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Modelling the Absolute Returns of Different Stock Indices: Exploring the Forecastability of an Alternative Measure of Risk

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Author Info
Clive Granger (University of California, San Diego)
Chor-yiu Sin (Xiamen University)

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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 95-th quantiles, can be interpreted as "volatility of volatility". We apply both models to three stock indices, namely Hang Seng Index, Nikkei 225 Index and 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

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Publisher Info
Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 1999-12.

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Date of creation: 01 Jun 1999
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Handle: RePEc:cdl:ucsdec:1999-12

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Related research
Keywords: absolute returns; asymmetric least squares; log-likelihood; return; risk; volatility;

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References listed on IDEAS
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  1. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-96, June. [Downloadable!] (restricted)
  2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  3. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  4. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Helinä Laakkonen, 2007. "The Impact of Macroeconomic News on Exchange Rate Volatility," Finnish Economic Papers, Finnish Economic Association, vol. 20(1), pages 23-40, Spring. [Downloadable!]
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  2. Jeannette H.C. Woerner, 2002. "Variational Sums and Power Variation: a unifying approach to model selection and estimation in semimartingale models," OFRC Working Papers Series 2002mf05, Oxford Financial Research Centre. [Downloadable!]
  3. De Arce Borda, R., 2004. "20 años de modelos ARCH: una visión de conjunto de las distintas variantes de la familia/20 Years of Arch Modelling: a Survey of Different Models in the Family," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 22, pages 27, Abril. [Downloadable!] (restricted)
  4. Jeannette H.C. Woerner, 2003. "Estimation of Integrated Volatility in Stochastic Volatility Models," OFRC Working Papers Series 2003mf05, Oxford Financial Research Centre. [Downloadable!]
  5. DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics 0660, Faculty of Economics, University of Cambridge. [Downloadable!]
    Other versions:
  6. Laakkonen, Helinä, 2007. "Exchange rate volatility, macro announcements and the choice of intraday seasonality filtering method," Research Discussion Papers 23/2007, Bank of Finland. [Downloadable!]
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