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

Clive W. J. Granger · Chor-yiu Sin

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Financial Risk and Volatility Modeling Forecasting Techniques and Applications Stock Market Forecasting Methods

Abstract

Conventional measures of the risk of a financial asset make use of the unobserved (conditional) variance or standard deviation of its return. In this paper, we treat the observed absolute return as a measure of risk and explore its forecastability. Two simple models are considered. One is a new AR-like 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 itself. While the absolute return is interpreted as ‘volatility’, some quantities of its entire distribution, such as the 95th quantiles, can be interpreted as ‘volatility of volatility’. We apply both models to three stock indices, namely the Hang Seng Index, the Nikkei 225 Index and the Standard and Poors 500 Index. The new model by and large outperforms the ARCH-like model in both in-sample goodness of fit and post-sample forecastability. It performs exceptionally well in the post-sample period after the outbreak of the Asian financial crisis. Copyright © 2000 John Wiley & Sons, Ltd.

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References

1998Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts 1993A long memory property of stock market returns and a new model 1998Evaluating Density Forecasts with Applications to Financial Risk Management 1994Chapter 49 Arch models 1994Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator 1996Consistency and Asymptotic Normality of the Quasi-Maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models 1976On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function 1995Some Properties of Absolute Return: An Alternative Measure of Risk

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