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The efficient index hypothesis and its implications in the BSM model

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  • Vladimir Vovk
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    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.

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    File URL: http://arxiv.org/pdf/1109.2327
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    Paper provided by arXiv.org in its series Papers with number 1109.2327.

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    Date of creation: Sep 2011
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    Handle: RePEc:arx:papers:1109.2327

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    1. 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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