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Balance, growth and diversity of financial markets

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  • Constantinos Kardaras

Abstract

A financial market comprising of a certain number of distinct companies is considered, and the following statement is proved: either a specific agent will surely beat the whole market unconditionally in the long run, or (and this "or" is not exclusive) all the capital of the market will accumulate in one company. Thus, absence of any "free unbounded lunches relative to the total capital" opportunities lead to the most dramatic failure of diversity in the market: one company takes over all other until the end of time. In order to prove this, we introduce the notion of perfectly balanced markets, which is an equilibrium state in which the relative capitalization of each company is a martingale under the physical probability. Then, the weaker notion of balanced markets is discussed where the martingale property of the relative capitalizations holds only approximately, we show how these concepts relate to growth-optimality and efficiency of the market, as well as how we can infer a shadow interest rate that is implied in the economy in the absence of a bank.

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  • Constantinos Kardaras, 2008. "Balance, growth and diversity of financial markets," Papers 0803.1858, arXiv.org.
    • Handle: RePEc:arx:papers:0803.1858
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    References listed on IDEAS

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    1. 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.
    2. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    3. Fama, Eugene F & MacBeth, James D, 1974. "Long-Term Growth in a Short-Term Market," Journal of Finance, American Finance Association, vol. 29(3), pages 857-885, June.
    4. Roll, Richard, 1973. "Evidence on the "Growth-Optimum" Model," Journal of Finance, American Finance Association, vol. 28(3), pages 551-566, June.
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    Cited by:

    1. Johannes Ruf, 2010. "Hedging under arbitrage," Papers 1003.4797, arXiv.org, revised May 2011.
    2. Mikhail Zhitlukhin, 2022. "Optimal growth strategies for a representative agent in a continuous-time asset market," Papers 2211.05316, arXiv.org.
    3. Andrey Sarantsev, 2014. "On a class of diverse market models," Annals of Finance, Springer, vol. 10(2), pages 291-314, May.
    4. Andrey Sarantsev, 2017. "Reflected Brownian Motion in a Convex Polyhedral Cone: Tail Estimates for the Stationary Distribution," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1200-1223, September.
    5. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.

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