# Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation

## Author Info

• D. Sornette

(UCLA and CNRS-University of Nice)

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## Abstract

Firm foundation theory estimates a security's firm fundamental value based on four determinants: expected growth rate, expected dividend payout, the market interest rate and the degree of risk. In contrast, other views of decision-making in the stock market, using alternatives such as human psychology and behavior, bounded rationality, agent-based modeling and evolutionary game theory, expound that speculative and crowd behavior of investors may play a major role in shaping market prices. Here, we propose that the two views refer to two classes of companies connected through a phase transition''. Our theory is based on 1) the identification of the fundamental parity symmetry of prices ($p \to -p$), which results from the relative direction of payment flux compared to commodity flux and 2) the observation that a company's risk-adjusted growth rate discounted by the market interest rate behaves as a control parameter for the observable price. We find a critical value of this control parameter at which a spontaneous symmetry-breaking of prices occurs, leading to a spontaneous valuation in absence of earnings, similarly to the emergence of a spontaneous magnetization in Ising models in absence of a magnetic field. The low growth rate phase is described by the firm foundation theory while the large growth rate phase is the regime of speculation and crowd behavior. In practice, while large finite-time horizon'' effects round off the predicted singularities, our symmetry-breaking speculation theory accounts for the apparent over-pricing and the high volatility of fast growing companies on the stock markets.

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File URL: http://arxiv.org/pdf/cond-mat/0004001

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0004001.

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Publication status: Published in Physica A 284 (Nos. 104), 355-375 (2000)
Handle: RePEc:arx:papers:cond-mat/0004001

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Web page: http://arxiv.org/

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## References

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1. Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
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## Citations

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Cited by:
1. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.
2. Jaehyung Choi, 2012. "Physical approach to price momentum and its application to momentum strategy," Papers 1208.2775, arXiv.org, revised Sep 2012.
3. Pawe{\l} Sieczka & Didier Sornette & Janusz A. Ho{\l}yst, 2010. "The Lehman Brothers Effect and Bankruptcy Cascades," Papers 1002.1070, arXiv.org, revised Sep 2011.
4. Yukalov, V.I. & Sornette, D. & Yukalova, E.P., 2009. "Nonlinear dynamical model of regime switching between conventions and business cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 206-230, May.
5. Jaehyung Choi, 2011. "Spontaneous symmetry breaking of arbitrage," Papers 1107.5122, arXiv.org, revised Apr 2012.
6. D. Sornette, 2000. ""Slimming" of power law tails by increasing market returns," Papers cond-mat/0010112, arXiv.org, revised Sep 2001.
7. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.

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