IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v133y2021ics0378426621002077.html
   My bibliography  Save this article

Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation

Author

Listed:
  • Merlo, Luca
  • Petrella, Lea
  • Raponi, Valentina

Abstract

In this paper, we propose a multivariate quantile regression framework to forecast Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets simultaneously, extending Taylor (2019). We generalize the Multivariate Asymmetric Laplace (MAL) joint quantile regression of Petrella and Raponi (2019) to a time-varying setting, which allows us to specify a dynamic process for the evolution of both the VaR and ES of each asset. The proposed methodology accounts for the dependence structure among asset returns. By exploiting the properties of the MAL distribution, we propose a new portfolio optimization method that minimizes portfolio risk and controls for well-known characteristics of financial data. We evaluate the advantages of the proposed approach on both simulated and real data, using weekly returns on three major stock market indices. We show that our method outperforms other existing models and provides more accurate risk measure forecasts than univariate methods.

Suggested Citation

  • Merlo, Luca & Petrella, Lea & Raponi, Valentina, 2021. "Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation," Journal of Banking & Finance, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:jbfina:v:133:y:2021:i:c:s0378426621002077
    DOI: 10.1016/j.jbankfin.2021.106248
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426621002077
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2021.106248?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. Gilbert W. Bassett, 2004. "Pessimistic Portfolio Allocation and Choquet Expected Utility," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 477-492.
    2. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    3. Arditti, Fred D., 1971. "Another Look at Mutual Fund Performance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(3), pages 909-912, June.
    4. Shangmei Zhao & Qing Lu & Liyan Han & Yong Liu & Fei Hu, 2015. "A mean-CVaR-skewness portfolio optimization model based on asymmetric Laplace distribution," Annals of Operations Research, Springer, vol. 226(1), pages 727-739, March.
    5. Yiu, K. F. C., 2004. "Optimal portfolios under a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1317-1334, April.
    6. Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 997-1015, April.
    7. Barone-Adesi, Giovanni, 1985. "Arbitrage Equilibrium with Skewed Asset Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(3), pages 299-313, September.
    8. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    9. Marc S. Paolella, 2015. "Multivariate asset return prediction with mixture models," The European Journal of Finance, Taylor & Francis Journals, vol. 21(13-14), pages 1214-1252, November.
    10. Bonaccolto, Giovanni & Caporin, Massimiliano & Paterlini, Sandra, 2019. "Decomposing and backtesting a flexible specification for CoVaR," Journal of Banking & Finance, Elsevier, vol. 108(C).
    11. Bu, Di & Liao, Yin & Shi, Jing & Peng, Hongfeng, 2019. "Dynamic expected shortfall: A spectral decomposition of tail risk across time horizons," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    12. 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.
    13. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    14. James W. Taylor, 2019. "Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 121-133, January.
    15. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    16. James W. Taylor, 2005. "Generating Volatility Forecasts from Value at Risk Estimates," Management Science, INFORMS, vol. 51(5), pages 712-725, May.
    17. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    18. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    19. Baur, Dirk G., 2013. "The structure and degree of dependence: A quantile regression approach," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 786-798.
    20. Laporta, Alessandro G. & Merlo, Luca & Petrella, Lea, 2018. "Selection of Value at Risk Models for Energy Commodities," Energy Economics, Elsevier, vol. 74(C), pages 628-643.
    21. White, Halbert & Kim, Tae-Hwan & Manganelli, Simone, 2015. "VAR for VaR: Measuring tail dependence using multivariate regression quantiles," Journal of Econometrics, Elsevier, vol. 187(1), pages 169-188.
    22. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    23. Friend, Irwin & Westerfield, Randolph, 1980. "Co-Skewness and Capital Asset Pricing," Journal of Finance, American Finance Association, vol. 35(4), pages 897-913, September.
    24. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    25. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
    26. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    27. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    28. 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.).
    29. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
    30. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    31. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    32. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2018. "The sparse method of simulated quantiles: An application to portfolio optimization," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 375-398, August.
    33. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    34. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    35. Alexander, Gordon J. & Baptista, Alexandre M., 2008. "Active portfolio management with benchmarking: Adding a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 779-820, March.
    36. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    37. 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.
    38. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    39. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    40. Tobias Fissler & Johanna F. Ziegel & Tilmann Gneiting, 2015. "Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting," Papers 1507.00244, arXiv.org, revised Jul 2015.
    41. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    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. Taylor, James W., 2022. "Forecasting Value at Risk and expected shortfall using a model with a dynamic omega ratio," Journal of Banking & Finance, Elsevier, vol. 140(C).
    2. Iacopini, Matteo & Poon, Aubrey & Rossini, Luca & Zhu, Dan, 2023. "Bayesian mixed-frequency quantile vector autoregression: Eliciting tail risks of monthly US GDP," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    3. Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Expectile hidden Markov regression models for analyzing cryptocurrency returns," Papers 2301.09722, arXiv.org, revised Jan 2024.
    4. Ning Zhang & Yujing Gong & Xiaohan Xue, 2023. "Less disagreement, better forecasts: Adjusted risk measures in the energy futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(10), pages 1332-1372, October.
    5. Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market," Papers 2307.06400, arXiv.org.
    6. Yun Feng & Weijie Hou & Yuping Song, 2024. "Tail risk forecasting and its application to margin requirements in the commodity futures market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1513-1529, August.
    7. Storti, Giuseppe & Wang, Chao, 2022. "A multivariate semi-parametric portfolio risk optimization and forecasting framework," MPRA Paper 115266, University Library of Munich, Germany.
    8. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    9. Federico Gatta & Fabrizio Lillo & Piero Mazzarisi, 2024. "CAESar: Conditional Autoregressive Expected Shortfall," Papers 2407.06619, arXiv.org.
    10. Luca Merlo & Lea Petrella & Nikos Tzavidis, 2022. "Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's Strengths and Difficulties Questionnaire scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 417-448, March.
    11. Giuseppe Storti & Chao Wang, 2022. "A semi-parametric marginalized dynamic conditional correlation framework," Papers 2207.04595, arXiv.org, revised Jul 2024.

