IDEAS home Printed from https://ideas.repec.org/a/kap/annfin/v17y2021i3d10.1007_s10436-021-00390-8.html
   My bibliography  Save this article

A stock market model based on CAPM and market size

Author

Listed:
  • Brandon Flores

    (University of Nevada, Reno)

  • Blessing Ofori-Atta

    (University of Nevada, Reno)

  • Andrey Sarantsev

    (University of Nevada, Reno)

Abstract

We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French’s data library. This model is somewhat similar to generalized volatility-stabilized models. The novelty of our work is twofold. First, we take into account the difference between price and total returns (in other words, between market size and wealth processes). Second, we work with actual market data. We study the long-term properties of this system of equations, and reproduce observed linearity of the capital distribution curve. In the “Appendix”, we analyze size-based real-world index funds.

Suggested Citation

  • Brandon Flores & Blessing Ofori-Atta & Andrey Sarantsev, 2021. "A stock market model based on CAPM and market size," Annals of Finance, Springer, vol. 17(3), pages 405-424, September.
    • Handle: RePEc:kap:annfin:v:17:y:2021:i:3:d:10.1007_s10436-021-00390-8
    DOI: 10.1007/s10436-021-00390-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10436-021-00390-8
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10436-021-00390-8?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. Shkolnikov, Mykhaylo, 2013. "Large volatility-stabilized markets," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 212-228.
    2. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
    3. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Post-Print hal-00921151, HAL.
    4. Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
    5. van Dijk, Mathijs A., 2011. "Is size dead? A review of the size effect in equity returns," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3263-3274.
    6. Semenov, Andrei, 2015. "The small-cap effect in the predictability of individual stock returns," International Review of Economics & Finance, Elsevier, vol. 38(C), pages 178-197.
    7. Shkolnikov, Mykhaylo, 2012. "Large systems of diffusions interacting through their ranks," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1730-1747.
    8. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    9. Radka Picková, 2014. "Generalized volatility-stabilized processes," Annals of Finance, Springer, vol. 10(1), pages 101-125, February.
    10. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Annals of Finance, Springer, vol. 11(2), pages 151-198, May.
    11. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    12. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    13. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
    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. Hu, Debao & Li, Xin & Xiang, George & Zhou, Qiyao, 2023. "Asset pricing models in the presence of higher moments: Theory and evidence from the U.S. and China stock market," Pacific-Basin Finance Journal, Elsevier, vol. 79(C).

    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. Abraham Atsiwo & Andrey Sarantsev, 2024. "Capital Asset Pricing Model with Size Factor and Normalizing by Volatility Index," Papers 2411.19444, arXiv.org, revised Dec 2024.
    2. Sergio A. Almada Monter & Mykhaylo Shkolnikov & Jiacheng Zhang, 2018. "Dynamics of observables in rank-based models and performance of functionally generated portfolios," Papers 1802.03593, arXiv.org.
    3. Turan G. Bali & Robert F. Engle & Yi Tang, 2017. "Dynamic Conditional Beta Is Alive and Well in the Cross Section of Daily Stock Returns," Management Science, INFORMS, vol. 63(11), pages 3760-3779, November.
    4. Christian Fieberg & Daniel Metko & Thorsten Poddig & Thomas Loy, 2023. "Machine learning techniques for cross-sectional equity returns’ prediction," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 289-323, March.
    5. Anton Astakhov & Tomas Havranek & Jiri Novak, 2019. "Firm Size And Stock Returns: A Quantitative Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 33(5), pages 1463-1492, December.
    6. Qianwei Ying & Tahir Yousaf & Qurat ul Ain & Yasmeen Akhtar & Muhammad Shahid Rasheed, 2019. "Stock Investment and Excess Returns: A Critical Review in the Light of the Efficient Market Hypothesis," JRFM, MDPI, vol. 12(2), pages 1-22, June.
    7. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    8. Will Gans & Beat Hintermann, 2013. "Market Effects of Voluntary Climate Action by Firms: Evidence from the Chicago Climate Exchange," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 55(2), pages 291-308, June.
    9. Bäumer, Marcus, 2020. "What matters to investment professionals in decision making? The role of soft factors in stock selection," EIKV-Schriftenreihe zum Wissens- und Wertemanagement, European Institute for Knowledge & Value Management (EIKV), Luxembourg, volume 44, number 44, July.
    10. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    11. Anton Astakhov & Tomas Havranek & Jiri Novak, 2017. "Firm Size and Stock Returns: A Meta-Analysis," Working Papers IES 2017/14, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2017.
    12. Durand, Robert B. & Lan, Yihui & Ng, Andrew, 2011. "Conditional beta: Evidence from Asian emerging markets," Global Finance Journal, Elsevier, vol. 22(2), pages 130-153.
    13. Winkler, Julian, 2023. "Managing fundamentals versus preferences: Re-balancing portfolios and stock returns," MPRA Paper 119149, University Library of Munich, Germany.
    14. Zaremba Adam & Konieczka Przemysław, 2017. "Size, Value, and Momentum in Polish Equity Returns: Local or International Factors?," International Journal of Management and Economics, Warsaw School of Economics, Collegium of World Economy, vol. 53(3), pages 26-47, September.
    15. Teresa Garcia & Daniel Borrego, 2017. "Markowitz Efficient Frontier And Capital Market Line – Evidence From The Portuguese Stock Market," Portuguese Journal of Management Studies, ISEG, Universidade de Lisboa, vol. 22(1), pages 3-23.
    16. Misund, Bard & Mohn, Klaus, 2014. "Exploration Risk in Oil & Gas Shareholder Returns," UiS Working Papers in Economics and Finance 2014/4, University of Stavanger.
    17. Argiro Svingou, 2013. "Cross-sectional Analysis of Stock Returns in Athens Stock Exchange for the Period 2004-2011," SPOUDAI Journal of Economics and Business, SPOUDAI Journal of Economics and Business, University of Piraeus, vol. 63(1-2), pages 100-120, June.
    18. Fabian T. Lutzenberger, 2015. "Multifactor Models and their Consistency with the ICAPM: Evidence from the European Stock Market," European Financial Management, European Financial Management Association, vol. 21(5), pages 1014-1052, November.
    19. Victoria Atanasov & Thomas Nitschka, 2013. "The Size Effect in Value and Momentum Factors: Implications for the Cross-section of International Stock Returns," Tinbergen Institute Discussion Papers 13-180/IV/DSF66, Tinbergen Institute.
    20. Kaserer Christoph & Hanauer Matthias X., 2017. "25 Jahre Fama-French-Modell: Erklärungsgehalt, Anomalien und praktische Implikationen," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 18(2), pages 98-116, June.

    More about this item

    Keywords

    Capital asset pricing model; Stochastic differential equations; Capital distribution curve; Stochastic stability; Market weight;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    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:kap:annfin:v:17:y:2021:i:3:d:10.1007_s10436-021-00390-8. 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.