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When various risk measures are computed, it is often assumed that the conditional mean of an asset return is constant. However, it is well documented that the predictability of returns increases as the horizon of prediction increases. This paper assesses the impact of ignoring such possible predictability of returns on computing risk measures, especially Value-at-Risk(VaR). For this purpose, we study the term structure of VaR when the conditional mean of returns is actually time-varying, and when one assumes it to be time-varying and constant. First we compute VaR analytically when one knows parameter values, and show that the impact of ignoring time-variability of the conditional mean is non-negligible. Simulation studies show that, when one has a parameter uncertainty, estimating a model with time-varying conditional mean yields VaR that is closer to the true VaR, even though a model with constant conditional mean is often times not statistically rejected. In the empirical studies, we estimate a GARCH-in-Mean model which has a time-varying conditional mean and a GARCH model with constant conditional mean. We compare their predictive ability by Diebold-Mariano test and show that the GARCH-in-Mean model outperforms GARCH model for horizons over 10 days.
