  The study of long-horizon returns has received a great deal of attention in
recent years (see, for example, Boudoukh, Richardson, and Whitelaw (2008),
Neuberger (2012) and Lee (2013), Fama and French (2018)). While most of the
discussions are concerned with some practical issues in investment, few have
touched the important aspect on risk management. The approach adopted in this
article is to predict the future distribution of the returns of a fixed
long-horizon by which the risk measures of interest that come in the form of a
distributional functional such as the value at risk (VaR) and the conditional
tail expectation (CTE) can be easily derived. The characteristic feature of our
approach which requires no specification of the volatility dynamics nor
parametric assumptions of the shock distribution extends the work by Ho et al.
(2016) and Ho ( 2017) to a more general volatility dynamics that includes both
the widely-used SV model and the GARCH model (Bollerslev, 1986) as special
cases.
