Analysis of the five-factor asset pricing model with wavelet multiscaling approach

We study the relationship between average returns and risk factors through wavelet multiscaling approach which enables us to investigate the risk-return relationship based on different time scales. The data for the period July 1963–February 2018 are gathered from the Kenneth French website. Each time series in the dataset is decomposed into five time scales. In order to make a comparison, the five-factor model is estimated based on both the scale basis and raw data. There are several key implications from our estimation results: i) The effects of risk factors on average returns vary over the time scales by their coefficient magnitudes and statistical significance. ii) Gibbons, Ross, and Shanken (1989) test results show that the intercepts of scale basis models are close to zero. iii) There is a period of unexpectedly higher cash flow for big value portfolios for long-term investments. iv) There is a minimum (maximum) risk level for aggressive (conservative) portfolios at different time horizons. Finally, we identify the risk factors in our five-factor model that have a significant effect on returns, and our model can capture the variations in average returns for different investment horizons.