Relationship between downside risk and return: new evidence through a multiscaling approach

In the multiscaling approach, a time series is decomposed into different time horizons referred to as timescales. In this article, we investigate the risk–return relationship in a downside framework using timescales. Two measures of downside risk; downside beta and downside co-skewness are investigated. A sample of Australian industry portfolios does not reveal a positive linear relationship between downside beta and portfolio return. At a high timescale where dynamics over a longer horizon (32–64 days) is captured, a positive linear association between downside co-skewness and portfolio return is observed. Overall, our results suggest that when investigating the validity of asset pricing models whether in the downside framework or in the traditional mean-variance framework, it may be prudent to consider other horizons in addition to the usual daily and monthly frequencies.