The Risk Return Relationship: Evidence from Index Returns and Realised Variances

Abstract

This paper provides new evidence on the risk return relationship by jointly analysing index return and realised variance (RV) series. It is argued that the contemporaneous correlation (CC) between the return and RV, which has been largely overlooked in the literature, is a crucial component in the empirical risk return relationship. Based on daily and weekly time series from 21 international market indices, the findings support the predictions of the risk premium, volatility feedback and statistical balance. However, little support is found for the short-memory-volatility-component risk premium. It is argued that the empirical risk return relationship is primarily shaped by the CC and the vastly-different autocorrelation structures of the return and RV.

Keywords: risk premium, volatility feedback, return predictability, statistical balance, normal variance-mean mixture, realised variance model

JEL Classification: C32, G10, G13