Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-08T10:27:56.433Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonstationarity and Portfolio Choice

Published online by Cambridge University Press:  19 October 2009

Christopher B. Barry  and
Robert L. Winkler
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper, a Bayesian model for forecasting future security prices under nonstationarity has been described and compared with a corresponding stationary model. In terms of the short-run behavior of the models, greater uncertainty is retained under nonstationarity than under stationarity. In terms of the limiting behavior of the models, the values of the parameters of interest cannot be ascertained with certainty under nonstationarity, even after the process has been observed for many time periods, and any given observed returns receive less weight as the length of time since the observed returns increases. These properties are not shared by the corresponding stationary model, and in general, the nonstationary model considered in this paper appears to have more realistic properties than the corresponding stationary model.

With respect to portfolio choice under linear utility, nonstationarity has no effect in the short run but may prevent the curtailment of trading in the long run that occurs under the stationary model. For a risk-averse decision maker considering one risky security and one risk-free security, nonstationarity decreases the attractiveness of the risky security. This implies that in general, a risk-averse decision maker will invest less money in a portfolio of risky securities in the nonstationary case than in the stationary case. When the two securities under consideration are both risky, the effect of nonstationarity for a risk-averse decision maker can be related to the expected returns for the two securities. With respect to traditional mean-variance analysis, nonstationarity does not affect membership in the efficient set of portfolios, but the efficient set does shift in mean-variance space due to the additional uncertainty under nonstationarity, and this causes a change in the optimal portfolio.

Various extensions of the forecasting model could be considered, and the portfolio selection and revision model could be reexamined in the light of such extensions. In view of recent empirical support for nonstationary variance terms in stock price distributions, the analysis of the effects of nonstationary variances and covariances on portfolio choice would be a logical extension of the analysis in this paper. Winkler [25] considered the case of an unknown covariance matrix, and that approach could be extended to include a nonstationary covariance matrix. Another possible extension is to consider the case in which changes in the unknown parameters occur at random intervals of time rather than at fixed intervals of time. Carter [6] considered such an extension for the univariate situation studied by Bather [3], and it appears to add considerable realism to the model. However, analytical results for that case may be difficult to obtain.

