Security behavior in bull and bear markets has received some attention in recent years. Fabozzi and Francis [5] first documented evidence that security betas are not influenced by the alternating forces of bull and bear markets. Their subsequent study of mutual fund betas also indicated that mutual funds generally respond indifferently to bull and bear market conditions. Using the concept of bull and bear market variations, Kim and Zumwa1t [9] developed and tested the risk premiums associated with the upside and the downside portions of returns variation. They concluded that investors expect to receive a risk premium for downside risk and pay a premium for upside variation of returns. From their results, Kim and Zumwalt [9] suggested that the down-market beta measuring downside risk (downside variation of returns) may be a more appropriate measure of portfolio risk than the single beta in the market model.

Over the past years the beta coefficient has been widely used as a measure of systematic risk in investment and portfolio analysis. The validity of using the beta coefficient as the proper measure of systematic risk is dependent upon the assumption that the beta coefficient is stationary over time. Unfortunately, this assumption has been challenged by a number of empirical studies which have found the beta coefficient to be unstable over time. Examples of such empirical investigations are those documented by Blume [4], Levy [12], Levitz [11], Baesel [2], Altman, Jacquillat, and Levasseur [1], and Roenfelt, Griepentrong, and Pflaum [16]. Most recently, Fabozzi and Francis [9] reported that some security beta coefficients tend to be random over time. Their findings also support the regression tendency of the beta coefficients towards the mean over time, as found by Blume [4]. Thus, because the beta coefficient is changing over time, the use of the ordinary least-squares (OLS) method in investment and portfolio analysis will yield an inefficient estimate of systematic risk. Furthermore, the OLS estimates of security and portfolio residual risks will be influenced by the variability of beta coefficient. Therefore, the purpose of this paper is to investigate the relationship between the variability of the beta coefficient and portfolio residual risk, and hence to provide a real picture of the process of portfolio diversification under the condition of beta nonstationarity. It is shown that the use of the OLS method to estimate security and portfolio residual risks will produce an incorrect conclusion that larger residual risks tend to be associated with higher variability in the beta coefficient.

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.

I. Customary dynamic analysis, 489. — II. Alternative dynamic system, 492.— III. Concluding remarks, 493.

I. The model, 97. — II. The equations of change: Free currency interflow and the “Rybczynski” effect, 99. — III. Comparative statics and comparative systems, 104. — IV. Concluding remarks, 107. — Appendix: The case of perfect mobility of capital, 109.

Son-Nan Chen, William T. Moore, Investment Decisions under Uncertainty: Application of Estimation Risk in the Hillier Approach, The Journal of Financial and Quantitative Analysis, Vol. 17, No. 3 (Sep., 1982), pp. 425-440

Chau-nan Chen, Tien-wang Tsaur; Currency Substitution and Foreign Inflation*, The Quarterly Journal of Economics, Volume 98, Issue 1, 1 February 1983, Page

The paper provides a rigorous and exact formulation of the relationship between the Gini measure of inequality in total income across families, and corresponding measures of inequality in such components of total income as wages, transfer income, etc. It is shown that serious problems of bias arise when individual family data are not available and when data on averages for families grouped by the size of total income are used instead. These problems are illustrated with reference to data for Taiwan, 1964 to 1976.