The Non-Random Walk of Stock Prices: The Long-Term Correlation between Signs and Sizes

9 Pages Posted: 29 Nov 2007 Last revised: 16 Jun 2008

See all articles by Gabriele La Spada

Gabriele La Spada

Federal Reserve Banks - Federal Reserve Bank of New York

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

Fabrizio Lillo

Università di Bologna

Date Written: June 15, 2008

Abstract

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.

Keywords: Econophysics, Brownian motion, Stochastic processes

Suggested Citation

La Spada, Gabriele and Farmer, J. Doyne and Lillo, Fabrizio, The Non-Random Walk of Stock Prices: The Long-Term Correlation between Signs and Sizes (June 15, 2008). Available at SSRN: https://ssrn.com/abstract=1033176 or http://dx.doi.org/10.2139/ssrn.1033176

Gabriele La Spada (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States
212-720-5164 (Phone)

HOME PAGE: http://https://www.newyorkfed.org/research/economists/laspada

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

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