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DEA-Risk Efficiency and Stochastic Dominance Efficiency of Stock Indices

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Abstract

In this article, the authors deal with the efficiency of world stock indices. Basically, they compare three approaches: mean-risk, data envelopment analysis (DEA), and stochastic dominance (SD) efficiency. In the DEA methodology, efficiency is defined as a weighted sum of outputs compared to a weighted sum of inputs when optimal weights are used. In DEA-risk efficiency, several risk measures and functionals which quantify the risk of the indices (var, VaR, CVaR, etc.) as DEA inputs are used. Mean gross return is considered as the only DEA output. When only one risk measure as the input and mean gross return as the output are considered, the DEA-risk efficiency is related to the mean-risk efficiency. The authors test the DEA-risk efficiency of 25 indices and they analyze the sensitivity of their results with respect to the selected inputs. Using stochastic dominance criteria, they test pairwise efficiency as well as portfolio efficiency, allowing full diversification across assets. While SD pairwise efficiency testing is performed for first-order stochastic dominance (FSD) as well as for second-order stochastic dominance (SSD), the SD portfolio efficiency test is considered only for the SSD case. The authors´ numerical analysis compares the results using two sample datasets: before- and during-crisis. The results show that SSD portfolio efficiency is the most powerful efficiency criterion, that is, it classifies only one index as efficient, while FSD (SSD) pairwise efficiency tends to be very weak. The proposed DEA-risk efficiency approach represents a compromise offering a reasonable set of efficient indices.

Suggested Citation

  • Martin Branda & Miloš Kopa, 2012. "DEA-Risk Efficiency and Stochastic Dominance Efficiency of Stock Indices," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(2), pages 106-124, May.
  • Handle: RePEc:fau:fauart:v:62:y:2012:i:2:p:106-124
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    References listed on IDEAS

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    1. Basso, Antonella & Funari, Stefania, 2001. "A data envelopment analysis approach to measure the mutual fund performance," European Journal of Operational Research, Elsevier, vol. 135(3), pages 477-492, December.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
    4. Scaillet, Olivier & Topaloglou, Nikolas, 2010. "Testing for Stochastic Dominance Efficiency," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 169-180.
    5. Lozano, Sebastián & Gutiérrez, Ester, 2008. "Data envelopment analysis of mutual funds based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 189(1), pages 230-244, August.
    6. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    7. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, vol. 175(1), pages 516-542, November.
    8. repec:pal:jorsoc:v:54:y:2003:i:5:d:10.1057_palgrave.jors.2601541 is not listed on IDEAS
    9. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. repec:spr:comgts:v:14:y:2017:i:4:d:10.1007_s10287-017-0282-9 is not listed on IDEAS
    2. Liu, Wenbin & Zhou, Zhongbao & Liu, Debin & Xiao, Helu, 2015. "Estimation of portfolio efficiency via DEA," Omega, Elsevier, vol. 52(C), pages 107-118.
    3. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    4. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.

    More about this item

    Keywords

    Data Envelopment Analysis; risk measures; index efficiency; stochastic dominance;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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