Testing for Longer Horizon Predictability of Return Volatility with an Application to the German

Volatility of financial returns as a measure of risk is a key parameter in asset pricing and risk management and holding periods for financial instruments of several weeks or month are common. Nevertheless, little is known about the predictability of return volatility at longer horizons. This paper investigates the predictability of return volatility of the German DAX for forecasting horizons from one day to 45 days with a new model-free test procedure that avoids joint assessments of predictability and assumed volatility models. In Monte Carlo simulatiost is compared with two alternative model-free test procedures. The simulations indicate that the new test has good statistical properties and is more powerful then the other two tests if the distribution of returns is fat tailed. Contrary to earlier findings according to which the return volatility of the DAX is only predictable for 10 to 15 trading days, the empirical evidence provided in this study suggests that the volatility of DAX returns is predictable for horizons of up to 35 trading days and may be forecastable at even longer horizons.