The efficient index hypothesis and its implications in the BSM model
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.
References listed on IDEAS
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- R. Mehra & E. Prescott, 2010.
"The equity premium: a puzzle,"
Levine's Working Paper Archive
1401, David K. Levine.
- Mehra, Rajnish, 2007. "The Equity Premium Puzzle: A Review," Foundations and Trends(R) in Finance, now publishers, vol. 2(1), pages 1-81, September.
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