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Temporal Aggregation and Risk-Return Relation

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Jun Yu () (School of Economics, Singapore Management University)

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Abstract

The function form of a linear intertemporal relation between risk and return is suggested by Merton’s (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 Heston’s (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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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 01-2007.

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Length: 16 pages
Date of creation: Mar 2006
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Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:01-2007

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  1. David K. Backus & Allan W. Gregory, 1992. "Theoretical Relations Between Risk Premiums and Conditional Variances," Working Papers 92-18a, New York University, Leonard N. Stern School of Business, Department of Economics.
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  2. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June. [Downloadable!] (restricted)
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  6. 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.
  7. 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. [Downloadable!] (restricted)
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  10. Brandt, Michael W. & Wang, Kevin Q., 2003. "Time-varying risk aversion and unexpected inflation," Journal of Monetary Economics, Elsevier, vol. 50(7), pages 1457-1498, October. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. 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.
  13. Hui Guo & Robert Whitelaw, 2005. "Uncovering the risk-return relation in the stock market," Working Papers 2001-001, Federal Reserve Bank of St. Louis. [Downloadable!]
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  14. 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. [Downloadable!]
  15. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December. [Downloadable!] (restricted)
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  16. Breen, William & Glosten, Lawrence R & Jagannathan, Ravi, 1989. " Economic Significance of Predictable Variations in Stock Index Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1177-89, December. [Downloadable!] (restricted)
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