Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractWe explore the cross-sectional pricing of volatility risk by decomposing equity market volatility into short-and long-run components. Our finding that prices of risk are negative and significant for both volatility components implies that investors pay for insurance against increases in volatility, even if those increases have little persistence. The short-run component captures market skewness risk, which we interpret as a measure of the tightness of financial constraints. The long-run component relates closely to business cycle risk. Furthermore, a three-factor pricing model with the market return and the two volatility components compares favorably to benchmark models. 1When market volatility is stochastic, intertemporal models predict that asset risk premia are not only determined by covariation of returns with the market return, but also covariation with the state variables that govern market volatility. To study this prediction, we model the log-volatility of the market portfolio as the sum of a short-and a long-run volatility component. This approach parsimoniously captures shocks to systematic risk at different horizons.Market volatility is a significant cross sectional asset pricing factor as shown by Ang et al. (2006).1 Their two-factor model with the market return and market volatility does reduce pricing errors compared to the capital asset pricing model (CAPM), though not by as much as the Fama-French model. In contrast, our benchmark asset pricing model with the market return and the two volatility components as cross sectional pricing factors achieves lower pricing errors than the Fama and French (1993) model for size and book-to-market sorted portfolios. Our finding that the short-and long-run volatility components have negative, highly significant prices of risk is robust across sets of portfolios, sub-periods, and volatility model specifications.Consistent with previous research, we also find that the average compensation for volatility risk is positive. This is because the prices of risk of both volatility components are negative, and average sensitivities to the volatility components are also negative. Our two-factor decomposition shows that the average risk premium for short-run volatility is 0.17% monthly versus 0.23% monthly for long-run volatility.Across individual portfolios, we see a wide dispersion in sensitivity to the volatility components, which generates cross sectional varia...

CAPM, Components of Beta and the Cross Section of Expected Returns

“…These results suggest that the impact of the business cycle on asset returns in our three component beta model is primarily captured through the medium-and long-run beta components. This is in line with Adrian and Rosenberg (2008) who also find that the business cycle is correlated with a long-run component of risk in their factor pricing model containing a short-and long-run volatility component. Overall, these results suggest that the more immediate changes in risk such as changes in portfolio characteristics are captured in the short-run beta component while the medium-and long-run beta components capture more slowly changing risk which we find to be correlated with the business cycle.…”

“…2 As we discuss below, we also take a closer look at the pricing errors for individual assets, which allow us to analyze which assets are mispriced across different models. The second and third metrics are the sum of square pricing errors (SSPE) and root mean square pricing errors (RMSPE) (see Adrian and Rosenberg (2008)):…”

An analytical review of volatility metrics for bubbles and crashes

“…Importantly, however, Bollerslev et al (2014) and (2009) Indeed, Bollerslev and Zhou (2006) showed that the volatility series "exhibit pronounced own temporal dependencies" and Adrian and Rosenberg (2008) showed that investors require compensation when holding assets that depreciate as volatility rises. 4…”

What is beneath the surface? Option pricing with multifrequency latent states

“…3 However, 1 See, for example, Garcia et al (2009), Jones (2003), Li and Zhang (2013), and the literature cited therein. 2 See also Adrian and Rosenberg (2008), Bates (2000Bates ( , 2012, Campbell et al (2012), Chernov et al (2003), Christoffersen et al (2009), Christoffersen, Dorion, Jacobs andWang (2010), Egloff et al (2010), and Lux and Kaizoji (2007).…”