructed from the perspective of noncooperative game. An iterative algorithm is then proposed to obtain the game cross efficiencies for the overall systems and subsystems. We use the proposed game model to evaluate the performance of top 30 US commercial banks. The results show that the game model can lead to a unique reasonable cross efficiency for each DMU.

How relevant is the choice of risk management control variable to non-parametric bank profit efficiency analysis? The case of South Korean banks

Adopting a profit-based approach to the estimation of the efficiency of South Korean banks over the 2007Q3 to 2011Q2 period, we systematically analyse, within a non-parametric DEA analysis, how the choice of risk management control variable impacts upon such estimates. This is in recognition of previous findings that such estimates are dependent on the choice of risk management control variable and the lack of guidance from such studies on the optimal choice of risk control variable. Using the model of Liu et al. (Ann Operat Res 173:177–194, 2010), we examine the dependency of the estimated efficiency scores on the chosen risk control variables embracing loan loss provisions and equity as good inputs and non-performing loans as a bad output. We duly find that, both for individual banks and banking groups, the mean estimates are indeed model dependent although, for the former, rank correlations do not change much at the extremes. Based on the application of the Simar and Zelenyuk (Econom Rev 25:497–522, 2006) adapted Li (Econom Rev 15: 261–274, 1996) test, we then find that, if only one of the three risk control variables is to be included in such an analysis, then it should be loan loss provisions. We also show, however, that the inclusion of all three risk control variable is to be preferred to just including one, but that the inclusion of two such variables is about as good as including all three. We therefore conclude that the optimal approach is to include (any) two of the three risk control variables identified. The wider implication for research into bank efficiency is that the optimal choice of risk management control variable is likely to be crucial to both the delivery of risk-adjusted estimates of bank efficiency and the specification of the model to be estimated.

DEA frontier improvement and portfolio rebalancing: An application of China mutual funds on considering sustainability information disclosure

Abstract Data envelopment analysis (DEA) has been a widely used methodology for evaluating the relative performance of portfolios. Extensive work has appeared for realizing the role of DEA in the aspect of assessing portfolio performance and deriving the relative rankings. However, the role of providing realizable benchmarks is not fully explored in the existing literatures. Most importantly, the DEA-based portfolio performance evaluation methods developed in the existing literatures can hardly provide support for fund managers in pursuing sustainability performance. In this paper, we first propose a DEA frontier improvement approach under the mean-variance framework. This approach provides investor with a rebalancing strategy as well as an improved DEA frontier which approximates the portfolio efficient frontier better than the traditional DEA model does. Then, this approach is extended to a general return-risk framework. Our in-sample simulation results verify the effectiveness of the proposed approach for a wide range of applications. In addition, the out-of-sample tests show that the rebalancing investment strategies can achieve higher Sharpe ratios and Sortino ratios than those of the original ones. Finally, we apply the proposed approach to evaluate mutual fund performance in China with the consideration of sustainability information disclosure. We construct a disclosure index to indicate the extent of sustainable information disclosure of each mutual fund. The results show that the proposed approach provides not only investment recommendations, but also references for constructing sustainable green funds.

Stochastic network DEA models for two-stage systems under the centralized control organization mechanism

Abstract This paper deals with an extension of the conventional DEA formulations by taking into account the serial relationship of two-stage processes with stochastic data. The stochastic two-stage network DEA model is proposed based on centralized control organization mechanism. The stochastic two-stage network DEA model is converted into a deterministic linear programming model under the assumption that components of inputs, outputs and intermediate products are related with some basic stochastic factors. Stochastic efficiency analysis including the relationships of the whole process and the two sub-processes are then discussed. In addition, an example of 16 commercial banks in China is used to calculate the efficiencies under different levels by applying the proposed model.

Banks efficiency and productivity in Togo after the financial liberalization: a combined Malmquist index approach

ABSTRACT The objective of this study is to analyze the productivity growth of Togolese banks. The study period (2000–2008) corresponds to the post-financial liberalization in the West African Economic and Monetary Union (WAEMU) zone and the third phase of a changed banking and financial environment. We develop a new combined Malmquist index based on ‘P-index II’ in order to estimate the total factor productivity (TFP) growth and its components. The empirical results show that the TFP has considerably increased for the whole industry, in which technical change is found to be a more important source of productivity growth to Togolese banks compared to efficiency change. In line with this, it is indicated that the financial liberalization does not improve the technical efficiencies of banks in Togo on a whole.

Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.