The Risk–Return Nexus: Risk Aversion v Power and Proxy Bias
37 Pages Posted: 20 Nov 2018
Date Written: November 20, 2018
Whether high sentiment among investors is associated with lower risk aversion (Yu and Yuan ) is not so clear. First, in regressions of returns on a proxy for variance, high sentiment comes with a relatively larger noise-to-signal ratio (lower power) and a bigger errors-in-the-regressor problem (attenuation bias). Second, when we add the change of risk as a regressor (following French, Schwert, and Stambaugh ), the ‘indirect evidence’ of risk aversion contradicts the direct one. Worse, the results are also non-robust over time: going from the original Baker-Wurgler period (-2010) to the updated one (-2015), we find that the high sentiment is no longer associated with a lower risk-aversion estimate, whether direct or indirect. Even the calculated impact of the power and bias issues differs substantially across these two samples.
These issues arise because the realised returns used to detect the variation in the CAPM-style expected return are high-noise. For a cleaner answer we propose to focus exclusively on the indirect evidence, the effect of a change in risk on the unexpected return. So we start not from the CAPM but from a Taylor expansion of the stock’s price, which induces as regressors the changes in variance, expected earnings, the risk-free rate, and longer-term earnings growth. The coefficient of the change of risk implies a plausible level RRA. In the original sample, risk sensitivity does look less negative when sentiment is high, but this seems to reflect a lower and shorter-lived predictive power of the proxy conditional on high sentiment; we do not need lower risk aversion to explain this, in short. In fact, the implied point estimate of RRA for high sentiment is higher, not lower. In the updated sample, risk sensitivity likewise appears to be higher when sentiment is positive.
Keywords: Investor Sentiment, midas, Risk aversion estimation, errors in variables, power of CAPM tests
JEL Classification: G12, G14, G17
Suggested Citation: Suggested Citation