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Optimal portfolio allocation with volatility and co-jump risk that Markowitz would like

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  • Oliva, I.
  • Renò, R.

Abstract

We study a continuous time optimal portfolio allocation problem with volatility and co-jump risk, allowing prices, variances and covariances to jump simultaneously. Differently from the traditional approach, we deviate from affine models by specifying a flexible Wishart jump-diffusion for the co-precision (the inverse of the covariance matrix). The optimal portfolio weights that solve the dynamic programming problem are genuinely dynamic and proportional to the instantaneous co-precision, reconciling optimal dynamic allocation with the static Markowitz-type economic intuition. An application to the optimal allocation problem across hedge fund investment styles illustrates the importance of having jumps in volatility associated with jumps in price.

Suggested Citation

  • Oliva, I. & Renò, R., 2018. "Optimal portfolio allocation with volatility and co-jump risk that Markowitz would like," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 242-256.
    • Handle: RePEc:eee:dyncon:v:94:y:2018:i:c:p:242-256
    DOI: 10.1016/j.jedc.2018.05.004
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    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
    3. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    4. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    5. repec:hal:journl:peer-00741630 is not listed on IDEAS
    6. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, February.
    7. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    9. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    11. Branger, Nicole & Muck, Matthias & Seifried, Frank Thomas & Weisheit, Stefan, 2017. "Optimal portfolios when variances and covariances can jump," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 59-89.
    12. Andrew W. Lo & Mila Getmansky & Peter A. Lee, 2015. "Hedge Funds: A Dynamic Industry in Transition," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 483-577, December.
    13. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    14. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    15. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    16. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    17. Sanjiv Ranjan Das & Raman Uppal, 2004. "Systemic Risk and International Portfolio Choice," Journal of Finance, American Finance Association, vol. 59(6), pages 2809-2834, December.
    18. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    19. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
    20. Marius Ascheberg & Nicole Branger & Holger Kraft & Frank Thomas Seifried, 2016. "When do jumps matter for portfolio optimization?," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1297-1311, August.
    21. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
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    Cited by:

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    4. Semeyutin, Artur & Gozgor, Giray & Lau, Chi Keung Marco & Xu, Bing, 2021. "Effects of idiosyncratic jumps and co-jumps on oil, gold, and copper markets," Energy Economics, Elsevier, vol. 104(C).
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    6. Xu, Fang & Bouri, Elie & Cepni, Oguzhan, 2022. "Blockchain and crypto-exposed US companies and major cryptocurrencies: The role of jumps and co-jumps," Finance Research Letters, Elsevier, vol. 50(C).
    7. Amen Aissi Harzallah & Mouna Boujelbene Abbes, 2020. "The Impact of Financial Crises on the Asset Allocation: Classical Theory Versus Behavioral Theory," Journal of Interdisciplinary Economics, , vol. 32(2), pages 218-236, July.
    8. Bouri, Elie & Roubaud, David & Shahzad, Syed Jawad Hussain, 2020. "Do Bitcoin and other cryptocurrencies jump together?," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 396-409.
    9. Wei, Pengyu & Yang, Charles & Zhuang, Yi, 2023. "Robust consumption and portfolio choice with derivatives trading," European Journal of Operational Research, Elsevier, vol. 304(2), pages 832-850.
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    More about this item

    Keywords

    Asset allocation; Stochastic volatility; Co-jumps; Wishart process; Dynamic programming; Hedge funds;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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