IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v14y2021i11p540-d676017.html
   My bibliography  Save this article

Return Based Risk Measures for Non-Normally Distributed Returns: An Alternative Modelling Approach

Author

Listed:
  • Eyden Samunderu

    (International School of Management (ISM), Otto Hahn Str., 19, 44227 Dortmund, Germany)

  • Yvonne T. Murahwa

    (Independent Researcher, 16 Cheshire Road, Mt Pleasant, Harare P.O. Box MP163, Zimbabwe)

Abstract

Developments in the world of finance have led the authors to assess the adequacy of using the normal distribution assumptions alone in measuring risk. Cushioning against risk has always created a plethora of complexities and challenges; hence, this paper attempts to analyse statistical properties of various risk measures in a not normal distribution and provide a financial blueprint on how to manage risk. It is assumed that using old assumptions of normality alone in a distribution is not as accurate, which has led to the use of models that do not give accurate risk measures. Our empirical design of study firstly examined an overview of the use of returns in measuring risk and an assessment of the current financial environment. As an alternative to conventional measures, our paper employs a mosaic of risk techniques in order to ascertain the fact that there is no one universal risk measure. The next step involved looking at the current risk proxy measures adopted, such as the Gaussian-based, value at risk (VaR) measure. Furthermore, the authors analysed multiple alternative approaches that do not take into account the normality assumption, such as other variations of VaR, as well as econometric models that can be used in risk measurement and forecasting. Value at risk (VaR) is a widely used measure of financial risk, which provides a way of quantifying and managing the risk of a portfolio. Arguably, VaR represents the most important tool for evaluating market risk as one of the several threats to the global financial system. Upon carrying out an extensive literature review, a data set was applied which was composed of three main asset classes: bonds, equities and hedge funds. The first part was to determine to what extent returns are not normally distributed. After testing the hypothesis, it was found that the majority of returns are not normally distributed but instead exhibit skewness and kurtosis greater or less than three. The study then applied various VaR methods to measure risk in order to determine the most efficient ones. Different timelines were used to carry out stressed value at risks, and it was seen that during periods of crisis, the volatility of asset returns was higher. The other steps that followed examined the relationship of the variables, correlation tests and time series analysis conducted and led to the forecasting of the returns. It was noted that these methods could not be used in isolation. We adopted the use of a mosaic of all the methods from the VaR measures, which included studying the behaviour and relation of assets with each other. Furthermore, we also examined the environment as a whole, then applied forecasting models to accurately value returns; this gave a much more accurate and relevant risk measure as compared to the initial assumption of normality.

Suggested Citation

  • Eyden Samunderu & Yvonne T. Murahwa, 2021. "Return Based Risk Measures for Non-Normally Distributed Returns: An Alternative Modelling Approach," JRFM, MDPI, vol. 14(11), pages 1-48, November.
  • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:11:p:540-:d:676017
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/14/11/540/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1911-8074/14/11/540/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. repec:cup:cbooks:9781107034662 is not listed on IDEAS
    3. Francis X. Diebold & Glenn D. Rudebusch, 2012. "Yield Curve Modeling and Forecasting: The Dynamic Nelson-Siegel Approach," Economics Books, Princeton University Press, edition 1, volume 1, number 9895.
    4. A. B. M. Rabiul Alam Beg & Sajid Anwar, 2014. "Detecting volatility persistence in GARCH models in the presence of the leverage effect," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2205-2213, December.
    5. Alexander, Carol & Sheedy, Elizabeth, 2008. "Developing a stress testing framework based on market risk models," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2220-2236, October.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Bams, Dennis & Blanchard, Gildas & Lehnert, Thorsten, 2017. "Volatility measures and Value-at-Risk," International Journal of Forecasting, Elsevier, vol. 33(4), pages 848-863.
    8. Francq, Christian & Zakoïan, Jean-Michel, 2018. "Estimation risk for the VaR of portfolios driven by semi-parametric multivariate models," Journal of Econometrics, Elsevier, vol. 205(2), pages 381-401.
    9. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    10. Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
    11. Christiane Goodfellow & Christian Salm, 2016. "Risky Risk Measures: A Note On Underestimating Financial Risk Under The Normal Assumption," Copernican Journal of Finance & Accounting, Uniwersytet Mikolaja Kopernika, vol. 5(2), pages 85-108.
    12. Robert Engle, 2004. "Risk and Volatility: Econometric Models and Financial Practice," American Economic Review, American Economic Association, vol. 94(3), pages 405-420, June.
    13. Lidija Lovreta & Joaquín López Pascual, 2020. "Structural breaks in the interaction between bank and sovereign default risk," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 11(4), pages 531-559, December.
    14. Robert F. Engle & Emil N. Siriwardane, 2018. "Structural GARCH: The Volatility-Leverage Connection," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 449-492.
    15. Mico Loretan & William B English, 2000. "Evaluating changes in correlations during periods of high market volatility," BIS Quarterly Review, Bank for International Settlements, pages 29-36, June.
    16. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    17. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    18. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    19. Brooks,Chris, 2014. "Introductory Econometrics for Finance," Cambridge Books, Cambridge University Press, number 9781107661455, December.
    20. Iulia Cristina Iuga & Anastasia Mihalciuc, 2020. "Major Crises of the XXIst Century and Impact on Economic Growth," Sustainability, MDPI, vol. 12(22), pages 1-20, November.
    21. Milan Rippel & Ivo Jánský, 2011. "Value at Risk forecasting with the ARMA-GARCH family of models in times of increased volatility," Working Papers IES 2011/27, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2011.
    22. Jose A. Lopez, 2005. "Stress tests: useful complements to financial risk models," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, issue jun24.
    23. Shrey Jain & Siddhartha P. Chakrabarty, 2020. "Does Marginal VaR Lead to Improved Performance of Managed Portfolios: A Study of S&P BSE 100 and S&P BSE 200," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(2), pages 291-323, June.
    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. Eyden Samunderu, 2023. "Jet Fuel Price Risk and Proxy Hedging in Spot Markets: A Two-Tier Model Analysis," Commodities, MDPI, vol. 2(3), pages 1-32, August.

