Chaos theory has received considerable attention in the aftermath of the Crash of 1987. However, an alternative non-linear statistical model is far more useful for understanding both the coherent bull market prior to the crash and the subsequent chaotic market fluctuations in October 1987. Unlike chaos theory, which seeks to forecast the path of stock prices in a deterministic sense, the non-linear statistical model, based on “A Theory of Social Imitation,” can forecast transitions from trendless (random-walk) markets to periods of coherent, or orderly, price trends and periods of chaotic fluctuations (the panics and crashes associated with abrupt trend reversals).

A coherent bull market is characterized by an “inversion” in the historical risk-reward ratio. Over the past 60 years, the stock market has provided an average 10 per cent total yearly return, with a standard deviation of 20 per cent. During coherent bull markets, the return from the stock market averages over 25 per cent, while the standard deviation drops to the neighborhood of 10 per cent. Missing these low-risk opportunities can lead to underperformance, because the rest of the time the market presents more risk than reward, in the form of chaotic markets and periods of true random walk.

This article describes the theoretical basis and practical indicators of coherent markets. The results suggest that both technical and fundamental analysis can add real value to the investment decision-making process.