Time-varying tails and the tail risk premium

This paper considers the possibility that the tails of the excess return distribution may evolve over time and investigates the intertemporal risk-return relationship under time-varying tails. We employ the autoregressive conditional density model of Hansen (1994) to allow time-varying tails beyond dynamic dependence through the conditional mean and variance. The conditional density of the excess return is modeled by an asymmetric Student’s t distribution with tail parameters that rely on past information. Then, tail risk is measured using tail parameters and is considered a determinant of expected return, alongside conventional volatility risk. The model is applied to daily excess returns for seven portfolios worldwide. The empirical results suggest significant time-varying tails across all portfolios, and tail risk is an important determinant of expected return.