IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v85y2023i1d10.1007_s13571-022-00285-2.html
   My bibliography  Save this article

Reliability in Portfolio Optimization using Uncertain Estimates

Author

Listed:
  • Raghu Nandan Sengupta

    (IIT Kanpur)

  • Rachit Seth

    (IIT Kanpur)

  • Peter Winker

    (University Giessen)

Abstract

Portfolio optimization problems are rather easy to solve if one assumes normality of the (joint) distribution of returns with given parameters and a linear objective function, subject to some risk constraints. Higher degrees of complexities arise when taking into account (i) non- linear asset classes, (ii) non-normal distributions, (iii) constraints on lot size, portfolio shares etc., and (iv) uncertainty of parameter estimates. In this paper a Reliability-Based Design Optimization (RBDO) framework is developed to tackle the last two issues, namely, to solve portfolio optimization problems, taking into account the constraints on lot sizes, portfolio shares, etc., and the uncertainty of parameter estimates (i.e., return and risk). Thereby, standard methods and heuristics, available in the literature for handling reliability-based constraints, are adopted. The Block-Bootstrap method is used to obtain estimates of the uncertainty of parameter estimates. For an application to stocks which are components of the DAX, efficient portfolios are obtained taking into account the trade-off between optimal values of the objective function and the reliability of results.

Suggested Citation

  • Raghu Nandan Sengupta & Rachit Seth & Peter Winker, 2023. "Reliability in Portfolio Optimization using Uncertain Estimates," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 199-233, May.
    • Handle: RePEc:spr:sankhb:v:85:y:2023:i:1:d:10.1007_s13571-022-00285-2
    DOI: 10.1007/s13571-022-00285-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-022-00285-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13571-022-00285-2?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. Politis, D. N. & Romano, J. P., 1993. "Nonparametric Resampling for Homogeneous Strong Mixing Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 301-328, November.
    2. Luca Chiodi & Renata Mansini & Maria Speranza, 2003. "Semi-Absolute Deviation Rule for Mutual Funds Portfolio Selection," Annals of Operations Research, Springer, vol. 124(1), pages 245-265, November.
    3. Raghu Nandan Sengupta & Siddharth Sahoo, 2013. "Reliability-based portfolio optimization with conditional value at risk (CVaR)," Quantitative Finance, Taylor & Francis Journals, vol. 13(10), pages 1637-1651, October.
    4. Sourish Das & Aritra Halder & Dipak K. Dey, 2017. "Regularizing Portfolio Risk Analysis: A Bayesian Approach," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 865-889, September.
    5. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    6. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    7. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    8. Angelelli, Enrico & Mansini, Renata & Speranza, M. Grazia, 2008. "A comparison of MAD and CVaR models with real features," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1188-1197, July.
    9. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
    10. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    11. Lahiri, S. N., 1993. "On the moving block bootstrap under long range dependence," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 405-413, December.
    Full references (including those not matched with items on IDEAS)

    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. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2015. "Linear vs. quadratic portfolio selection models with hard real-world constraints," Computational Management Science, Springer, vol. 12(3), pages 345-370, July.
    2. Enrico Angelelli & Renata Mansini & M. Speranza, 2012. "Kernel Search: a new heuristic framework for portfolio selection," Computational Optimization and Applications, Springer, vol. 51(1), pages 345-361, January.
    3. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2013. "Portfolio rebalancing with an investment horizon and transaction costs," Omega, Elsevier, vol. 41(2), pages 406-420.
    4. Angelelli, Enrico & Mansini, Renata & Speranza, M. Grazia, 2008. "A comparison of MAD and CVaR models with real features," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1188-1197, July.
    5. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    6. Bedi, Prateek & Nashier, Tripti, 2020. "On the investment credentials of Bitcoin: A cross-currency perspective," Research in International Business and Finance, Elsevier, vol. 51(C).
    7. Damian Jelito & Marcin Pitera, 2018. "New fat-tail normality test based on conditional second moments with applications to finance," Papers 1811.05464, arXiv.org, revised Apr 2020.
    8. Liusha Yang & Romain Couillet & Matthew R. McKay, 2015. "A Robust Statistics Approach to Minimum Variance Portfolio Optimization," Papers 1503.08013, arXiv.org.
    9. Ladislav KRISTOUFEK & Petra LUNACKOVA, 2013. "Long-term Memory in Electricity Prices: Czech Market Evidence," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(5), pages 407-424, November.
    10. Andrew Paskaramoorthy & Tim Gebbie & Terence van Zyl, 2021. "The efficient frontiers of mean-variance portfolio rules under distribution misspecification," Papers 2106.10491, arXiv.org, revised Jul 2021.
    11. Andrej Stenšin & Daumantas Bloznelis, 2022. "Copulas and Portfolios in the Electric Vehicle Sector," JRFM, MDPI, vol. 15(3), pages 1-20, March.
    12. Yuichi Takano & Keisuke Nanjo & Noriyoshi Sukegawa & Shinji Mizuno, 2015. "Cutting plane algorithms for mean-CVaR portfolio optimization with nonconvex transaction costs," Computational Management Science, Springer, vol. 12(2), pages 319-340, April.
    13. Arvid Oskar Ivar Hoffmann & Wander Jager & J. H. Von Eije, 2007. "Social Simulation of Stock Markets: Taking It to the Next Level," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(2), pages 1-7.
    14. Liu, Wenbin & Zhou, Zhongbao & Liu, Debin & Xiao, Helu, 2015. "Estimation of portfolio efficiency via DEA," Omega, Elsevier, vol. 52(C), pages 107-118.
    15. Nathan Lassance & Frédéric Vrins, 2021. "Minimum Rényi entropy portfolios," Annals of Operations Research, Springer, vol. 299(1), pages 23-46, April.
    16. Gianfranco Guastaroba & Renata Mansini & M. Speranza, 2009. "Models and Simulations for Portfolio Rebalancing," Computational Economics, Springer;Society for Computational Economics, vol. 33(3), pages 237-262, April.
    17. Sourish Das & Rituparna Sen, 2021. "Sparse Portfolio Selection via Bayesian Multiple Testing," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 585-617, November.
    18. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    19. Liu, Li & Chen, Ching-Cheng & Wan, Jieqiu, 2013. "Is world oil market “one great pool”?: An example from China's and international oil markets," Economic Modelling, Elsevier, vol. 35(C), pages 364-373.
    20. Eduardo Bered Fernandes Vieira & Tiago Pascoal Filomena, 2020. "Liquidity Constraints for Portfolio Selection Based on Financial Volume," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 1055-1077, December.

    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:spr:sankhb:v:85:y:2023:i:1:d:10.1007_s13571-022-00285-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.