  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.