    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. Gatfaoui, Hayette, 2013. "Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets," Economic Modelling, Elsevier, vol. 30(C), pages 776-791.
    2. Ardia, David & Bluteau, Keven & Boudt, Kris & Catania, Leopoldo, 2018. "Forecasting risk with Markov-switching GARCH models:A large-scale performance study," International Journal of Forecasting, Elsevier, vol. 34(4), pages 733-747.
    3. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    4. Rama K. Malladi & Prakash L. Dheeriya, 2021. "Time series analysis of Cryptocurrency returns and volatilities," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 45(1), pages 75-94, January.
    5. Degiannakis, Stavros & Floros, Christos & Dent, Pamela, 2013. "Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence," International Review of Financial Analysis, Elsevier, vol. 27(C), pages 21-33.
    6. Pavel Ciaian & d'Artis Kancs & Miroslava Rajcaniova, 2018. "The Price of BitCoin: GARCH Evidence from High Frequency Data," EERI Research Paper Series EERI RP 2018/14, Economics and Econometrics Research Institute (EERI), Brussels.
    7. Degiannakis, Stavros & Potamia, Artemis, 2017. "Multiple-days-ahead value-at-risk and expected shortfall forecasting for stock indices, commodities and exchange rates: Inter-day versus intra-day data," International Review of Financial Analysis, Elsevier, vol. 49(C), pages 176-190.
    8. Weiß, Gregor N.F., 2011. "Are Copula-GoF-tests of any practical use? Empirical evidence for stocks, commodities and FX futures," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(2), pages 173-188, May.
    9. Caporale, Guglielmo Maria & Zekokh, Timur, 2019. "Modelling volatility of cryptocurrencies using Markov-Switching GARCH models," Research in International Business and Finance, Elsevier, vol. 48(C), pages 143-155.
    10. Tao Chen & Yixuan Li & Renfang Tian, 2023. "A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics," Mathematics, MDPI, vol. 11(20), pages 1-27, October.
    11. Cathy W. S. Chen & Edward M. H. Lin & Tara F. J. Huang, 2022. "Bayesian quantile forecasting via the realized hysteretic GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(7), pages 1317-1337, November.
    12. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. David Feldman & Xin Xu, 2018. "Equilibrium-based volatility models of the market portfolio rate of return (peacock tails or stotting gazelles)," Annals of Operations Research, Springer, vol. 262(2), pages 493-518, March.
    14. Malek, Jiri & Nguyen, Duc Khuong & Sensoy, Ahmet & Tran, Quang Van, 2023. "Modeling dynamic VaR and CVaR of cryptocurrency returns with alpha-stable innovations," Finance Research Letters, Elsevier, vol. 55(PA).
    15. Charles, Amélie & Darné, Olivier, 2014. "Volatility persistence in crude oil markets," Energy Policy, Elsevier, vol. 65(C), pages 729-742.
    16. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    17. Stanislav Bozhkov & Habin Lee & Uthayasankar Sivarajah & Stella Despoudi & Monomita Nandy, 2020. "Idiosyncratic risk and the cross-section of stock returns: the role of mean-reverting idiosyncratic volatility," Annals of Operations Research, Springer, vol. 294(1), pages 419-452, November.
    18. Jules Clement Mba & Sutene Mwambi, 2020. "A Markov-switching COGARCH approach to cryptocurrency portfolio selection and optimization," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(2), pages 199-214, June.
    19. Abokyi, Emmanuel & Asiedu, Kofi Fred, 2021. "Agricultural policy and commodity price stabilisation in Ghana: The role of buffer stockholding operations," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 16(4), December.
    20. Minot, Nicholas, 2014. "Food price volatility in sub-Saharan Africa: Has it really increased?," Food Policy, Elsevier, vol. 45(C), pages 45-56.

    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:gam:jjrfmx:v:14:y:2021:i:11:p:540-:d:676017. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.