Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1803.05861.html
   My bibliography  Save this paper

Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises

Author

Listed:
  • Ludovic Cales
  • Apostolos Chalkis
  • Ioannis Z. Emiris
  • Vissarion Fisikopoulos
Abstract
We examine volume computation of general-dimensional polytopes and more general convex bodies, defined as the intersection of a simplex by a family of parallel hyperplanes, and another family of parallel hyperplanes or a family of concentric ellipsoids. Such convex bodies appear in modeling and predicting financial crises. The impact of crises on the economy (labor, income, etc.) makes its detection of prime interest. Certain features of dependencies in the markets clearly identify times of turmoil. We describe the relationship between asset characteristics by means of a copula; each characteristic is either a linear or quadratic form of the portfolio components, hence the copula can be constructed by computing volumes of convex bodies. We design and implement practical algorithms in the exact and approximate setting, we experimentally juxtapose them and study the tradeoff of exactness and accuracy for speed. We analyze the following methods in order of increasing generality: rejection sampling relying on uniformly sampling the simplex, which is the fastest approach, but inaccurate for small volumes; exact formulae based on the computation of integrals of probability distribution functions; an optimized Lawrence sign decomposition method, since the polytopes at hand are shown to be simple; Markov chain Monte Carlo algorithms using random walks based on the hit-and-run paradigm generalized to nonlinear convex bodies and relying on new methods for computing a ball enclosed; the latter is experimentally extended to non-convex bodies with very encouraging results. Our C++ software, based on CGAL and Eigen and available on github, is shown to be very effective in up to 100 dimensions. Our results offer novel, effective means of computing portfolio dependencies and an indicator of financial crises, which is shown to correctly identify past crises.

Suggested Citation

  • Ludovic Cales & Apostolos Chalkis & Ioannis Z. Emiris & Vissarion Fisikopoulos, 2018. "Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises," Papers 1803.05861, arXiv.org.
    • Handle: RePEc:arx:papers:1803.05861
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1803.05861
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ludovic Cales & Apostolos Chalkis & Ioannis Z. Emiris & Vissarion Fisikopoulos, 2018. "Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises," Papers 1803.05861, arXiv.org.
    2. Dominique Guegan & Ludovic Calès & Monica Billio, 2011. "A Cross-Sectional Score for the Relative Performance of an Allocation," PSE-Ecole d'économie de Paris (Postprint) halshs-00646070, HAL.
    3. Billio, Monica & Getmansky, Mila & Pelizzon, Loriana, 2012. "Dynamic risk exposures in hedge funds," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3517-3532.
    4. Lo Duca, Marco & Koban, Anne & Basten, Marisa & Bengtsson, Elias & Klaus, Benjamin & Kusmierczyk, Piotr & Lang, Jan Hannes & Detken, Carsten & Peltonen, Tuomas, 2017. "A new database for financial crises in European countries," ESRB Occasional Paper Series 13, European Systemic Risk Board.
    5. Banerjee, Anurag & Hung, Chi-Hsiou, 2011. "Informed momentum trading versus uninformed "naive" investors strategies," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3077-3089, November.
    6. John M. Griffin & Xiuqing Ji & J. Spencer Martin, 2003. "Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole," Journal of Finance, American Finance Association, vol. 58(6), pages 2515-2547, December.
    7. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    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. Apostolos Chalkis & Emmanouil Christoforou & Ioannis Z. Emiris & Theodore Dalamagas, 2020. "Modeling asset allocation strategies and a new portfolio performance score," Papers 2012.05088, arXiv.org, revised Sep 2021.
    2. Ludovic Cales & Apostolos Chalkis & Ioannis Z. Emiris & Vissarion Fisikopoulos, 2018. "Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises," Papers 1803.05861, arXiv.org.
    3. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2024. "Randomized Control in Performance Analysis and Empirical Asset Pricing," Papers 2403.00009, arXiv.org.

