IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v118y2020ics0378426620301369.html
   My bibliography  Save this article

Modeling asset returns under time-varying semi-nonparametric distributions

Author

Listed:
  • León, Ángel
  • Ñíguez, Trino-Manuel

Abstract

We extend the semi-nonparametric (SNP) density of León et al. (2009) to time-varying higher-order moments for daily asset return innovations of stock indexes and foreign-exchange rates. We estimate robust tail-indexes for testing the existence of the unconditional higher-order moments. We obtain closed-form expressions of partial moments and expected shortfall under the time-varying SNP density with the GJR-GARCH for modeling returns. A comparative study between SNP and Hansen’s skewed-t, based on skewness-kurtosis frontiers, in-sample and backtesting analyses, is also implemented. Finally, we conduct an out-of-sample portfolio selection exercise for the stocks of the S&P 100 index through an equity screening method based on our parametric one-sided reward/risk performance measures and compare with the Sharpe ratio portfolio.

Suggested Citation

  • León, Ángel & Ñíguez, Trino-Manuel, 2020. "Modeling asset returns under time-varying semi-nonparametric distributions," Journal of Banking & Finance, Elsevier, vol. 118(C).
    • Handle: RePEc:eee:jbfina:v:118:y:2020:i:c:s0378426620301369
    DOI: 10.1016/j.jbankfin.2020.105870
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426620301369
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2020.105870?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    2. Javier Mencía & Enrique Sentana, 2018. "Volatility-Related Exchange Traded Assets: An Econometric Investigation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 599-614, October.
    3. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    4. Trino-Manuel Ñíguez & Ivan Paya & David Peel & Javier Perote, 2019. "Flexible distribution functions, higher-order preferences and optimal portfolio allocation," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 699-703, April.
    5. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    6. Caporin, Massimiliano & Lisi, Francesco, 2011. "Comparing and selecting performance measures using rank correlations," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-34.
    7. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    8. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    9. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    10. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
    11. Farinelli, Simone & Tibiletti, Luisa, 2008. "Sharpe thinking in asset ranking with one-sided measures," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1542-1547, March.
    12. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    13. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    14. Bruno Feunou & Mohammad R. Jahan-Parvar & Roméo Tédongap, 2016. "Which parametric model for conditional skewness?," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1237-1271, October.
    15. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 745-773.
    16. León, Angel & Navarro, Lluís & Nieto, Belén, 2019. "Screening rules and portfolio performance," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 642-662.
    17. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    18. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    19. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    20. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    21. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    22. Rongmao Zhang & Chenxue Li & Liang Peng, 2019. "Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 151-169, February.
    23. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    24. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    25. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    26. Boudt, Kris & Lu, Wanbo & Peeters, Benedict, 2015. "Higher order comoments of multifactor models and asset allocation," Finance Research Letters, Elsevier, vol. 13(C), pages 225-233.
    27. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    28. Stephen Thiele, 2020. "Modeling the conditional distribution of financial returns with asymmetric tails," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 46-60, January.
    29. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 461-504.
    30. Liquet, Benoit & Nazarathy, Yoni, 2015. "A dynamic view to moment matching of truncated distributions," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 87-93.
    31. Ivana Komunjer, 2007. "Asymmetric power distribution: Theory and applications to risk measurement," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 891-921.
    32. Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
    33. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
    34. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    35. Stanislav Anatolyev & Anton Petukhov, 2016. "Uncovering the Skewness News Impact Curve," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 746-771.
    36. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    37. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Heavy tails and asymmetry of returns in the Russian stock market," Emerging Markets Review, Elsevier, vol. 32(C), pages 200-219.
    38. Zoia, Maria Grazia & Biffi, Paola & Nicolussi, Federica, 2018. "Value at risk and expected shortfall based on Gram-Charlier-like expansions," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 92-104.
    39. Leon, Angel & Rubio, Gonzalo & Serna, Gregorio, 2005. "Autoregresive conditional volatility, skewness and kurtosis," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 599-618, September.
    40. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    41. Simon Lalancette & Jean†Guy Simonato, 2017. "The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation," European Financial Management, European Financial Management Association, vol. 23(2), pages 325-354, March.
    42. Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 765-778, September.
    43. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    44. Sun, Pengfei & Zhou, Chen, 2014. "Diagnosing the distribution of GARCH innovations," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 287-303.
    Full references (including those not matched with items on IDEAS)

    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. León, Ángel & Ñíguez, Trino-Manuel, 2021. "The transformed Gram Charlier distribution: Parametric properties and financial risk applications," Journal of Empirical Finance, Elsevier, vol. 63(C), pages 323-349.
    2. Wang, Tianyi & Liang, Fang & Huang, Zhuo & Yan, Hong, 2022. "Do realized higher moments have information content? - VaR forecasting based on the realized GARCH-RSRK model," Economic Modelling, Elsevier, vol. 109(C).
    3. Lin, Chu-Hsiung & Changchien, Chang-Cheng & Kao, Tzu-Chuan & Kao, Wei-Shun, 2014. "High-order moments and extreme value approach for value-at-risk," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 421-434.
    4. Trung H. Le, 2024. "Forecasting VaR and ES in emerging markets: The role of time‐varying higher moments," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(2), pages 402-414, March.
    5. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    6. Ñíguez, Trino-Manuel & Perote, Javier, 2017. "Moments expansion densities for quantifying financial risk," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 53-69.
    7. Brenda Castillo-Brais & Ángel León & Juan Mora, 2022. "Estimating Value-at-Risk and Expected Shortfall: Do Polynomial Expansions Outperform Parametric Densities?," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    8. Sylvia J. Soltyk & Felix Chan, 2023. "Modeling time‐varying higher‐order conditional moments: A survey," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 33-57, February.
    9. Ergün, A. Tolga & Jun, Jongbyung, 2010. "Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(3), pages 264-272, August.
    10. Steven J. Cochran & Iqbal Mansur & Babatunde Odusami, 2016. "Conditional higher order moments in metal asset returns," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 151-167, January.
    11. Huang, Zhuo & Liang, Fang & Wang, Tianyi & Li, Chao, 2021. "Modeling dynamic higher moments of crude oil futures," Finance Research Letters, Elsevier, vol. 39(C).
    12. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    13. Trung H. Le & Apostolos Kourtis & Raphael Markellos, 2023. "Modeling skewness in portfolio choice," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(6), pages 734-770, June.
    14. Gao, Chun-Ting & Zhou, Xiao-Hua, 2016. "Forecasting VaR and ES using dynamic conditional score models and skew Student distribution," Economic Modelling, Elsevier, vol. 53(C), pages 216-223.
    15. Timo Dimitriadis & iaochun Liu & Julie Schnaitmann, 2023. "Encompassing Tests for Value at Risk and Expected Shortfall Multistep Forecasts Based on Inference on the Boundary," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 412-444.
    16. Wu, Qi & Yan, Xing, 2019. "Capturing deep tail risk via sequential learning of quantile dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    17. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
    18. Trino-Manuel Ñíguez & Javier Perote, 2012. "Forecasting Heavy-Tailed Densities with Positive Edgeworth and Gram-Charlier Expansions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(4), pages 600-627, August.
    19. Julia S. Mehlitz & Benjamin R. Auer, 2021. "Time‐varying dynamics of expected shortfall in commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 895-925, June.
    20. Nieto, María Rosa, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item

    Keywords

    Backtesting; Equity screening; Expected shortfall; Conditional higher-order moments; Tail-index;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    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:eee:jbfina:v:118:y:2020:i:c:s0378426620301369. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jbf .

    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.