The efficient index hypothesis and its implications in the BSM model

Details The efficient index hypothesis and its implications in the BSM model The efficient index hypothesis and its implications in the BSM model

2011-09-11

arxiv.org/abs/1109.2327v1

Economy

Quantitative Finance

General Finance

8 pages

Scientific paper

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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