[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1806.08005.html
   My bibliography  Save this paper

Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios

Author

Listed:
  • Taras Bodnar
  • Dmytro Ivasiuk
  • Nestor Parolya
  • Wofgang Schmid
Abstract
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal portfolios belong to the set of mean-variance feasible portfolios and establish necessary and sufficient conditions such that they are mean-variance efficient. Furthermore, an application to the stock market is presented and the behavior of the optimal portfolio is discussed for different values of the relative risk aversion coefficient. It turns out that the assumption of log-normality does not seem to be a strong restriction.

Suggested Citation

  • Taras Bodnar & Dmytro Ivasiuk & Nestor Parolya & Wofgang Schmid, 2018. "Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios," Papers 1806.08005, arXiv.org, revised May 2019.
    • Handle: RePEc:arx:papers:1806.08005
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1806.08005
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael W. Brandt & Pedro Santa‐Clara, 2006. "Dynamic Portfolio Selection by Augmenting the Asset Space," Journal of Finance, American Finance Association, vol. 61(5), pages 2187-2217, October.
    2. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    3. Merton, Robert C. & Samuelson, Paul A., 1974. "Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods," Journal of Financial Economics, Elsevier, vol. 1(1), pages 67-94, May.
    4. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    5. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2013. "On the equivalence of quadratic optimization problems commonly used in portfolio theory," European Journal of Operational Research, Elsevier, vol. 229(3), pages 637-644.
    6. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2015. "On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability," European Journal of Operational Research, Elsevier, vol. 246(2), pages 528-542.
    7. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    8. Grauer, Robert R & Hakansson, Nils H, 1987. "Gains from International Diversification: 1968-85 Returns on Portfolios of Stocks and Bonds," Journal of Finance, American Finance Association, vol. 42(3), pages 721-739, July.
    9. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    10. Elton, Edwin J & Gruber, Martin J, 1974. "Portfolio Theory when Investment Relatives are Lognormally Distributed," Journal of Finance, American Finance Association, vol. 29(4), pages 1265-1273, September.
    11. Robert R. Grauer and Nils H. Hakansson., 1987. "Gains from International Diversification: l968-85 Returns on Portfolios of Stocks and Bonds," Research Program in Finance Working Papers 168, University of California at Berkeley.
    12. Lynch, Anthony W. & Tan, Sinan, 2010. "Multiple Risky Assets, Transaction Costs, and Return Predictability: Allocation Rules and Implications for U.S. Investors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(4), pages 1015-1053, August.
    13. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, September.
    14. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2015. "A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function," Annals of Operations Research, Springer, vol. 229(1), pages 121-158, June.
    15. 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.
    16. 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.
    17. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    18. Hakansson, Nils H, 1971. "Multi-Period Mean-Variance Analysis: Toward A General Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 26(4), pages 857-884, September.
    19. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    20. Grauer, Robert R., 1986. "Normality, Solvency, and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 265-278, September.
    21. repec:nys:sunysb:93-02 is not listed on IDEAS
    22. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," The Journal of Business, University of Chicago Press, vol. 55(2), pages 233-251, April.
    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. Dmytro Ivasiuk, 2019. "An approximate solution for the power utility optimization under predictable returns," Papers 1911.06552, arXiv.org, revised Oct 2021.

    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. Dmytro Ivasiuk, 2019. "An approximate solution for the power utility optimization under predictable returns," Papers 1911.06552, arXiv.org, revised Oct 2021.
    2. Taras Bodnar & Yarema Okhrin & Valdemar Vitlinskyy & Taras Zabolotskyy, 2018. "Determination and estimation of risk aversion coefficients," Computational Management Science, Springer, vol. 15(2), pages 297-317, June.
    3. Bodnar, Taras & Mazur, Stepan & Okhrin, Yarema, 2017. "Bayesian estimation of the global minimum variance portfolio," European Journal of Operational Research, Elsevier, vol. 256(1), pages 292-307.
    4. Taras Bodnar & Dmytro Ivasiuk & Nestor Parolya & Wolfgang Schmid, 2023. "Multi-period power utility optimization under stock return predictability," Computational Management Science, Springer, vol. 20(1), pages 1-27, December.
    5. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2015. "A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function," Annals of Operations Research, Springer, vol. 229(1), pages 121-158, June.
    6. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    7. Bauder, David & Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2020. "Bayesian inference of the multi-period optimal portfolio for an exponential utility," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    8. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2015. "On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability," European Journal of Operational Research, Elsevier, vol. 246(2), pages 528-542.
    9. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    10. Martin D. D. Evans & Viktoria Hnatkovska, 2005. "Solving General Equilibrium Models with Incomplete Markets and Many Assets," NBER Technical Working Papers 0318, National Bureau of Economic Research, Inc.
    11. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2018. "Estimation of the global minimum variance portfolio in high dimensions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 371-390.
    12. Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim & Wolf, Avner, 2009. "Bonds versus stocks: Investors' age and risk taking," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 817-830, September.
    13. Mark E. Wohar & David E. Rapach, 2005. "Return Predictability and the Implied Intertemporal Hedging Demands for Stocks and Bonds: International Evidence," Computing in Economics and Finance 2005 329, Society for Computational Economics.
    14. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    15. Wan-Yi Chiu, 2024. "Portfolio Selection with Hierarchical Isomorphic Risk Aversion," Mathematics, MDPI, vol. 12(21), pages 1-22, October.
    16. Engsted, Tom & Pedersen, Thomas Q., 2012. "Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 241-253.
    17. Simaan, Majeed & Simaan, Yusif & Tang, Yi, 2018. "Estimation error in mean returns and the mean-variance efficient frontier," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 109-124.
    18. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    19. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    20. Guidolin, Massimo & Timmermann, Allan, 2007. "Asset allocation under multivariate regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3503-3544, November.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1806.08005. 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.