  In this article we discuss the distribution of asset price movements by the
market potential function. From the principle of free energy minimization we
analyze two different kinds of market potentials. We obtain a U-shaped
potential when market reversion (i.e. contrarian investors) is dominant. On the
other hand, if there are more trend followers, flat and logarithmic--like
potentials appeared. By using the Cyclical Adjusted Price-to-Earning ratio,
which is a common valuation tool, we empirically investigate the market data.
By studying long term data we observe the historical change of the market
potential of the US stock market. Recent US data shows that the market
potential looks more likely as the trending followers' potential. Next, we
compare the market potentials for 12 different countries. Though some countries
have similar market potentials, there are specific examples like Japan which
exhibits very flat potential.
