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A second-order stock market model

Author

Listed:
  • Robert Fernholz
  • Tomoyuki Ichiba
  • Ioannis Karatzas

Abstract

A first-order model for a stock market assigns to each stock a return parameter and a variance parameter that depend only on the rank of the stock. A second-order model assigns these parameters based on both the rank and the name of the stock. First- and second-order models exhibit stability properties that make them appropriate as a backdrop for the analysis of the idiosyncratic behavior of individual stocks. Methods for the estimation of the parameters of second-order models are developed in this paper. Copyright Springer-Verlag 2013

Suggested Citation

  • Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Annals of Finance, Springer, vol. 9(3), pages 439-454, August.
    • Handle: RePEc:kap:annfin:v:9:y:2013:i:3:p:439-454
    DOI: 10.1007/s10436-012-0193-2
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    References listed on IDEAS

    as
    1. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    2. Mitchel Y. Abolafia (ed.), 2005. "Markets," Books, Edward Elgar Publishing, number 2788.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Benjamin Jourdain & Julien Reygner, 2013. "Capital distribution and portfolio performance in the mean-field Atlas model," Papers 1312.5660, arXiv.org, revised Aug 2014.
    2. Ali Al-Aradi & Sebastian Jaimungal, 2019. "Active and Passive Portfolio Management with Latent Factors," Papers 1903.06928, arXiv.org.
    3. Kangjianan Xie, 2020. "Leakage of rank-dependent functionally generated trading strategies," Annals of Finance, Springer, vol. 16(4), pages 573-591, December.
    4. David Itkin & Martin Larsson, 2024. "Calibrated rank volatility stabilized models for large equity markets," Papers 2403.04674, arXiv.org.
    5. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    6. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Post-Print hal-00921151, HAL.
    7. Sergey Sosnovskiy, 2015. "Market shape formation, statistical equilibrium and neutral evolution theory," Papers 1506.07163, arXiv.org.
    8. Sergey Sosnovskiy, 2015. "On financial applications of the two-parameter Poisson-Dirichlet distribution," Papers 1501.01954, arXiv.org, revised Jul 2015.
    9. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org, revised Oct 2024.

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    More about this item

    Keywords

    Stochastic portfolio theory; Atlas model; First-order model; Second-order model; G10;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    Statistics

    Access and download statistics

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