Tail risk premia and return predictability

Abstract

JEL classification: C13 C14 G10 G12 Keywords:Variance risk premium Time-varying jump tails Market sentiment and fears Return predictability a b s t r a c tThe variance risk premium, defined as the difference between the actual and risk-neutral expectations of the forward aggregate market variation, helps predict future market returns. Relying on a new essentially model-free estimation procedure, we show that much of this predictability may be attributed to time variation in the part of the variance risk premium associated with the special compensation demanded by investors for bearing jump tail risk, consistent with the idea that market fears play an important role in understanding the return predictability.

Comments on: Nonparametric Tail Risk, Stock Returns and the Macroeconomy

“…and similar measures of implied market tail risk (e.g., Bollerslev et al 2015), as well as from model-free proxies of implied market volatility, such as V IX m,t . Therefore, we expect an imperfect empirical comovement of T RM t,h , T RM m,t,h , and V IX m,t , e.g., in presence of stochastic return correlations or a time-varying conditional return nonnormality.…”

International Tail Risk and World Fear

“…Using deep-out-of-the-money and short maturity options of the S&P 500 index, Bollerslev et al (2015) decompose the variance risk premium into a premium for diffusive and a premium for large movements referred to as jump tail variation or fear. Cremers et al (2015) use at-the-money S&P 500 straddles to capture jump and volatility risk portfolios.…”

“…Recent literature finds for the U.S. that high (low) tail risk is associated with relatively high (low) market returns in the future (see, e.g., Kelly & Jiang (2014), Bollerslev et al (2014) and Bollerslev et al (2015)). We test whether this finding holds outside of the U.S.…”

The Probability of Rare Disasters: Estimation and Implications

“…The risk-neutral 3 Other evidence of tail risk being priced in the cross section of equities can be found in Kelly and Jiang (2014), who rely on extreme value theory to learn about the tails of asset prices from realized stock returns (not options). Bollerslev, Todorov, and Xu (2015) also use options to relate jump risk to stock returns. They use S&P 500 options to parametrize option-implied tails and find that their estimated jump risk premia forecast future stock returns.…”