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

*(English)*Zbl 1206.91019Summary: 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.

##### MSC:

91B06 | Decision theory |

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

62P20 | Applications of statistics to economics |

##### Keywords:

data envelopment analysis; value of expert information; portfolio selection; fundamental investment analysis
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\textit{N. C. P. Edirisinghe} and \textit{X. Zhang}, Eur. J. Oper. Res. 207, No. 3, 1669--1678 (2010; Zbl 1206.91019)

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##### References:

[1] | Andersen, P.; Petersen, N.C., A procedure for ranking efficient units in data envelopment analysis, Management science, 39, 1261-1264, (1993) · Zbl 0800.90096 |

[2] | Bala, K.; Cook, W.D., Performance measurement with classification information: an enhanced additive DEA model, The international journal of management science – omega, 31, 439-450, (2003) |

[3] | Banker, R.D., Estimating most productive scale size using data envelopment analysis, European journal of operational research, 17, 35-44, (1984) · Zbl 0538.90030 |

[4] | Banker, R.D.; Natarajan, R., Evaluating contextual variables affecting productivity using data envelopment analysis, Operations research, 56, 1, 48-58, (2008) · Zbl 1167.90527 |

[5] | Banker, R.D.; Charnes, A.; Cooper, W.W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management science, 30, 1078-1092, (1984) · Zbl 0552.90055 |

[6] | Banker, R.D.; Charnes, A.; Cooper, W.W.; Swarts, J.; Thomas, D.A., An introduction to data envelopment analysis with some of its models and their uses, (), 125-164 |

[7] | Box, G.E.P.; Cox, D.R., An analysis of transformations, Journal of royal statistical society, series B, 26, 211-246, (1964) · Zbl 0156.40104 |

[8] | Carrico, C.S.; Hogan, S.M.; Dyson, R.G.; Athanassopoulos, A.D., Data envelopment analysis and university selection, Journal of the operational research society, 48, 1163-1177, (1997) · Zbl 0895.90142 |

[9] | Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision-making units, European journal of operational research, 2, 429-444, (1978) · Zbl 0416.90080 |

[10] | Cook, W.D.; Bala, K., Performance measurement and classification data in DEA: input-oriented model, The international journal of management science – omega, 35, 39-52, (2007) |

[11] | Cook, W.D.; Green, R.H.; Zhu, J., Dual-role factors in data envelopment analysis, IIE transactions, 38, 105-115, (2006) |

[12] | Cooper, W.W.; Park, K.S.; Yu, G., An illustrative application of IDEA (imprecise data envelopment analysis) to a Korean mobile telecommunication company, Operations research, 49, 6, 807-820, (2001) · Zbl 1163.90539 |

[13] | Dyson, R.G.; Allen, R.; Camanho, A.S.; Podinovski, V.V.; Sarrico, C.S.; Shale, E.A., Pitfalls and protocols in DEA, European journal of operational research, 132, 245-259, (2001) · Zbl 0980.90038 |

[14] | Edirisinghe, N.C.P., Integrated risk control using stochastic programming ALM models for money management, (), 707-750, chapter 16 |

[15] | Edirisinghe, N.C.P.; Zhang, X., Generalized DEA model of fundamental analysis and its application to portfolio optimization, Journal of banking and finance, 31, 3311-3335, (2007) |

[16] | Edirisinghe, N.C.P.; Zhang, X., Portfolio selection under DEA-based relative financial strength indicators: case of US industries, Journal of the operational research society, 59, 842-856, (2008) · Zbl 1153.90454 |

[17] | Fama, E.F., Efficient capital markets: A review of theory and empirical work, Journal of finance, 25, 383-417, (1970) |

[18] | Hougaard, J.L., Theory and methodology-fuzzy scores of technical efficiency, European journal of operational research, 115, 529-541, (1999) · Zbl 0946.91002 |

[19] | Joro, T.; Viitala, E.J., Weight-restricted DEA in action: from expert opinions to mathematical models, Journal of the operational research society, 55, 814-821, (2004) · Zbl 1060.90666 |

[20] | Lasdon, L.S., Optimization theory for large systems, (1970), MacMillan London · Zbl 0224.90038 |

[21] | Markowitz, H.M., Portfolio selection, Journal of finance, 7, 77-91, (1952) |

[22] | Miliotis, P.A., Data envelopment analysis applied to electricity distribution districts, Journal of the operational research society, 43, 549-555, (1992) · Zbl 0825.90657 |

[23] | Post, T., Performance evaluation in stochastic environments using Mean-variance data envelopment analysis, Operations research, 49, 2, 281-292, (2001) · Zbl 1163.90564 |

[24] | Tamhane, A.C.; Dunlop, D.D., Statistics and data analysis from elementary to intermediate, (2000), Prentice-Hall New Jersey |

[25] | Zhu, J., Imprecise DEA via standard linear DEA models with a revisit to a Korean mobile telecommunication company, Operations research, 52, 2, 323-329, (2004) · Zbl 1165.90563 |

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