Bollerslev, TimOsterrieder, DanielaSizova, NataliaTauchen, George2015-07-102015-07-102013Bollerslev, Tim, Osterrieder, Daniela, Sizova, Natalia, et al.. "Risk and return: Long-run relations, fractional cointegration, and return predictability." <i>Journal of Financial Economics,</i> 108, no. 2 (2013) Elsevier: 409-424. http://dx.doi.org/10.1016/j.jfineco.2013.01.002.https://hdl.handle.net/1911/80887Univariate dependencies in market volatility, both objective and risk neutral, are best described by long-memory fractionally integrated processes. Meanwhile, the ex post difference, or the variance swap payoff reflecting the reward for bearing volatility risk, displays far less persistent dynamics. Using intraday data for the Standard & Poor's 500 and the volatility index (VIX), coupled with frequency domain methods, we separate the series into various components. We find that the coherence between volatility and the volatility-risk reward is the strongest at long-run frequencies. Our results are consistent with generalized long-run risk models and help explain why classical efforts of establishing a naïve return-volatility relation fail. We also estimate a fractionally cointegrated vector autoregression (CFVAR). The model-implied long-run equilibrium relation between the two variance variables results in nontrivial return predictability over interdaily and monthly horizons, supporting the idea that the cointegrating relation between the two variance measures proxies for the economic uncertainty rewarded by the market.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.Journal articlehigh-frequency datarealized and options implied volatilitiesvolatility risk premiumlong-memory and fractional cointegrationreturn predictabilityhttp://dx.doi.org/10.1016/j.jfineco.2013.01.002