IDEAS home Printed from https://ideas.repec.org/a/ora/journl/v1y2016i1p548-557.html
   My bibliography  Save this article

Differences Between Mean-Variance And Mean-Cvar Portfolio Optimization Models

Author

Listed:
  • Panna Miskolczi

    (University of Debrecen Faculty of Economics and Business)

Abstract

Everybody heard already that one should not expect high returns without high risk, or one should not expect safety without low returns. The goal of portfolio theory is to find the balance between maximizing the return and minimizing the risk. To do so we have to first understand and measure the risk. Naturally a good risk measure has to satisfy several properties - in theory and in practise. Markowitz suggested to use the variance as a risk measure in portfolio theory. This led to the so called mean-variance model - for which Markowitz received the Nobel Prize in 1990. The model has been criticized because it is well suited for elliptical distributions but it may lead to incorrect conclusions in the case of non-elliptical distributions. Since then many risk measures have been introduced, of which the Value at Risk (VaR) is the most widely used in the recent years. Despite of the widespread use of the Value at Risk there are some fundamental problems with it. It does not satisfy the subadditivity property and it ignores the severity of losses in the far tail of the profit-and-loss (P&L) distribution. Moreover, its non-convexity makes VaR impossible to use in optimization problems. To come over these issues the Expected Shortfall (ES) as a coherent risk measure was developed. Expected Shortfall is also called Conditional Value at Risk (CVaR). Compared to Value at Risk, ES is more sensitive to the tail behaviour of the P&L distribution function. In the first part of the paper I state the definition of these three risk measures. In the second part I deal with my main question: What is happening if we replace the variance with the Expected Shortfall in the portfolio optimization process. Do we have different optimal portfolios as a solution? And thus, does the solution suggests to decide differently in the two cases? To answer to these questions I analyse seven Hungarian stock exchange companies. First I use the mean-variance portfolio optimization model, and then the mean-CVaR model. The results are shown in several charts and tables.

Suggested Citation

  • Panna Miskolczi, 2016. "Differences Between Mean-Variance And Mean-Cvar Portfolio Optimization Models," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 548-557, July.
    • Handle: RePEc:ora:journl:v:1:y:2016:i:1:p:548-557
    as

    Download full text from publisher

    File URL: http://anale.steconomiceuoradea.ro/volume/2016/n1/53.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:hal:journl:hal-00921283 is not listed on IDEAS
    2. Suzanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures," Working Papers hal-00921283, HAL.
    3. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    4. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Osman, Myriam Ben & Galariotis, Emilios & Guesmi, Khaled & Hamdi, Haykel & Naoui, Kamel, 2023. "Diversification in financial and crypto markets," International Review of Financial Analysis, Elsevier, vol. 89(C).
    2. Peter Zweifel, 2021. "Solvency Regulation—An Assessment of Basel III for Banks and of Planned Solvency III for Insurers," JRFM, MDPI, vol. 14(6), pages 1-22, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bassetti, Federico & De Giuli, Maria Elena & Nicolino, Enrica & Tarantola, Claudia, 2018. "Multivariate dependence analysis via tree copula models: An application to one-year forward energy contracts," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1107-1121.
    2. Nikola RADIVOJEVIĆ & Luka FILIPOVI & Тomislav D. BRZAKOVIĆ, 2020. "A New Semiparametric Mirrored Historical Simulation Value-At-Risk Model," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 5-21, March.
    3. Marc Busse & Michel Dacorogna & Marie Kratz, 2014. "The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio," Risks, MDPI, vol. 2(3), pages 1-17, July.
    4. Eric Beutner & Henryk Zähle, 2018. "Bootstrapping Average Value at Risk of Single and Collective Risks," Risks, MDPI, vol. 6(3), pages 1-30, September.
    5. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    6. Ruodu Wang & Johanna F. Ziegel, 2014. "Distortion Risk Measures and Elicitability," Papers 1405.3769, arXiv.org, revised May 2014.
    7. Elisabetta Cagna & Giulio Casuccio, 2014. "Equally-weighted Risk Contribution Portfolios: an empirical study using expected shortfall," CeRP Working Papers 142, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    8. Tobias Fissler & Johanna F. Ziegel, 2015. "Higher order elicitability and Osband's principle," Papers 1503.08123, arXiv.org, revised Sep 2015.
    9. Rafael Frongillo & Ian A. Kash, 2015. "Elicitation Complexity of Statistical Properties," Papers 1506.07212, arXiv.org, revised Aug 2020.
    10. Osmundsen, Kjartan Kloster, 2017. "Using Expected Shortfall for Credit Risk Regulation," UiS Working Papers in Economics and Finance 2017/4, University of Stavanger.
    11. Bignozzi, Valeria & Merlo, Luca & Petrella, Lea, 2024. "Inter-order relations between equivalence for Lp-quantiles of the Student's t distribution," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 44-50.
    12. Winter, Peter, 2007. "Managerial Risk Accounting and Control – A German perspective," MPRA Paper 8185, University Library of Munich, Germany.
    13. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2024. "Testing Granger non-causality in expectiles," Econometric Reviews, Taylor & Francis Journals, vol. 43(1), pages 30-51, January.
    14. Juan Carlos Escanciano & Zaichao Du, 2015. "Backtesting Expected Shortfall: Accounting for Tail Risk," CAEPR Working Papers 2015-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    15. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    16. Chen, Yu & Ma, Mengyuan & Sun, Hongfang, 2023. "Statistical inference for extreme extremile in heavy-tailed heteroscedastic regression model," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 142-162.
    17. Maria Logvaneva & Mikhail Tselishchev, 2022. "On a Stochastic Model of Diversification," Papers 2204.01284, arXiv.org.
    18. Nan Zhang & Heng Xu, 2024. "Fairness of Ratemaking for Catastrophe Insurance: Lessons from Machine Learning," Information Systems Research, INFORMS, vol. 35(2), pages 469-488, June.
    19. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    20. Eugene N. Gurenko & Alexander Itigin, 2009. "Solvency Measures for Insurance Companies : Is There a Room for Improvement?," World Bank Publications - Reports 12831, The World Bank Group.

    More about this item

    Keywords

    risk; Value at Risk; Expected Shortfall; Mean-Variance Portfolio Optimization; Mean-CVaR Portfolio Optimization;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ora:journl:v:1:y:2016:i:1:p:548-557. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catalin ZMOLE (email available below). General contact details of provider: https://edirc.repec.org/data/feoraro.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.