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How many independent bets are there?

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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