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Portfolio Risk Assessment under Dynamic (Equi)Correlation and Semi-Nonparametric Estimation: An Application to Cryptocurrencies

Author

Listed:
  • Inés Jiménez

    (Department of Economics and Economic History and IME, Faculty of Economics and Business, University of Salamanca, Campus Miguel de Unamuno (Edif. F.E.S.), 37007 Salamanca, Spain)

  • Andrés Mora-Valencia

    (School of Management, Universidad de los Andes, Calle 21 No. 1-20, Bogotá 111711, Colombia)

  • Trino-Manuel Ñíguez

    (School of Organizations, Economy and Society, Westminster Business School, University of Westminster, 35 Marylebone Road, London NW1 5LS, UK)

  • Javier Perote

    (Department of Economics and Economic History and IME, Faculty of Economics and Business, University of Salamanca, Campus Miguel de Unamuno (Edif. F.E.S.), 37007 Salamanca, Spain)

Abstract

The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of dynamic equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio of cryptocurrencies by implementing backtesting techniques and for different risk measures: value-at-risk, expected shortfall and median shortfall. The results support our proposal showing that the SNP-DCC model has better performance for lower confidence levels than the SNP-DECO model and is more appropriate for portfolio diversification purposes.

Suggested Citation

  • Inés Jiménez & Andrés Mora-Valencia & Trino-Manuel Ñíguez & Javier Perote, 2020. "Portfolio Risk Assessment under Dynamic (Equi)Correlation and Semi-Nonparametric Estimation: An Application to Cryptocurrencies," Mathematics, MDPI, vol. 8(12), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2110-:d:451220
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    References listed on IDEAS

