IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v19y2016i03ns0219024916500187.html
   My bibliography  Save this article

Learning And Portfolio Decisions For Crra Investors

Author

Listed:
  • MICHELE LONGO

    (Università Cattolica del Sacro Cuore, Largo Gemelli, 1, Milano, 20123, Italy)

  • ALESSANDRA MAININI

    (Università Cattolica del Sacro Cuore, Largo Gemelli, 1, Milano, 20123, Italy)

Abstract

We maximize the expected utility from terminal wealth for a Constant Relative Risk Aversion (CRRA) investor when the market price of risk is an unobservable random variable and explore the effects of learning by comparing the optimal portfolio under partial observation with the corresponding myopic policy. In particular, we show that, for a market price of risk constant in sign, the ratio between the portfolio under partial observation and its myopic counterpart increases with respect to risk tolerance. As a consequence, the absolute value of the partial observation case is larger (smaller) than the myopic one if the investor is more (less) risk tolerant than the logarithmic investor. Moreover, our explicit computations enable to study in detail the so called hedging demand induced by parameter uncertainty.

Suggested Citation

  • Michele Longo & Alessandra Mainini, 2016. "Learning And Portfolio Decisions For Crra Investors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-21, May.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:03:n:s0219024916500187
    DOI: 10.1142/S0219024916500187
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024916500187
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024916500187?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. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    2. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    3. 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.
    4. Dothan, Michael U & Feldman, David, 1986. "Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 41(2), pages 369-382, June.
    5. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    6. Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
    7. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    8. Yoichi Kuwana, 1995. "Certainty Equivalence And Logarithmic Utilities In Consumption/Investment Problems," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 297-309, October.
    9. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    10. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    11. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    12. Jakša Cvitanić & Ali Lazrak & Lionel Martellini & Fernando Zapatero, 2006. "Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations," The Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1113-1156.
    13. Nicole Bäuerle & Ulrich Rieder, 2007. "Portfolio Optimization With Jumps And Unobservable Intensity Process," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 205-224, April.
    14. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    15. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.
    16. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    17. Detemple, Jerome B, 1986. "Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-391, June.
    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. Bäuerle Nicole & Chen An, 2019. "Optimal retirement planning under partial information," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 37-55, December.
    2. Michele Longo & Alessandra Mainini, 2017. "Welfare effects of information and rationality in portfolio decisions under parameter uncertainty," Papers 1709.04387, arXiv.org.
    3. Nicole Bauerle & Stefanie Grether, 2017. "Extremal Behavior of Long-Term Investors with Power Utility," Papers 1703.04423, arXiv.org, revised Jun 2017.
    4. Nicole Bäuerle & Stefanie Grether, 2017. "Extremal Behavior Of Long-Term Investors With Power Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-13, August.
    5. Bäuerle, Nicole & Mahayni, Antje, 2024. "Optimal investment in ambiguous financial markets with learning," European Journal of Operational Research, Elsevier, vol. 315(1), pages 393-410.

    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. Michele Longo & Alessandra Mainini, 2015. "Learning and Portfolio Decisions for HARA Investors," Papers 1502.02968, arXiv.org.
    2. David Feldman, 2007. "Incomplete information equilibria: Separation theorems and other myths," Annals of Operations Research, Springer, vol. 151(1), pages 119-149, April.
    3. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    4. Michele Longo & Alessandra Mainini, 2017. "Welfare effects of information and rationality in portfolio decisions under parameter uncertainty," Papers 1709.04387, arXiv.org.
    5. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.
    6. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    7. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    8. Lubos Pastor & Pietro Veronesi, 2009. "Learning in Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 361-381, November.
    9. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    10. Hening Liu, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Post-Print hal-00781344, HAL.
    11. 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.
    12. Flavio Angelini & Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "Implicit incentives for fund managers with partial information," Computational Management Science, Springer, vol. 18(4), pages 539-561, October.
    13. Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "The value of knowing the market price of risk," Annals of Operations Research, Springer, vol. 299(1), pages 101-131, April.
    14. Lundtofte, Frederik, 2008. "Expected life-time utility and hedging demands in a partially observable economy," European Economic Review, Elsevier, vol. 52(6), pages 1072-1096, August.
    15. Thomas Lim & Marie-Claire Quenez, 2010. "Portfolio optimization in a default model under full/partial information," Papers 1003.6002, arXiv.org, revised Nov 2013.
    16. Daniel Andrei & Michael Hasler, 2020. "Dynamic Attention Behavior Under Return Predictability," Management Science, INFORMS, vol. 66(7), pages 2906-2928, July.
    17. 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.
    18. Constantin Mellios, 2007. "Interest rate options valuation under incomplete information," Annals of Operations Research, Springer, vol. 151(1), pages 99-117, April.
    19. Jessica A. Wachter, 2010. "Asset Allocation," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 175-206, December.
    20. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.

    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:wsi:ijtafx:v:19:y:2016:i:03:n:s0219024916500187. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.