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, 2012. "Large systems of diffusions interacting through their ranks," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1730-1747.
    2. Shkolnikov, Mykhaylo, 2013. "Large volatility-stabilized markets," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 212-228.
    3. 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.
    4. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    5. Radka Picková, 2014. "Generalized volatility-stabilized processes," Annals of Finance, Springer, vol. 10(1), pages 101-125, February.
    6. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Post-Print hal-00921151, HAL.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    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. 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.
    2. 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.
    3. 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.
    4. Sabine Elmiger, 2019. "CAPM-anomalies: quantitative puzzles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 643-667, October.
    5. De Moor, Lieven & Sercu, Piet, 2013. "The smallest firm effect: An international study," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 129-155.
    6. 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.
    7. Mabekebeke Segojane & Godfrey Ndlovu, 2022. "An Investigation of the Beta Anomaly in Emerging Markets: A South African Case," JRFM, MDPI, vol. 15(5), pages 1-18, May.
    8. 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.
    9. Petros Messis & Achilleas Zapranis, 2014. "Asset pricing with time-varying betas for stocks traded on S&P 500," Applied Economics, Taylor & Francis Journals, vol. 46(36), pages 4508-4518, December.
    10. 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.
    11. Stuart Hyde & Mohamed Sherif, 2010. "Tests of the conditional asset pricing model: further evidence from the cross-section of stock returns," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(2), pages 198-211.
    12. 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.
    13. 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.
    14. Artmann, Sabine & Finter, Philipp & Kempf, Alexander, 2011. "Determinants of expected stock returns: Large sample evidence from the German market," CFR Working Papers 10-01 [rev.], University of Cologne, Centre for Financial Research (CFR).
    15. Kim, Jang Ho & Han, Jiwoon & Kang, Taehyeon & Fabozzi, Frank J., 2023. "A machine learning approach for comparing the largest firm effect," Emerging Markets Review, Elsevier, vol. 54(C).
    16. Amir Amel†Zadeh, 2011. "The Return of the Size Anomaly: Evidence from the German Stock Market," European Financial Management, European Financial Management Association, vol. 17(1), pages 145-182, January.
    17. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    18. Skočir, Matevž & Lončarski, Igor, 2018. "Multi-factor asset pricing models: Factor construction choices and the revisit of pricing factors," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 55(C), pages 65-80.
    19. 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.
    20. 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.

    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.