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Time Aggregation, Autocorrelation, and Systematic Risk Estimates–Additive versus Multiplicative Assumptions

Published online by Cambridge University Press:  06 April 2009

Son-Nan Chen
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Extract

The problems associated with the investment horizon and systematic risk estimation have been investigated in some detail. Jensen [7] has shown that investment horizon has some impact on the estimated systematic risk; Cheng and Deets [1] have raised some questions about Jensen's instantaneous systematic risk estimation method; Lee [9] has derived the relationship between the estimated instantaneous systematic risk and the estimated finite systematic risk; Levhari and Levy [11] have shown that there exist some relationships between the magnitude of estimated systematic risk and the length of investment horizon; based upon Zellner and Montimarquette's [19] time aggregation technique, Lee and Morimune [10] have shown that the investment horizon problem can be treated either as a time aggregation problem or as a specification problem. However, systematic risk estimates in terms of additive and multiplicative rates of return have not been investigated in detail. The purpose of this paper is to employ the time aggregation technique proposed by Zellner and Montimarquette [19] to investigate the impact of time aggregation on systematic risk associated with the market model. It is shown that autocorrelation and variation in market rates of return are two important factors in determining the magnitude of the estimated systematic risk associated with additive as well as multiplicative models.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 15 , Issue 1 , March 1980 , pp. 151 - 174
Copyright
Copyright © School of Business Administration, University of Washington 1980

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References

REFERENCES

[1]Cheng, P. L., and Deets, M. K.. “Systematic Risk and the Horizon Problem.” Journal of Financial and Quantitative Analysis, Vol. 8 (1973), pp. 299–316.CrossRefGoogle Scholar
[2]Box, G., and Jenkins, G.. Time Series Analysis, 2nd ed.Holden-Day, Inc. (1976).Google Scholar
[3]Dimson, E. “Dependencies in Stock Market Indices.” Presented at the Third Congress on Financial Theory and Decision Models, Garmisch-Parten-Kirchen (06 1974).Google Scholar
[4]Fama, E.; Fisher, L.; Jensen, M.; and Roll, R.. “The Adjustment of Stock Prices to New Information.” International Economic Review, Vol. 10 (1969), PP. 1–21.CrossRefGoogle Scholar
[5]Fisher, L. “Some New Stock Market Indexes.” Journal of Business (01 1966), pp. 191–225.CrossRefGoogle Scholar
[6]Griliches, Z. “Discussion on the paper by R. F. Engle and T. C. Liu.” In Econometric Models of Cyclical Behaviors, Vol. 2 (1972), pp. 733–737.Google Scholar
[7]Jensen, M. C. “Risk, the Pricing of Capital Assets and the Evaluation of Investment Portfolio.” Journal of Business, Vol. 42 (1969), pp. 167–247.Google Scholar
[8]Kmenta, J.Elements of Econometrics. New York: Macmillan Publishing Co., Inc. (1971).Google Scholar
[9]Lee, Cheng F. “On the Relationship between the Systematic Risk and the Investment Horizon.” Journal of Financial and Quantitative Analysis (1976), pp. 803–815.CrossRefGoogle Scholar
[10]Lee, Cheng F., and Morimune, K.. “Time Aggregation, Coefficient of Determination and Systematic Risk of the Market Model.” The Financial Review (Spring 1978), pp. 36–47.Google Scholar
[11]Levhari, D., and Levy, H.. “The Capital Asset Pricing Model and the Investment Horizon.” The Review of Economics and Statistics, Vol. 49 (1977), pp. 92–104.CrossRefGoogle Scholar
[12][Levy, H. “Portfolio Performance and Investment Horizon.” Management Science (08 1972), pp. 645–653.Google Scholar
[13]Levy, H.. “Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio.” American Economic Review, Vol. 68 (09 1978), pp. 643–658.Google Scholar
[14]Pogue, G. A., and Solnik, B. H.. “The Market Model Applied to European Common Stock: Some Empirical Results.” Journal of Financial and Quantitative Analysis, Vol. 9 (1974), pp. 917–944.Google Scholar
[15]Schwartz, R. A., and Whitcomb, D. K.. “The Time-Variance Relationship: Evidence on Autocorrelation in Common Stock Returns.” Journal of Finance, Vol. 32 (1977), pp. 41–55.Google Scholar
[16]Schwartz, R. A.. “Evidence on the Presence and Causes of Serial Correlation in Market Model Residuals.” Journal of Financial and Quantitative Analysis (06 1977), pp. 291–311.Google Scholar
[17]Tiao, G. C., and Wei, W. S.. “Effect of Temporal Aggregation on the Dynamic Relationship of Two Time Series Variables.” Biometrika, Vol. 63 (1976).CrossRefGoogle Scholar
[18]Working, H. “The Investigation of Economic Expectations.” American Economic Review (05 1949).Google Scholar
[19]Zellner, A., and Montimarquette, C.. “A Study of Some Aspects of Temporal Aggregation Problem in Economic Analysis.” The Review of Economics and Statistics, Vol. 53 (1971), pp. 335–342.Google Scholar