IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/125083.html
   My bibliography  Save this paper

Market-Based Portfolio Variance

Author

Listed:
  • Olkhov, Victor

Abstract

The investor, who holds his portfolio and doesn’t trade his shares, at current time can use the time series of the market trades that were made during the averaging interval with the securities of his portfolio to assess the current variance of the portfolio. We show how the time series of trades with the securities of the portfolio determine the time series of trades with the portfolio as a single market security. The time series of portfolio trades determine the return and variance of the portfolio in the same form as the time series of trades with securities determine their returns and variances. The description of any portfolio and any single market security is equal. The time series of portfolio trades define the decomposition of the portfolio variance by its securities. If the volumes of trades with all securities are assumed constant, the decomposition of the portfolio variance coincides with Markowitz’s (1952) expression of variance. However, the real markets expose random volumes of trades. The portfolio variance that accounts for the randomness of trade volumes is a polynomial of the 4th degree in the variables of relative amounts invested into securities and with the coefficients different from covariances of securities returns. We discuss the possible origin of the latent and unintended assumption that Markowitz (1952) made to derive his result. Our description of the portfolio variance that accounts for the randomness of real trade volumes could help the portfolio managers and the majors like BlackRock’s Aladdin and Asimov, JP Morgan, and the U.S. Fed to adjust their models and forecasts to the reality of random markets.

Suggested Citation

  • Olkhov, Victor, 2025. "Market-Based Portfolio Variance," MPRA Paper 125083, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:125083
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/125083/1/MPRA_paper_125083.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duffie, Darrell & Dworczak, Piotr, 2021. "Robust benchmark design," Journal of Financial Economics, Elsevier, vol. 142(2), pages 775-802.
    2. Andrew W. Lo & Jiang Wang, 2006. "Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2805-2840, December.
    3. Mark Rubinstein, 2002. "Markowitz's “Portfolio Selection”: A Fifty‐Year Retrospective," Journal of Finance, American Finance Association, vol. 57(3), pages 1041-1045, June.
    4. Victor Olkhov, 2022. "Market-Based Asset Price Probability," Papers 2205.07256, arXiv.org, revised Dec 2024.
    5. Stephen Boyd & Kasper Johansson & Ronald Kahn & Philipp Schiele & Thomas Schmelzer, 2024. "Markowitz Portfolio Construction at Seventy," Papers 2401.05080, arXiv.org.
    6. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, vol. 69(1), pages 1-49, February.
    7. Pogue, G A, 1970. "An Extension of the Markowitz Portfolio Selection Model to Include Variable Transactions' Costs, Short Sales, Leverage Policies and Taxes," Journal of Finance, American Finance Association, vol. 25(5), pages 1005-1027, December.
    8. Karpoff, Jonathan M, 1986. "A Theory of Trading Volume," Journal of Finance, American Finance Association, vol. 41(5), pages 1069-1087, December.
    9. repec:bla:jfinan:v:43:y:1988:i:1:p:97-112 is not listed on IDEAS
    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. Ravi Kashyap, 2024. "The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments," Papers 2407.09536, arXiv.org.
    2. Griffin, John M. & Nardari, Federico & Stulz, Rene M., 2004. "Stock Market Trading and Market Conditions," Working Paper Series 2004-13, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    3. Zhong-Guo Zhou, 2010. "The high-volume return premium: evidence from the Chinese stock market," Review of Quantitative Finance and Accounting, Springer, vol. 35(3), pages 295-313, October.
    4. Zhaodan Huang & James B. Heian, 2010. "Trading‐Volume Shocks And Stock Returns: An Empirical Analysis," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 33(2), pages 153-177, June.
    5. Omid Sabbaghi & Navid Sabbaghi, 2014. "An empirical analysis of the Carbon Financial Instrument," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 38(2), pages 209-234, April.
    6. Longsheng Cheng & Mahboubeh Shadabfar & Arash Sioofy Khoojine, 2023. "A State-of-the-Art Review of Probabilistic Portfolio Management for Future Stock Markets," Mathematics, MDPI, vol. 11(5), pages 1-34, February.
    7. Bruce I. Jacobs & Kenneth N. Levy, 2025. "Portfolio insurance, portfolio theory, market simulation, and risks of portfolio leverage," Annals of Operations Research, Springer, vol. 346(1), pages 67-97, March.
    8. Victor Olkhov, 2023. "Market-Based Probability of Stock Returns," Papers 2302.07935, arXiv.org, revised Dec 2024.
    9. Philip Barrett & Mariia Bondar & Sophia Chen & Mali Chivakul & Deniz Igan, 2024. "Pricing protest: the response of financial markets to social unrest," Review of Finance, European Finance Association, vol. 28(4), pages 1419-1450.
    10. Allan, Grant & Eromenko, Igor & McGregor, Peter & Swales, Kim, 2011. "The regional electricity generation mix in Scotland: A portfolio selection approach incorporating marine technologies," Energy Policy, Elsevier, vol. 39(1), pages 6-22, January.
    11. Samuel B. Bonsall & Brian P. Miller, 2017. "The impact of narrative disclosure readability on bond ratings and the cost of debt," Review of Accounting Studies, Springer, vol. 22(2), pages 608-643, June.
    12. Lof, Matthijs & van Bommel, Jos, 2023. "Asymmetric information and the distribution of trading volume," Journal of Corporate Finance, Elsevier, vol. 82(C).
    13. Choi, Jong-Seo & Choe, Chongwoo, 1998. "Explanatory factors for trading volume responses to annual earnings announcements: Evidence from the Korean stock market," Pacific-Basin Finance Journal, Elsevier, vol. 6(1-2), pages 193-212, May.
    14. Daniella Acker & Mathew Stalker & Ian Tonks, 2002. "Daily Closing Inside Spreads and Trading Volumes Around Earnings Announcements," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 29(9‐10), pages 1149-1179.
    15. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    16. Kromidha, Endrit & Li, Matthew C., 2019. "Determinants of leadership in online social trading: A signaling theory perspective," Journal of Business Research, Elsevier, vol. 97(C), pages 184-197.
    17. Duffie, Darrell & Dworczak, Piotr, 2021. "Robust benchmark design," Journal of Financial Economics, Elsevier, vol. 142(2), pages 775-802.
    18. Alex Frankel & Navin Kartik, 2022. "Improving Information from Manipulable Data," Journal of the European Economic Association, European Economic Association, vol. 20(1), pages 79-115.
    19. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    20. Chen, Deqiu & Ma, Yujing & Martin, Xiumin & Michaely, Roni, 2022. "On the fast track: Information acquisition costs and information production," Journal of Financial Economics, Elsevier, vol. 143(2), pages 794-823.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    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:pra:mprapa:125083. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.