Abstract
This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple trading strategies, and their trades together determine the stock prices. Computer simulations show that a basic case of this model is already capable of generating price graphs which are visually similar to the recent price movements of high tech stocks. In the general model, we prove that if there are a large number of traders but they employ a relatively small number of strategies, then there is a polynomial-time algorithm for predicting future price movements with high accuracy. On the other hand, if the number of strategies is large, market prediction becomes complete for two new computational complexity classes CPP and promise-BCPP, where PNP[o(logn)] C BPPpath C promise-BCPP C CPP = PP. These computational hardness results open up a novel possibility that the price graph of an actual stock could be sufficiently deterministic for various prediction goals but appear random to all polynomial-time prediction algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P.B. Andreassen, S. Krause: J. Forecasting 9 347 (1990)
D. Applegate, R. Kannan: ‘Sampling and integration of near log-concave functions’. In Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, 1999,pp 156-163
P. Billingsley: Probability and Measure, 2nd ed. ( Wiley, New York 1986 )
F. Black: J. Finance 41 529 (1986)
J.-Y. Cai, L.A. Hemachandra, J. Vyskoc: ‘Promises and fault-tolerant database access’ In: Complexity Theory: Current Research,Ed. by: K. Ambos-Spies, S. Homer, U. Schöning (Cambridge University Press, Cambridge 1993) pp 101146
J.Y. Campbell, A.W. Lo, A.C. MacKinlay: The Econometrics of Financial Markets (Princeton University Press, Princeton 1997 )
R.G. Clarke, M. Statman: Financial Analysts Journal 54, 63 (1998)
P.A. Cootner: The Random Character of Stock Market Prices MIT Press, Cambridge 1964
R.H. Day, W.H. Huang: J. Econom. Behavior Org. 14, 299 (1990)
W. De Bondt: J. Portfolio Manag. 17, 84 (1991)
W. DeBondt: Int. J. Forecasting 9, 355 (1993)
J.B. DeLong, A. Shleifer, L.H. Summers, R.J. Waldmann: J. Pol. Econom. 98, 703 (1990)
S. Even, A. Selman, Y. Yacobi: Information and Control 61, 159 (1984)
S. Even, Y. Yacobi: ‘Cryptocomplexity and NP-completeness’ In Lecture Notes in Computer Science 85: Proceedings of the 7th International Colloquium on Automata, Languages, and Programming, Ed. by J.W. de Bakker, J. van Leeuwen ( Springer Verlag, New York 1980 ) pp 195 - 207
E. Fama: J. Finance 46, 1575 (1991)
L. Fortnow: Private communication, March 2001
Y. Han, L.A. Hemaspaandra, T. Thierauf: SIAM J. Computing 26, 59 (1997)
I. Karatzas, S.E. Shreve: Methods of Mathematical Finance Volume 39 of Applications of Mathematics ( Springer Verlag, New York 1998 )
A. Kumar: ‘Behavior of momentum following and contrarian market timers’ Working Paper 99-01, International Center for Finance, School of Management, Yale University, January 1999
A.W. Lo, A.C. MacKinlay: A Non-Random Walk Down Wall Street (Princeton University Press, Princeton 1999 )
T. Lux: J. Econom. Behavior Organ. 33, 143 (1998)
B.G. Malkiel: A Random Walk down Wall Street ( Norton, New York 1990 )
B.B. Mandelbrot: Fractals and Scaling in Finance ( Springer Verlag, New York 1997 )
S. Mullainathan: ‘A memory based model of bounded rationality’ Working paper, Department of Economics, MIT, April 1998
R. Sullivan, A Timmermann, H. White: J. Finance 54 1647 (1999)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Aspnes, J., Fischer, D.F., Fischer, M.J., Kao, MY., Kumar, A. (2004). Towards Understanding the Predictability of Stock Markets from the Perspective of Computational Complexity. In: Wille, L.T. (eds) New Directions in Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08968-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-08968-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07739-5
Online ISBN: 978-3-662-08968-2
eBook Packages: Springer Book Archive