Trading in chaos : analysis of active management in a fractal market.

Abstract

Many Nobel Laureates and thousands of academic papers have espoused the concept that risk is compensated by return. However, the low volatility anomaly - the phenomenon where low-risk stocks display markedly higher returns than the market portfolio on a risk-adjusted basis and vice versa - contradicts this basic finance principle of risk-return trade-off and is possibly one of the greatest anomalies in finance. Among the explanations for this anomaly are, the behavioural bias of overconfidence, agency problems and the type of manager compensation. This study investigates and confirms the low volatility anomaly on the Johannesburg Stock Exchange (JSE) using the risk-adjusted return measure of the Sharpe ratio. According to the Efficient Market Hypothesis, this is not expected to happen and consequently offers no explanation for this phenomenon. This study applies the Fractal Market Hypothesis (FMH) formalised within the framework of Chaos Theory, to explain the existence of the low volatility anomaly on the JSE. Building upon the Fractal Market Hypothesis to provide evidence on the behaviour of returns time series of selected indices of the JSE, the BDS test is applied to test for non-random chaotic dynamics and further applies the rescaled range analysis to ascertain mean reversion, persistence or randomness on the JSE. The BDS test confirms that all the indices considered in this study are not independent and identically distributed. Applying the re-scaled range analysis, the FTSE/JSE Top 40 and the FTSE/JSE All Share Index appear relatively efficient and riskier than the FTSE/JSE Small Cap Index, which exhibits significant persistence and appears to be less risky and less efficient contrary to the popular assertion that small cap indices are riskier than large cap indices. The study further analyses the three fundamentals of the FMH namely, the impact of information, the role of liquidity and time horizon on the top 40 and small cap indices. Information is not uniformly distributed among the two indices as the FTSE/JSE Top 40 index receives more publications form sources such as newspapers, online publications and journals as well as JSE issued news and historical company news. The FTSE/JSE Top 40 also receives more analyst coverage than the FTSE/JSE Small Cap Index. Using the absolute and normalised volume of trade as a proxy for liquidity, the FTSE/JSE Top 40 index exhibits a relatively higher level of liquidity than the FTSE/JSE Small Cap index. The study finds that domestic equity fund managers in South Africa hold in their portfolios, a disproportionately greater percentage of FTSE/JSE Top 40 companies relative to other companies on the JSE and concludes that these managers contribute to the low volatility anomaly on the JSE. The study further concludes that in line with the FMH, lack of information and the illiquidity of the FTSE/JSE Small Cap attracts long-term investors who become the dominant class of investors on the index and are compensated for taking on the risk of illiquidity in the form of illiquidity premium and low volatility. The highly liquid FTSE/JSE Top 40, which has relatively high availability of information on the other hand attracts different classes of investors with differing horizons who take opposite sides of each trade as different classes of investors interpret the same set of information differently. The high liquidity and information leads to high volatility as investors continually adjust their holdings with the emergence of new information. The high volatility and subsequent underperformance of the FTSE/JSE Top 40 therefore is a cost of efficiency and liquidity (liquidity discount). Studies on the FMH are generally focused on market crashes. This study provides a novel approach by using the FMH to explain the low-volatility anomaly. This synthesis of the FMH and the low volatility anomaly provides an alternative technique of evaluating risk and also provides insights into the efficiency of financial markets and contributes to the literature on the FMH as well as the low volatility anomaly.