Relationship between Downside Risk and Return: New Evidence through a Multiscaling Approach

Abstract

In the multiscaling approach a time series is decomposed into different time horizons referred to as timescales. In this paper 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.