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Some Properties of Absolute Return, An Alternative Measure of Risk

UCSD Department of Economics Discussion Paper 93- 38

Posted: 26 Jan 1995  

Clive W. J. Granger

University of California, San Diego (UCSD) - Department of Economics; Tinbergen Institute

Zhuanxin Ding

University of California, San Diego (UCSD) - Department of Economics

Abstract

Let a(theta) represent the absolute value of the daily return (after subtraction of mean return) raised to the power theta, so that a(two) is just the return squared. Duncan Luce (Theory and Decision, 1980) using an axiomatic approach suggested that a(theta) was a suitable class of measures of risk, with theta as the choice of the individual. The empirical properties of these measures are investigated using daily S&P 500 index data for the period January 3, 1928 to August 30, 1991. It is found that: (i) correlation (a(theta, day t), a(theta, day t-k)) remains positive and significant for many lags k (up to two thousand) for most positive values of theta. (ii) this "long-memory" property is strongest for theta=1 compared to theta values both larger and smaller than one. (iii) if a few outliers are reduced, the marginal distribution of the absolute return has approximately an exponential distribution. Reasons for and implications of these results are explored.

JEL Classification: C00

Suggested Citation

Granger, Clive W. J. and Ding, Zhuanxin, Some Properties of Absolute Return, An Alternative Measure of Risk. UCSD Department of Economics Discussion Paper 93- 38. Available at SSRN: https://ssrn.com/abstract=5796

Clive W. J. Granger (Contact Author)

University of California, San Diego (UCSD) - Department of Economics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
858-534-3383 (Phone)
858-534-7040 (Fax)

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Zhuanxin Ding

University of California, San Diego (UCSD) - Department of Economics

9500 Gilman Drive
La Jolla, CA 92093-0508
United States

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