A comparison of the efficient and fractal market hypotheses in developing markets

Abstract

The validity and descriptive accuracy of the Capital Asset Pricing Model and the Fama- French Three-Factor Model are tested by describing the variation in excess portfolio returns on the Johannesburg Stock Exchange (JSE). Portfolios of stocks are constructed based on an adapted Fama & French (1993) approach, using a 3 × 2 annual sorting procedure and based on Size and Book-to-Market metrics, respectively. The sample period spans six years, 2010 to 2015, and includes 46 companies listed on the JSE. The results indicate that both models perform relatively poorly because of inadequate market proxy measures, market liquidity restrictions, unpriced risk factors and volatility inherent in an emerging market environment. The value premium is found to explain a larger proportion of variation in excess returns than the Size Premium and is more pronounced in portfolios with relatively higher book-to-market portfolios. The Efficient Market Hypothesis (EMH) has been repeatedly demonstrated to be an inferior − or at best incomplete − model of financial market behaviour. The Fractal Market Hypothesis (FMH) has been installed as a viable alternative to the EMH. The FMH asserts that markets are stabilised by matching demand and supply of investors' investment horizons while the EMH assumes the market is at equilibrium. A quantity known as the Hurst exponent determines whether a fractal time series evolves by random walk, a persistent trend or mean reversion. The time-dependence of this quantity is explored for two developed market indices and one emerging market index. Another quantity, intrinsically linked to the Hurst exponent, the fractal dimension of a time series, provides an indicator for the onset of chaos when market participants behave in the same way and breach a given threshold. A causal relationship is found between these quantities: the larger the change in the fractal dimension before breaching, the larger the rally in the price index after the breach. In addition, breaches are found to occur principally during times when the market is trending.