Fractal Markets, Frontiers, and Factors

Abstract

In this work we develop an alternative view to the modern finance theory that essentially suggests equilibria in efficient markets by taking a risk-based view of asset returns in stock markets. Based on a mathematical analysis of stock market data using multi-scale approaches, we will alternatively describe markets and factors as trend-based fractal processes and analyze well-known factor premiums, which leads to a return-based view of markets and a model of investors reacting to market environments. We conclude that markets could be viewed alternatively as fractal, non-stationary and, at most, asymptotically efficient.

Keywords: Momentum Effect, Low Volatility Effect, Value Effect, Size Effect, Efficient Market Theory, Mandelbrot, Fractional Brownian Motion, Fractal Markets

JEL Classification: G11, G12