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

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.