Forecasting Realized Volatility of Daily Returns

Abstract

Despite the vast academic literature on modelling stochastic volatility, many finance practitioners still use the simple approach of J. P. Morgan (1997), based on the exponentially weighted moving average (EWMA) volatility combined with the $\sqrt{h}$-rule for scaling volatility with horizon. In this paper, we evaluate this approach using a universe of 47 liquid futures contracts, including equity index, currency, commodity, and bond futures. We find that the true slope (persistence) coefficients capturing the dependence between past and future realized volatility are {\it always strictly smaller than $\sqrt{h}$} for all 47 instruments, and experience large fluctuations over time; in particular, for almost all instruments in our sample slope coefficients spiked during the 2008 financial crisis. However, while for equity index futures slope coefficients returned to their pre-crisis level, this is not the case for all other four asset classes: after the crisis, slope coefficients stay well above their pre-crisis level. Exploiting predictability of these slope coefficients using rolling linear regressions significantly improves efficiency of realized volatility forecasting relative to the RiskMetrics benchmark. Our forecasting procedure is implementable in real time, and its performance is comparable (and sometimes even superior) to that of ARCH-type models over an interval of horizons, from 5 days to 2 months. As a practical application, we show that our volatility forecasts can be efficiently used for {\it managing risk of momentum strategies} and significantly reduce drawdowns.