    as
    1. Dominique Guégan & Bertrand Hassani, 2015. "Distortion Risk Measure or the Transformation of Unimodal Distributions into Multimodal Functions," International Series in Operations Research & Management Science, in: Alain Bensoussan & Dominique Guegan & Charles S. Tapiero (ed.), Future Perspectives in Risk Models and Finance, edition 127, pages 71-88, Springer.
    2. Winfried G. Hallerbach, 1999. "Decomposing Portfolio Value-at-Risk: A General Analysis," Tinbergen Institute Discussion Papers 99-034/2, Tinbergen Institute.
    3. Dominique Guegan & Bertrand K. Hassani, 2018. "More accurate measurement for enhanced controls: VaR vs ES?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01917569, HAL.
    4. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    5. Anders Hald, 2000. "The Early History of the Cumulants and the Gram‐Charlier Series," International Statistical Review, International Statistical Institute, vol. 68(2), pages 137-153, August.
    6. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 537-572.
    7. Balcilar, Mehmet & Bouri, Elie & Gupta, Rangan & Roubaud, David, 2017. "Can volume predict Bitcoin returns and volatility? A quantiles-based approach," Economic Modelling, Elsevier, vol. 64(C), pages 74-81.
    8. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
    9. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    10. Dirk Tasche & Luisa Tibiletti, 2003. "A Shortcut to Sign Incremental Value at Risk for Risk Allocation," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 4(2), pages 43-46, January.
    11. Roger W. Barnard & Kent Pearce & A. Alexandre Trindade, 2018. "When is tail mean estimation more efficient than tail median? Answers and implications for quantitative risk management," Annals of Operations Research, Springer, vol. 262(1), pages 47-65, March.
    12. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2017. "The kidnapping of Europe: High-order moments' transmission between developed and emerging markets," Emerging Markets Review, Elsevier, vol. 31(C), pages 96-115.
    13. Dominique Guegan & Bertrand Hassani, 2015. "Distorsion Risk Measure or the Transformation of Unimodal Distributions into Multimodal Functions," Post-Print hal-01310467, HAL.
    14. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    15. 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.
    16. Ñíguez, Trino-Manuel & Perote, Javier, 2016. "Multivariate moments expansion density: Application of the dynamic equicorrelation model," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 216-232.
    17. 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.
    18. Kratz, Marie & Lok, Yen H. & McNeil, Alexander J., 2018. "Multinomial VaR backtests: A simple implicit approach to backtesting expected shortfall," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 393-407.
    19. 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.
    20. Lahmiri, Salim & Bekiros, Stelios & Salvi, Antonio, 2018. "Long-range memory, distributional variation and randomness of bitcoin volatility," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 43-48.
    21. Javier Perote, 2004. "The multivariate Edgeworth-Sargan density," Spanish Economic Review, Springer;Spanish Economic Association, vol. 6(1), pages 77-96, April.
    22. Qureshi, Saba & Aftab, Muhammad & Bouri, Elie & Saeed, Tareq, 2020. "Dynamic interdependence of cryptocurrency markets: An analysis across time and frequency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    23. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    24. 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.
    25. Blau, Benjamin M., 2018. "Price dynamics and speculative trading in Bitcoin," Research in International Business and Finance, Elsevier, vol. 43(C), pages 15-21.
    26. Aslanidis, Nektarios & Bariviera, Aurelio F. & Martínez-Ibañez, Oscar, 2019. "An analysis of cryptocurrencies conditional cross correlations," Finance Research Letters, Elsevier, vol. 31(C), pages 130-137.
    27. Corbet, Shaen & Meegan, Andrew & Larkin, Charles & Lucey, Brian & Yarovaya, Larisa, 2018. "Exploring the dynamic relationships between cryptocurrencies and other financial assets," Economics Letters, Elsevier, vol. 165(C), pages 28-34.
    28. Philippe Jorion, 2000. "Risk management lessons from Long‐Term Capital Management," European Financial Management, European Financial Management Association, vol. 6(3), pages 277-300, September.
    29. Del Brio, Esther B. & Ñíguez, Trino-Manuel & Perote, Javier, 2011. "Multivariate semi-nonparametric distributions with dynamic conditional correlations," International Journal of Forecasting, Elsevier, vol. 27(2), pages 347-364.
    30. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    31. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129, January.
    32. Canh, Nguyen Phuc & Wongchoti, Udomsak & Thanh, Su Dinh & Thong, Nguyen Trung, 2019. "Systematic risk in cryptocurrency market: Evidence from DCC-MGARCH model," Finance Research Letters, Elsevier, vol. 29(C), pages 90-100.
    33. Dominique Guegan & Bertrand Hassani, 2015. "Distorsion Risk Measure or the Transformation of Unimodal Distributions into Multimodal Functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01310467, HAL.
    34. Dominique Guegan & Bertrand K. Hassani, 2018. "More accurate measurement for enhanced controls: VaR vs ES?," Post-Print halshs-01917569, HAL.
    35. Dwyer, Gerald P., 2015. "The economics of Bitcoin and similar private digital currencies," Journal of Financial Stability, Elsevier, vol. 17(C), pages 81-91.
    36. Steven Kou & Xianhua Peng, 2014. "Expected shortfall or median shortfall," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-6.
    37. C. Baek & M. Elbeck, 2015. "Bitcoins as an investment or speculative vehicle? A first look," Applied Economics Letters, Taylor & Francis Journals, vol. 22(1), pages 30-34, January.
    38. Dyhrberg, Anne Haubo, 2016. "Hedging capabilities of bitcoin. Is it the virtual gold?," Finance Research Letters, Elsevier, vol. 16(C), pages 139-144.
    39. Andrés Mora-Valencia & Trino-Manuel Ñíguez & Javier Perote, 2017. "Multivariate approximations to portfolio return distribution," Computational and Mathematical Organization Theory, Springer, vol. 23(3), pages 347-361, September.
    40. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    41. Esther B. Del Brio & Andrés Mora-Valencia & Javier Perote, 2019. "Expected shortfall assessment in commodity (L)ETF portfolios with semi-nonparametric specifications," The European Journal of Finance, Taylor & Francis Journals, vol. 25(17), pages 1746-1764, November.
    42. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    43. Esther B. Del Brio & Trino-Manuel Niguez & Javier Perote, 2009. "Gram-Charlier densities: a multivariate approach," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 855-868.
    44. Guesmi, Khaled & Saadi, Samir & Abid, Ilyes & Ftiti, Zied, 2019. "Portfolio diversification with virtual currency: Evidence from bitcoin," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 431-437.
    45. 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.
    46. Guegan, Dominique & Hassani, Bertrand K., 2018. "More accurate measurement for enhanced controls: VaR vs ES?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 54(C), pages 152-165.
    47. Alfonso Novales & Laura Garcia-Jorcano, 2019. "Backtesting extreme value theory models of expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 799-825, May.
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    Cited by:

    1. Bouri, Elie & Jalkh, Naji, 2023. "Spillovers of joint volatility-skewness-kurtosis of major cryptocurrencies and their determinants," International Review of Financial Analysis, Elsevier, vol. 90(C).
    2. Jiménez, Inés & Mora-Valencia, Andrés & Perote, Javier, 2023. "Multivariate dynamics between emerging markets and digital asset markets: An application of the SNP-DCC model," Emerging Markets Review, Elsevier, vol. 56(C).

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