IDEAS home Printed from https://ideas.repec.org/p/arx/papers/physics-0601166.html
   My bibliography  Save this paper

How many independent bets are there?

Author

Listed:
  • Daniel Polakow
  • Tim Gebbie

Abstract

The benefits of portfolio diversification is a central tenet implicit to modern financial theory and practice. Linked to diversification is the notion of breadth. Breadth is correctly thought of as the number of in- dependent bets available to an investor. Conventionally applications us- ing breadth frequently assume only the number of separate bets. There may be a large discrepancy between these two interpretations. We uti- lize a simple singular-value decomposition (SVD) and the Keiser-Gutman stopping criterion to select the integer-valued effective dimensionality of the correlation matrix of returns. In an emerging market such as South African we document an estimated breadth that is considerably lower than anticipated. This lack of diversification may be because of market concentration, exposure to the global commodity cycle and local currency volatility. We discuss some practical extensions to a more statistically correct interpretation of market breadth, and its theoretical implications for both global and domestic investors.

Suggested Citation

  • Daniel Polakow & Tim Gebbie, 2006. "How many independent bets are there?," Papers physics/0601166, arXiv.org, revised Jan 2008.
    • Handle: RePEc:arx:papers:physics/0601166
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/physics/0601166
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert Fernholz, 1999. "Portfolio Generating Functions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 15, pages 344-367, World Scientific Publishing Co. Pte. Ltd..
    2. Wilcox, Diane & Gebbie, Tim, 2004. "On the analysis of cross-correlations in South African market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 294-298.
    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. Daniel Adam Polakow & Emlyn James Flint, 2015. "Global Risk Factors and South African Equity Indices," South African Journal of Economics, Economic Society of South Africa, vol. 83(4), pages 598-616, December.
    2. Jem Tugwell, 2011. "Skill or luck? The role of strategies and scenario analysis as a competitive differentiator for fund management firms," Journal of Asset Management, Palgrave Macmillan, vol. 12(4), pages 281-291, September.

    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. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    2. Robert Fernholz, 2015. "An example of short-term relative arbitrage," Papers 1510.02292, arXiv.org.
    3. Johannes Ruf & Kangjianan Xie, 2018. "Generalised Lyapunov Functions and Functionally Generated Trading Strategies," Papers 1801.07817, arXiv.org.
    4. D. L. Wilcox & T. J. Gebbie, 2013. "On pricing kernels, information and risk," Papers 1310.4067, arXiv.org, revised Oct 2013.
    5. Steven Campbell & Ting-Kam Leonard Wong, 2021. "Functional portfolio optimization in stochastic portfolio theory," Papers 2103.10925, arXiv.org, revised Oct 2021.
    6. Ricardo T. Fernholz & Robert Fernholz, 2022. "Permutation-weighted portfolios and the efficiency of commodity futures markets," Annals of Finance, Springer, vol. 18(1), pages 81-108, March.
    7. Ioannis Karatzas & Donghan Kim, 2020. "Trading strategies generated pathwise by functions of market weights," Finance and Stochastics, Springer, vol. 24(2), pages 423-463, April.
    8. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.
    9. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2024. "Quantifying dimensional change in stochastic portfolio theory," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 977-1021, July.
    10. Eterovic, Nicolas A. & Eterovic, Dalibor S., 2013. "Separating the wheat from the chaff: Understanding portfolio returns in an emerging market," Emerging Markets Review, Elsevier, vol. 16(C), pages 145-169.
    11. Yang, Yujun & Li, Jianping & Yang, Yimei, 2017. "The cross-correlation analysis of multi property of stock markets based on MM-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 23-33.
    12. Conlon, T. & Ruskin, H.J. & Crane, M., 2007. "Random matrix theory and fund of funds portfolio optimisation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 565-576.
    13. Soumik Pal & Ting-Kam Leonard Wong, 2016. "Exponentially concave functions and a new information geometry," Papers 1605.05819, arXiv.org, revised May 2017.
    14. Kangjianan Xie, 2019. "Leakage of rank-dependent functionally generated trading strategies," Papers 1912.04221, arXiv.org.
    15. Ioannis Karatzas & Johannes Ruf, 2016. "Trading Strategies Generated by Lyapunov Functions," Papers 1603.08245, arXiv.org.
    16. Dai, Yun-Shi & Huynh, Ngoc Quang Anh & Zheng, Qing-Huan & Zhou, Wei-Xing, 2022. "Correlation structure analysis of the global agricultural futures market," Research in International Business and Finance, Elsevier, vol. 61(C).
    17. Karatzas, Ioannis & Ruf, Johannes, 2017. "Trading strategies generated by Lyapunov functions," LSE Research Online Documents on Economics 69177, London School of Economics and Political Science, LSE Library.
    18. Winslow Strong & Jean-Pierre Fouque, 2011. "Diversity and arbitrage in a regulatory breakup model," Annals of Finance, Springer, vol. 7(3), pages 349-374, August.
    19. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2012. "The Japanese economy in crises: A time series segmentation study," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-81.
    20. Dalibor Eterovic & Nicolas Eterovic, 2012. "Separating the Wheat from the Chaff: Understanding Portfolio Returns in an Emerging Market," Working Papers wp_025, Adolfo Ibáñez University, School of Government.

    More about this item

    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:arx:papers:physics/0601166. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.