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Temporal Aggregation and Risk-Return Relation

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  • Xing Jin

    (University of Warwick, Singapore Management University)

  • LepingWang
  • JunYu
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    Abstract

    The function form of a linear intertemporal relation between risk and return is suggested by Mertons (1973) analytical work for instantaneous returns, whereas empirical studies have examined the nature of this relation using temporally aggregated data, i.e., daily, monthly, quarterly, or even yearly returns. Our paper carefully examines the temporal aggregation effect on the validity of the linear specification of the risk-return relation at discrete horizons, and on its implications on the reliablility of the resulting inference about the risk-return relation based on different observation intervals. Surprisingly, we show that, based on the standard Hestons (1993) dynamics, the linear relation between risk and return will not be distorted by the temporal aggregation at all. Neither will the sign of this relation be flipped by the temporal aggregation, even at the yearly horizon. This finding excludes the temporal aggregation issue as a potential source for the conflicting empirical evidence about the risk-return relation in the earlier studies.

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    Bibliographic Info

    Paper provided by East Asian Bureau of Economic Research in its series Finance Working Papers with number 21917.

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    Date of creation: Jan 2007
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    Handle: RePEc:eab:financ:21917

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    1. Hui Guo & Robert Whitelaw, 2005. "Uncovering the risk-return relation in the stock market," Working Papers 2001-001, Federal Reserve Bank of St. Louis.
    2. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    3. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
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    8. Andrew B. Abel, 1988. "Stock Prices Under Time-Varying Dividend Risk: An Exact Solution In An Infinite-Horizon General Equilibrium Model," NBER Working Papers 2621, National Bureau of Economic Research, Inc.
    9. Cartwright, Phillip A & Lee, Cheng F, 1987. "Time Aggregation and the Estimation of the Market Model: Empirical Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 131-43, January.
    10. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
    11. Campbell, John, 1987. "Stock Returns and the Term Structure," Scholarly Articles 3207699, Harvard University Department of Economics.
    12. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    13. Whitelaw, Robert F, 1994. " Time Variations and Covariations in the Expectation and Volatility of Stock Market Returns," Journal of Finance, American Finance Association, vol. 49(2), pages 515-41, June.
    14. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    15. Backus, David K & Gregory, Allan W, 1993. "Theoretical Relations between Risk Premiums and Conditional Variances," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 177-85, April.
    16. Bollerslev, Tim & Zhou, Hao, 2006. "Volatility puzzles: a simple framework for gauging return-volatility regressions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 123-150.
    17. Paul Harrison & Harold H. Zhang, 1999. "An Investigation Of The Risk And Return Relation At Long Horizons," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 399-408, August.
    18. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-36, January.
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