The VIX, the Variance Premium, and Expected Returns*

Abstract

Existing studies find conflicting estimates of the risk–return relation. We show that the trade-off parameter is inconsistently estimated when observed or estimated conditional variances measure risk. The inconsistency arises from misspecified, unbalanced, and endogenous return regressions. These problems are eliminated if risk is captured by the variance premium (VP) instead; it is unobservable, however. We propose a 2SLS estimator that produces consistent estimates without observing the VP. Using this method, we find a positive risk–return trade-off and long-run return predictability. Our approach outperforms commonly used risk–return estimation methods, and reveals a significant link between the VP and economic uncertainty.

Testing for Parameter Instability and Structural Change in Persistent Predictive Regressions

“…In particular, Bandi & Perron (2006), Christensen & Nielsen (2006), Nielsen (2007), Kellard, Dunis & Sarantis (2010) and Nielsen & Frederiksen (2011) provide solid support for these hypotheses. In addition, Bollerslev, Sizova & Tauchen (2011) and Bollerslev, Osterrieder, Sizova & Tauchen (2013), Osterrieder, Ventosa-Santaularia & Vera-Valdes (2019, Li, Izzeldin & Yao (2020) confirm the findings of fractional cointegration and proceed to exploit the equilibrium relation between IV and RV to estimate (components of) the volatility risk premium and forecast asset returns.…”

“…Specifically, most studies measure the volatility risk premium as VRP t = IV t −RV t . Other studies estimate the corresponding cointegrating relation between IV t and RV t to more accurately recover the "long-run" component of the volatility risk premium; see, e.g., ), Bollerslev et al (2013), Osterrieder et al (2019 and Li et al (2020). 14 Our rejection of stability of the cointegration models for RV, thus, suggest that such measures may convey different information across predictive regimes.…”

“…These studies take advantage of the differing persistence among the VIX t components and use NBLS-type estimators to identify the accuracy of the most persistent component. By the same logic, , Bollerslev et al (2013), Osterrieder et al (2019 and Li et al (2020) specify fractional cointegration models between IV and RV to estimate the volatility risk premium component associated with this long-run equilibrium and use it to forecast asset returns.…”

Long-Lasting Economic Effects of Pandemics:Evidence on Growth and Unemployment

“…For instance, Gil-Alana and Robinson (1997) analyze whether the macroeconomic variables involved in the original database of Nelson and Plosser (1982), GDP and unemployment among them, have long memory. Moreover, they have been used to model asset returns, exchange rates, and electricity prices; a few recent examples can be found in Varneskov and Perron (2018), Osterrieder et al (2019), and Ergemen et al (2016).…”

Long-Lasting Economic Effects of Pandemics: Evidence on Growth and Unemployment

“…For instance, (Gil-Alana and Robinson 1997) analyze whether the macroeconomic variables involved in the original database of (Nelson and Plosser 1982), GDP and unemployment among them, have long memory. Moreover, they have been used to model asset returns, exchange rates, and electricity prices; a few recent examples can be found in (Varneskov and Perron 2018), (Osterrieder et al 2019), and (Ergemen et al 2016).…”