Bridge over ocean
1 July 1989 Financial Analysts Journal Volume 45, Issue 4

Fractal Structure in the Capital Markets

  1. Edgar E. Peters

The much-touted randomness of stock and bond market returns masks an underlying fractal structure. That is, there are patterns, or trends, in capital market returns, and they persist over time and over time scales. Return behavior in one six-month period influences subsequent six-month periods; one 10-year period influences subsequent 10-year periods.

These patterns are revealed by rescaled range (R/S) analysis—a technique frequently applied to natural phenomena to detect any biases in behavior over time. When applied to stock, bond and relative stock/bond returns over the period from January 1950 through June 1988, R/S analysis reveals that capital market returns follow a biased random walk. That is, they tend to trend in one direction—until some exogenous event occurs to change their bias.

In particular, 16.8 per cent of stock returns, 21.5 per cent of bond returns and 24.5 per cent of relative stock/bond returns are influenced by the past. The level of persistence in the stock and bond markets indicates the presence of considerable “white noise,” which will make attempts to forecast these markets over the long term difficult (but not impossible). The higher persistence in relative stock/bond returns suggests that the relation between these two markets may at some time in the future be able to be modeled on the basis of non-linear dynamic systems.

The correlations derived from R/S analysis may be taken as a measure of the impact of market sentiment (generated by past events) upon future returns. They indicate that investors’ interpretation of events is not reflected immediately in price, as the Efficient Market Hypothesis suggests. Instead, it manifests itself as a bias in returns, one that persists for decades.

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