Nonstationarity and Portfolio Choice

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.