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

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  • 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
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    File URL: http://anale.steconomiceuoradea.ro/volume/2016/n1/53.pdf
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    References listed on IDEAS

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    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.
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    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.

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    More about this item

    Keywords

    risk; Value at Risk; Expected Shortfall; Mean-Variance Portfolio Optimization; Mean-CVaR Portfolio Optimization;
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    JEL classification:

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

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