An Unfair Coin of the Standard & Poor’s 500

Abstract

Based on the available data, we reconstructed a discrete model of S&P 500 stock market phase space and assessed predictability of market events as well as the amounts of predictable and unpredictable information in the historical data over the different time horizons. Inhomogeneous density of states in S&P 500 phase space leads to inequitable predictability of market events. In line with Mean Reversion theory, the frequent events are predicted better than the extreme, rare events, such as the market crashes. Stocks have different mobility in S&P 500 phase space. Highly mobile stocks are associated with less unsystematic risk, and vice versa, as less mobile stocks might be cast into disfavor almost indefinitely. Relations between the predictable and unpredictable information components calculated for the transitions between states in S&P 500 phase space resemble of those in unfair coin tossing.