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Jumps in Rank and Expected Returns. Introducing Varying Cross-sectional Risk

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  • Santosh Mishra
  • Gloria Gonzalez-Rivera
  • Tae-Hwy Lee

Abstract

Decision theorists claim that an ordinal measure of risk may be sufficient for an agent to make a rational choice under uncertainty. We propose a measure of financial risk, namely the Varying Cross-sectional Risk (VCR), that is based on a ranking of returns. VCR is defined as the probability of a sharp jump over time in the position of an asset return within the cross-sectional return distribution of the assets that constitute the market, which is represented by the Standard and Poor's 500 Index (SP500). We model the joint dynamics of the cross-sectional position and the asset return by analyzing (1) the marginal probability distribution of a sharp jump in the cross-sectional position within the context of a duration model, and (2) the probability distribution of the asset return conditional on a jump, for which we specify different return dynamics depending upon whether or not a jump has taken place. As a result, the marginal probability distribution of returns is a mixture of distributions. The performance of our model is assessed in an out-of-sample exercise. We design a set of trading rules that are evaluated according to their profitability and riskiness. A trading rule based on our VCR model is dominant providing superior mean trading returns and accurate estimation of the Value-at-Risk.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 356.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:356

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Keywords: Duration; Mixture of distributions; Nonlinearity; Reality check; Trading rule; VaR;

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  1. repec:att:wimass:9417 is not listed on IDEAS
  2. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
  3. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  4. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
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  6. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  7. Ravi Jagannathan & Zhenyu Wang, 1996. "The conditional CAPM and the cross-section of expected returns," Staff Report 208, Federal Reserve Bank of Minneapolis.
  8. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  10. Narasimhan Jegadeesh, 2002. "Cross-Sectional and Time-Series Determinants of Momentum Returns," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 143-157, March.
  11. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  12. Clive W. J. Granger, 2002. "Some comments on risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 447-456.
  13. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
  14. Narasimhan Jegadeesh, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, 04.
  15. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
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