Modelling the absolute returns of different stock indices: Exploring the forecastability of an alternative measure of risk

Conventional measures of the risk of a financial asset make use of the unob served (conditional) variance or standard deviation of its return. In this paper, we treat the observed absolute return as a measure of risk and explo re its forecastability. Two simple models an considered. One is a new AR-li ke model which is applied to the absolute return. The other is an ARCH-like model called Asymmetric Power ARCH. The forecastability is evaluated with the average log-likelihood of absolute return, instead of that of return it self. While the absolute return is interpreted as 'volatility', some quanti ties of its entire distribution, such as the 95th quantiles, can be interpr eted as 'volatility of volatility'. We apply both models to three stock ind ices, namely the Wang Seng Index, the Nikkei 225 Index and the Standard and Poors 500 Index. The new model by and large outperforms the ARCH-like mode l in both in-sample goodness of fit and post-sample forecastability. It per forms exceptionally well in the post-sample period after the outbreak of th e Asian financial crisis. Copyright (C) 2000 John Wiley Be Sons, Ltd.