Nonstationarity has long been neglected in the study of economic decision models in general and in the study of portfolio analysis in particular. Although the results of this paper are obtained under a relatively simple model, the point is that nonstationarity can have effects on portfolio decisions and hence upon the functioning of capital markets. Further work of both an empirical and analytical nature concerning the existence of and effects of nonstationarity appears warranted.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 11 , Issue 2 , June 1976 , pp. 217 - 235
Copyright
Copyright © School of Business Administration, University of Washington 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Barnea, Amir, and Downes, David H.. “A Reexamination of the Empirical Distribution of Stock Price Changes.” Journal of the American Statistical Association, vol. 68 (1973), pp. 348–350.CrossRefGoogle Scholar
[2]Barry, Christopher B. “Portfolio Analysis under Uncertain Means, Variances, and Covariances.” Journal of Finance, vol. 29 (1974), pp. 515–522.CrossRefGoogle Scholar
[3]Bather, J. A. “Control Charts and the Minimization of Costs.” Journal of the Royal Statistical Society, Series B, vol. 25 (1963), pp. 49–80.Google Scholar
[4]Blattberg, R. C., and Gonedes, N. J.. “A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices.” Journal of Business, vol. 47 (1974), pp. 244–280.CrossRefGoogle Scholar
[5]Boness, A. James; Chen, Andrew H.; and Jatusipitak, Som. “Investigations of Non-Stationarity in Prices.” Journal of Business, vol. 47 (1974), pp. 518–537.CrossRefGoogle Scholar
[6]Carter, Phillip L. “A Bayesian Approach to Quality Control.” Management Science, vol. 18 (1972), pp. 647–655.CrossRefGoogle Scholar
[7]Chen, Andrew H. Y.; Jen, Frank C.; and Zionts, Stanley. “The Optimal Portfolio Revision Policy.” Journal of Business, vol. 44 (1971), pp. 51–61.CrossRefGoogle Scholar
[8]Fama, Eugene F. “Multiperiod Consumption-Investment Decisions.” American Economic Review, vol. 60 (1970), pp. 163–174.Google Scholar
[9]Francis, Jack Clark, and Archer, Stephen H.. Portfolio Analysis. Englewood Cliffs, New Jersey: Prentice-Hall (1971).Google Scholar
[10]Hakansson, Nils H. “Optimal Consumption-Investment Strategies under Risk for a Class of Utility Functions.” Econometrica, vol. 38 (1970), pp. 587–607.CrossRefGoogle Scholar
[11]Hakansson, Nils H. “Multiperiod Mean-Variance Analysis: Toward a General Theory of Portfolio Choice.” Journal of Finance, vol. 26 (1971), pp. 857–884.Google Scholar
[12]Hakansson, Nils H. “On Optimal Myopic Portfolio Policies with and without Serial Correlation of Yields.” Journal of Business, vol. 44 (1971), pp. 324–334.CrossRefGoogle Scholar
[13]Hsu, Der-Ann; Miller, Robert B.; and Wichern, Dean W.. “On the Stable Paretian Behavior of Stock Market Prices.” Journal of the American Statistical Association, vol. 69 (1974), pp. 108–113.CrossRefGoogle Scholar
[14]Markowitz, Harry M.Portfolio Selection: Efficient Diversification of Investments. New York: Wiley (1959).Google Scholar
[15]Meyer, Richard F.“On the Relationship among the Utility of Assets, the Utility of Consumption, and Investment Strategy in an Uncertain but Time-Invariant World.”In Proceedings of the Fifth International Conference on Operational Research. London: Tavistock (1970), pp. 627–648.Google Scholar
[16]Mossin, Jan. “Optimal Multiperiod Portfolio Policies.” Journal of Business, vol. 41 (1968), pp. 215–229.CrossRefGoogle Scholar
[17]Praetz, Peter D. “The Distribution of Share Price Changes.” Journal of Business, vol. 45 (1972), pp. 49–55.CrossRefGoogle Scholar
[18]Raiffa, Howard, and Schlaifer, Robert. Applied Statistical Decision Theory. Boston: Graduate School of Business Administration, Harvard University (1961).Google Scholar
[19]Rosenberg, Barr. “A Survey of Stochastic Parameter Regression.” Annals of Economic and Social Measurement, vol. 2 (1973), pp. 381–397.Google Scholar
[20]Rothschild, Michael, and Stiglitz, Joseph E.. “Increasing Risk I: A I Definition.” Journal of Economic Theory, vol. 2 (1970), pp. 225–240.CrossRefGoogle Scholar
[21]Rothschild, Michael. “Increasing Risk II: Its Economic Consequences.” Journal of Economic Theory, vol. 3 (1971), pp. 66–84.CrossRefGoogle Scholar
[22]Samuelson, Paul A. “Lifetime Portfolio Selection by Dynamic Stochastic Programming.” Review of Economics and Statistics, vol. 51 (1969), pp. 239–246.CrossRefGoogle Scholar
[23]Tobin, James A. “Liquidity Preference as Behavior towards Risk.” Review of Economic Studies, vol. 26 (1958), pp. 65–86.CrossRefGoogle Scholar
[24]Tobin, James A. “The Theory of Portfolio Selection.” In the Theory of Interest Rates, edited by Hahn, F. H. and Brechling, F. P. R.. New York: Macmillan (1965).Google Scholar
[25]Winkler, Robert L. “Bayesian Models for Forecasting Future Security Prices.” Journal of Financial and Quantitative Analysis, vol. 8 (1973), pp. 387–405.CrossRefGoogle Scholar
[26]Winkler, Robert L., and Barry, Christopher B.. “A Bayesian Model for Portfolio Selection and Revision.” Journal of Finance, vol. 30 (1975), pp.179–192.CrossRefGoogle Scholar
[27]Winkler, Robert L. “Nonstationary Means in a Multinomial Process.” Research Report RR-73–9. Laxenburg, Austria: International Institute for Applied Systems Analysis (1973).Google Scholar
[28]Zellner, Arnold.An Introduction to Bayesian Inference in Econometrics. New York: Wiley (1971).Google Scholar