    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. Luca Merlo & Lea Petrella & Valentina Raponi, 2021. "Forecasting VaR and ES using a joint quantile regression and implications in portfolio allocation," Papers 2106.06518, arXiv.org.
    2. Timo Dimitriadis & Xiaochun Liu & Julie Schnaitmann, 2020. "Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary," Papers 2009.07341, arXiv.org.
    3. David Happersberger & Harald Lohre & Ingmar Nolte, 2020. "Estimating portfolio risk for tail risk protection strategies," European Financial Management, European Financial Management Association, vol. 26(4), pages 1107-1146, September.
    4. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    5. 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.
    6. Taylor, James W., 2022. "Forecasting Value at Risk and expected shortfall using a model with a dynamic omega ratio," Journal of Banking & Finance, Elsevier, vol. 140(C).
    7. Qifa Xu & Lu Chen & Cuixia Jiang & Yezheng Liu, 2022. "Forecasting expected shortfall and value at risk with a joint elicitable mixed data sampling model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 407-421, April.
    8. Gerlach, Richard & Wang, Chao, 2020. "Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 489-506.
    9. Arturo Leccadito & Alessandro Staino & Pietro Toscano, 2024. "A novel robust method for estimating the covariance matrix of financial returns with applications to risk management," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-28, December.
    10. Enrique Molina‐Muñoz & Andrés Mora‐Valencia & Javier Perote, 2021. "Backtesting expected shortfall for world stock index ETFs with extreme value theory and Gram–Charlier mixtures," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4163-4189, July.
    11. Xu, Qifa & Chen, Lu & Jiang, Cuixia & Yu, Keming, 2020. "Mixed data sampling expectile regression with applications to measuring financial risk," Economic Modelling, Elsevier, vol. 91(C), pages 469-486.
    12. Li, Dan & Clements, Adam & Drovandi, Christopher, 2023. "A Bayesian approach for more reliable tail risk forecasts," Journal of Financial Stability, Elsevier, vol. 64(C).
    13. Le, Trung H., 2020. "Forecasting value at risk and expected shortfall with mixed data sampling," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1362-1379.
    14. Fortin, Alain-Philippe & Simonato, Jean-Guy & Dionne, Georges, 2023. "Forecasting expected shortfall: Should we use a multivariate model for stock market factors?," International Journal of Forecasting, Elsevier, vol. 39(1), pages 314-331.
    15. Storti, Giuseppe & Wang, Chao, 2022. "A multivariate semi-parametric portfolio risk optimization and forecasting framework," MPRA Paper 115266, University Library of Munich, Germany.
    16. Federico Gatta & Fabrizio Lillo & Piero Mazzarisi, 2024. "CAESar: Conditional Autoregressive Expected Shortfall," Papers 2407.06619, arXiv.org.
    17. d’Addona, Stefano & Khanom, Najrin, 2022. "Estimating tail-risk using semiparametric conditional variance with an application to meme stocks," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 241-260.
    18. Vica Tendenan & Richard Gerlach & Chao Wang, 2020. "Tail risk forecasting using Bayesian realized EGARCH models," Papers 2008.05147, arXiv.org, revised Aug 2020.
    19. Ning Zhang & Yujing Gong & Xiaohan Xue, 2023. "Less disagreement, better forecasts: Adjusted risk measures in the energy futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(10), pages 1332-1372, October.
    20. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.

    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:133:y:2021:i:c:s0378426621002077. 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.