    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. Apostolos Chalkis & Emmanouil Christoforou & Ioannis Z. Emiris & Theodore Dalamagas, 2021. "Modeling asset allocations and a new portfolio performance score," Digital Finance, Springer, vol. 3(3), pages 333-371, December.
    2. Apostolos Chalkis & Emmanouil Christoforou & Ioannis Z. Emiris & Theodore Dalamagas, 2020. "Modeling asset allocation strategies and a new portfolio performance score," Papers 2012.05088, arXiv.org, revised Sep 2021.
    3. Hung, Chi-Hsiou D. & Banerjee, Anurag N., 2014. "How do momentum strategies ‘score’ against individual investors in Taiwan, Hong Kong and Korea?," Emerging Markets Review, Elsevier, vol. 21(C), pages 67-81.
    4. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2024. "Randomized Control in Performance Analysis and Empirical Asset Pricing," Papers 2403.00009, arXiv.org.
    5. Philip A. Stork, 2011. "The intertemporal mechanics of European stock price momentum," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 28(3), pages 217-232, August.
    6. Hou, Yang & Meng, Jiayin, 2018. "The momentum effect in the Chinese market and its relationship with the simultaneous and the lagged investor sentiment," MPRA Paper 94838, University Library of Munich, Germany.
    7. Cakici, Nusret & Tang, Yi & Yan, An, 2016. "Do the size, value, and momentum factors drive stock returns in emerging markets?," Journal of International Money and Finance, Elsevier, vol. 69(C), pages 179-204.
    8. Chen, Chun-nan, 2013. "The predictability of opening returns for the returns of the trading day: Evidence from Taiwan futures market," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 272-281.
    9. Clare, Andrew & Seaton, James & Smith, Peter N. & Thomas, Stephen, 2016. "The trend is our friend: Risk parity, momentum and trend following in global asset allocation," Journal of Behavioral and Experimental Finance, Elsevier, vol. 9(C), pages 63-80.
    10. de Oliveira Souza, Thiago, 2019. "A critique of momentum anomalies," Discussion Papers on Economics 5/2019, University of Southern Denmark, Department of Economics.
    11. Karim M. Abadir & Gabriel Talmain, 2012. "Beyond Co-Integration: Modelling Co-Movements in Macro finance," Working Paper series 25_12, Rimini Centre for Economic Analysis.
    12. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, January.
    13. Ruanmin Cao & Lajos Horváth & Zhenya Liu & Yuqian Zhao, 2020. "A study of data-driven momentum and disposition effects in the Chinese stock market by functional data analysis," Review of Quantitative Finance and Accounting, Springer, vol. 54(1), pages 335-358, January.
    14. Abdullah EJAZ & Petr POLAK, 2013. "Short term momentum profits and their source: a business indicators' approach," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 59(12), pages 563-577.
    15. Sabine Artmann & Philipp Finter & Alexander Kempf & Stefan Koch & Erik Theissen, 2012. "The Cross-Section of German Stock Returns: New Data and New Evidence," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 64(1), pages 20-43, January.
    16. Mohamed Sahbi Nakhli & Abderrazak Dhaoui & Julien Chevallier, 2022. "Bootstrap rolling-window Granger causality dynamics between momentum and sentiment: implications for investors," Annals of Finance, Springer, vol. 18(2), pages 267-283, June.
    17. Clark, Ephraim & Kassimatis, Konstantinos, 2014. "Exploiting stochastic dominance to generate abnormal stock returns," Journal of Financial Markets, Elsevier, vol. 20(C), pages 20-38.
    18. Daphne Yan Du & Qianqiu Liu & S. Ghon Rhee, 2009. "An Analysis of the Magnet Effect under Price Limits," International Review of Finance, International Review of Finance Ltd., vol. 9(1‐2), pages 83-110, March.
    19. Israel, Ronen & Moskowitz, Tobias J., 2013. "The role of shorting, firm size, and time on market anomalies," Journal of Financial Economics, Elsevier, vol. 108(2), pages 275-301.
    20. Timotheos Angelidis & Nikolaos Tessaromatis, 2014. "Global portfolio management under state dependent multiple risk premia," Proceedings of Economics and Finance Conferences 0400966, International Institute of Social and Economic Sciences.

    More about this item

    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:arx:papers:1803.05861. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.