**The efficient index hypothesis and its implications in the BSM model.** / Vovk, Vladimir.

Research output: Working paper

Published

**The efficient index hypothesis and its implications in the BSM model.** / Vovk, Vladimir.

Research output: Working paper

@techreport{0ff7b0bb356c47d08f3deaddaab840e9,

title = "The efficient index hypothesis and its implications in the BSM model",

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.",

keywords = "efficient index, efficient market hypothesis, equity premium",

author = "Vladimir Vovk",

note = "8 pages",

year = "2011",

month = sep,

day = "11",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - The efficient index hypothesis and its implications in the BSM model

AU - Vovk, Vladimir

N1 - 8 pages

PY - 2011/9/11

Y1 - 2011/9/11

N2 - 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.

AB - 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.

KW - efficient index

KW - efficient market hypothesis

KW - equity premium

M3 - Working paper

BT - The efficient index hypothesis and its implications in the BSM model

ER -