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Modeling asset allocations and a new portfolio performance score

Author

Listed:
  • Apostolos Chalkis

    (National and Kapodistrian University of Athens
    ATHENA Research and Innovation Center)

  • Emmanouil Christoforou

    (National and Kapodistrian University of Athens
    ATHENA Research and Innovation Center)

  • Ioannis Z. Emiris

    (National and Kapodistrian University of Athens
    ATHENA Research and Innovation Center)

  • Theodore Dalamagas

    (ATHENA Research and Innovation Center)

Abstract

We discuss and extend a powerful, geometric framework to represent the set of portfolios, which identifies the space of asset allocations with the points lying in a convex polytope. Based on this viewpoint, we survey certain state-of-the-art tools from geometric and statistical computing to handle important and difficult problems in digital finance. Although our tools are quite general, in this paper, we focus on two specific questions. The first concerns crisis detection, which is of prime interest for the public in general and for policy makers in particular because of the significant impact that crises have on the economy. Certain features in stock markets lead to this type of anomaly detection: Given the assets’ returns, we describe the relationship between portfolios’ return and volatility by means of a copula, without making any assumption on investors’ strategies. We examine a recent method relying on copulae to construct an appropriate indicator that allows us to automate crisis detection. On real data the indicator detects all past crashes in the cryptocurrency market and from the DJ600-Europe index, from 1990 to 2008, the indicator identifies correctly 4 crises and issues one false positive for which we offer an explanation. Our second contribution is to introduce an original computational framework to model asset allocation strategies, which is of independent interest for digital finance and its applications. Our approach addresses the crucial question of evaluating portfolio management, and is relevant the individual managers as well as financial institutions. To evaluate portfolio performance, we provide a new portfolio score, based on the aforementioned framework and concepts. In particular, it relies on statistical properties of portfolios, and we show how they can be computed efficiently.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:digfin:v:3:y:2021:i:3:d:10.1007_s42521-021-00040-8
    DOI: 10.1007/s42521-021-00040-8
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    References listed on IDEAS

    as
    1. Zhao Zhao & Olivier Ledoit & Hui Jiang, 2019. "Risk reduction and efficiency increase in large portfolios: leverage and shrinkage," ECON - Working Papers 328, Department of Economics - University of Zurich, revised Jan 2020.
    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. repec:dau:papers:123456789/4688 is not listed on IDEAS
    4. Grinblatt, Mark & Titman, Sheridan, 1994. "A Study of Monthly Mutual Fund Returns and Performance Evaluation Techniques," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(3), pages 419-444, September.
    5. Taras Bodnar & Solomiia Dmytriv & Nestor Parolya & Wolfgang Schmid, 2017. "Tests for the weights of the global minimum variance portfolio in a high-dimensional setting," Papers 1710.09587, arXiv.org, revised Jul 2019.
    6. Taras Bodnar & Stepan Mazur & Krzysztof Podgórski, 2017. "A test for the global minimum variance portfolio for small sample and singular covariance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 253-265, July.
    7. Billio, Monica & Getmansky, Mila & Pelizzon, Loriana, 2012. "Dynamic risk exposures in hedge funds," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3517-3532.
    8. 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.
    9. Bodnar, Taras & Mazur, Stepan & Podgórski, Krzysztof, 2016. "Singular inverse Wishart distribution and its application to portfolio theory," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 314-326.
    10. 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.
    11. 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.
    12. Taras Bodnar & Wolfgang Schmid, 2009. "Econometrical analysis of the sample efficient frontier," The European Journal of Finance, Taylor & Francis Journals, vol. 15(3), pages 317-335.
    13. Bodnar, Taras & Mazur, Stepan & Podgórski, Krzysztof & Tyrcha, Joanna, 2018. "Tangency portfolio weights for singular covariance matrix in small and large dimensions: estimation and test theory," Working Papers 2018:1, Örebro University, School of Business.
    14. Harry Markowitz, 1956. "The optimization of a quadratic function subject to linear constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 111-133, March.
    15. Mårten Gulliksson & Stepan Mazur, 2020. "An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 773-794, December.
    16. Vera Ivanyuk, 2021. "Formulating the Concept of an Investment Strategy Adaptable to Changes in the Market Situation," Economies, MDPI, vol. 9(3), pages 1-19, June.
    17. Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
    18. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. "Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    19. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    Full references (including those not matched with items on IDEAS)

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