Trend Momentum II: Driving Forces of Low Volatility and Momentum

Abstract

In discussions and critiques on the validity of the Efficient Market Hypothesis, there are two important research focuses: statistical analyses showing that the basic assumption of statistical independence in price series is violated and empirical findings that show that significant market anomalies exist. In this paper, we combine both viewpoints by analyzing two important mathematical factor anomalies: low volatility and momentum. By applying an explicit trend model, we show that both anomalies require trending. Additionally, we show that the trend model exhibits lognormal trend characteristics. Furthermore, the model allows us to describe how low volatility uses implicitly asymmetric trend characteristics while momentum directly exploits trends. Using Mandelbrot’s model of fractional Brownian Motions, we can finally link statistical analyses (measuring the Hurst exponent and persistence in returns) to the empirically observed momentum factor. Experimentally, the Hurst exponent in itself allows for a momentum strategy, and can be utilized to significantly improve low volatility strategies. In contrast to Mandelbrot’s approach, we offer a non-stationary view that allows us to describe both investment strategies using the trend model.

Fractal Markets, Frontiers, and Factors

“…As such, and consistent with fractional Brownian motions, the deviations can become stronger if the scale widens. In fact, fractional Brownian motions imply inefficient markets on longer-term scales and enable momentum (according to Berghorn (2015) and Berghorn et. al.…”

“…To simulate realistic portfolios, we also subtract 0.1% of the whole volume to anticipate trading costs on a monthly basis. To harmonize with Berghorn et al (2021), we will use 10% deciles, i.e., 110 out of 1,100 assets, to evaluate the factor performance.…”

“…According to Berghorn and Otto (2018) and Berghorn et al (2021), the low volatility factor is a side of the same coin when compared to momentum. It has been shown that the volatility of returns of the last trend seen under smoothing with scale a generates similar performance characteristics compared to the original factor.…”