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The efficient index hypothesis and its implications in the BSM model

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  • Vladimir Vovk

Abstract

This note studies the behavior of an index I_t which is assumed to be a tradable security, to satisfy the BSM model dI_t/I_t = \mu dt + \sigma dW_t, and to be efficient in the following sense: we do not expect a prespecified trading strategy whose value is almost surely always nonnegative to outperform the index greatly. The efficiency of the index imposes severe restrictions on its growth rate; in particular, for a long investment horizon we should have \mu\approx r+\sigma^2, where r is the interest rate. This provides another partial solution to the equity premium puzzle. All our mathematical results are extremely simple.

Suggested Citation

  • Vladimir Vovk, 2011. "The efficient index hypothesis and its implications in the BSM model," Papers 1109.2327, arXiv.org.
    • Handle: RePEc:arx:papers:1109.2327
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    References listed on IDEAS

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    1. Mehra, Rajnish, 2007. "The Equity Premium Puzzle: A Review," Foundations and Trends(R) in Finance, now publishers, vol. 2(1), pages 1-81, September.
    2. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
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    Cited by:

    1. Vladimir Vovk, 2011. "The Capital Asset Pricing Model as a corollary of the Black-Scholes model," Papers 1109.5144, arXiv.org.
    2. Vladimir Vovk & Glenn Shafer, 2016. "A probability-free and continuous-time explanation of the equity premium and CAPM," Papers 1607.00830, arXiv.org.

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