Measuring the Degree of Financial Market Efficiency

Finance India, Vol. 22, No. 4, December 2008

Posted: 4 Jun 2008

See all articles by Cornelis A. Los

Cornelis A. Los

University of California at Irvine - The Paul Merage School of Business; EMEPS Associates

Abstract

This paper compares, first, two competing hypotheses of market efficiency: the classical Efficient Market Hypothesis (EMH) of Samuelson (1965) and Fama (1970), and the Fractal Market Hypothesis (FMH) of Mandelbrot (1968) and Peters (1994). The market-neutral EMH risk depends on the empirically uncorroborated i.i.d. (= independence & stationarity) assumption of market innovations. The non-neutral FMH risk depends on the length of the investment time horizon: its degree of horizon dependence, or Long Memory (LM), is measured by the Hurst exponent. Next, it is demonstrated that an empirically better measurable definition of financial market risk is needed by all market participants. This new definition of market risk should allow for a measurement of the degree of market efficiency, which is both horizon and time dependent. The proposed definition of market risk is the time - frequency distribution P, where the shape of the P function is determined not only by second-order moments, differentiated by investment asset return categorization, but also by the length of the investment horizon, and by time t. In other words, the new definition of financial market risk embodied by the function P(s,w,t) should be able to account for the empirically observable strict non-stationarity to be scientifically acceptable. Such a categorized, horizon-dependent, time-varying, time - frequency distribution P(s,w,t) can be measured and identified by modern forms of time - frequency signal processing analysis, like wavelet multiresolution analysis. Two possible consistent diffusion models to generate such empirical time-frequency distributions P(s,w,t) are the non-arbitrage-neutral Fractional Brownian Motion and the, theoretically more acceptable) arbitrage-neutral Multifractional Model of Asset Returns.

Keywords: Market efficiency, risk, measurement, fractal, investment horizon, multiresolution analysis

JEL Classification: B41, C23, D42, E44, G13, G14, G15

Suggested Citation

Los, Cornelis A., Measuring the Degree of Financial Market Efficiency. Finance India, Vol. 22, No. 4, December 2008, Available at SSRN: https://ssrn.com/abstract=1139920

Cornelis A. Los (Contact Author)

University of California at Irvine - The Paul Merage School of Business ( email )

SB1
Irvine, CA 92697-3125
United States

HOME PAGE: http://merage.uci.edu/research-faculty/faculty-directory/Cornelis-Los.html

EMEPS Associates ( email )

Escondido, CA 92029
United States
760-294-0255 (Phone)
858-635-4783 (Fax)

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