An empirical analysis of the downside risk-return trade-off at daily frequency

a r t i c l e i n f o Keywords: Risk-return tradeoff Downside-risk MIDAS regressions HAR model Intraday data This paper considers the downside-risk aversion of investors as an explanation for the risk-return trade-off. We test empirically this hypothesis using intraday data along with the recent measure of downside-risk called realized semivariance developed in Barndorff-Nielsen et al. (2010). The empirical analysis over the period 1996–2008 provides evidence of a significant relation between semivariance and excess returns at the daily frequency. To gain better understanding of the relation between returns and downside-risk, we investigate the statistical relation between a new measure of conditional asymmetry, namely the ratio of the downside realized semivariance over the variance, and obtain a revealing pattern using a rolling window framework able to link asymmetry in the distribution to future returns. In particular, the asymmetry measure becomes significant when the past realized variance is not significant any more thereby providing insights about a possible change in the behavior of investors. The risk-return trade-off is one of the most pressing question in financial economics. Ghysels et al. (2005) even coin it as the " first fundamental law in finance ". This is also one of the main puzzles in finance. The puzzle arises from the fact that the ICAPM is not supported empirically. For instance, French et al. (1987) using the data from 1920 to 1984 do not provide evidence of a statistically significant relation between risk and returns. Recently, it has been suggested that the relation may only exist in the (very)-long term (Lundblad, 2007; Bandi and Perron, 2008, etc.). Conversely, Bali and Peng (2006) have shown that it could exist in the (very)-short term, namely at the daily level. In this paper, we examine the predictive power of the semivariance esti-mator for future returns. We show that this estimator allows to establish a robust relation between (downside-)risk and return in the short run. We thus show that investors' downside-risk aversion may partly explain the empirical puzzle and confirm this finding using a new measure of asymmetry for the distribution of returns. The problem of the empirical non-recovering of a significant relation for the theoretical ICAPM may have different sources: (i) the inadequacy of the ICAPM itself, (ii) risk preferences of agents who may not only be risk-averse but also exhibit preferences towards higher moments and/or (iii) the inaccuracy of the volatility proxy and the …