In recent years a number of papers have been concerned with the determination of necessary and sufficient conditions for portfolio separation and for myopia. As a result of these earlier investigations, it is known that a necessary and sufficient condition both for portfolio separation and for myopia is that the investor's utility function exhibit risk tolerance, that is a linear function of wealth. What is lacking in the existing literature is a clear demonstration of the economic relevance of linear risk tolerance for portfolio separation and myopia. It is hoped that this paper will help to fill the gap by an analysis of separation and myopia using the standard tools of price theory: indifference curves, budget lines, and Engel curves. Viewed in this perspective, a substantial part of the analysis can be amplified and clarified in terms of the geometry of the situation.

In this paper, the Markowitz and Sharpe portfolio selection approaches are viewed as alternative analytic processes for portfolio selection. By “analytic process,” we mean a process that begins with data collection and culminates when a decision is made. The properties of these analytic processes are examined in the same sense that one studies the properties of a statistical estimator, except that a global view of the analytic process is taken. The properties of decisions that result from applications of these processes are studied experimentally, and are reported in terms of the objectives of the portfolio manager.

The Securities and Exchange Commission (SEC) and the New York Stock Exchange are concerned with the full disclosure of information insiders normally would be expected to possess about their company, including any facts that would materially affect the market's valuation of the firm's worth if they were publicly known. At present, the regulatory agencies have limited their activities to the collection and dissemination of historical information and facts. The motives of insiders, based in large part, presumably, on their knowledge regarding future operating results are hidden from the public eye. The SEC in compiling the Official Summary of Stock Transactions does not require insider to reveal his motivation for trading.

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.

The simultaneity of security price determination has been recognized for many years. Lintner [6], Lerner and Carleton [5], Mossin [9], Sharpe [10], Tobin [15], and others have all advocated that securities be treated in a portfolio sense implying security prices are determined simultaneously. The empirical work in finance is just beginning to deal formally with this simultaneity.

This paper examined the empirical consequences of explicit consideration of purchasing power risk in portfolio decisions. It was shown that, during a period of significant inflation, the differences between the variance-covariance relations of nominal rates of return and those of real rates of return were sufficiently pronounced to change the composition of investment portfolios. Further, it was shown that the set of real efficient portfolios dominates any investment strategy that ignores purchasing power risk.

Empirical research has cast so much doubt on chart readers that most capital theorists have about as much faith in charts as astronomers have in astrology. Certainly there is overwhelming evidence that attempting to predict future price changes on the basis of past price behavior is unproductive. There is, however, another aspect of technical analysis which has received much less attention from academicians. In its narrow form technical analysis seeks to forecast the direction of price movements of individual securities from past price and volume data. A second and somewhat broader type of technical analysis concentrates on the prediction of general market movements and trends relying on a broader set of information. Various market indicators are said to offer signals useful in forecasting future prices. One type seeks to measure investor sentiment through what might be called mood variables. A second type of indicator is more closely related to fundamental factors affecting future supply and demand for securities. Both types of indicators, however, are designed to be used in predicting future market movements rather than the movements of individual stock prices. This is to be contrasted with fundamental analysis which is concerned with predicting future prices of individual securities by analyzing the underlying factors related to the firm's future profitability. Most of the prior work with market indicators takes one or another proposed market indicator and examines the historical relation, between the indicator and some market index such as the Dow Jones Industrial Average.

A market can be imperfectly competitive for a variety of reasons; in the context of an auction or a contract awarding, imperfections may stem from the limited number of bidders involved. Bidders, recognizing that their behavior (or that of others) can affect the market outcome, may adopt strategies that are unlikely to lead to a Pareto efficient allocation. Such inefficiencies can occur in the absence of any collusive behavior on the part of bidders. If barriers to bid entry are removed, and bidders are sufficiently homogeneous, the likelihood increases that bids will reflect full (private) valuations of the auctioned goods. Under these conditions Pareto efficient allocations would be guided by a set of minimum prices: a “sale to the highest bidder” would be transacted at a price approximate to the valuation of the second highest bidder, and contracts would be awarded at the competitive supply price. Even when the number of bidders is restricted, auction procedures can be adopted which will insure efficiency to a degree. This efficiency is achieved by changing the motivations of the available bidders, and by providing incentives for bidders to reveal their full valuations of the objects being auctioned. This paper describes a set of auction procedures which achieve these ends.

Recent financial literature has discussed how a creditor should determine its investigation and extension policy. Mehta [8,9] has developed a sequential process for credit extension, and others [1,2,4,7,10,12,14] have used credit-scoring functions to develop decisions rules. Instead of discussing the use of a particular system or the development of a new system, this paper shifts the focus to selection of the best of alternative systems. Different creditors face different profit-loss ratios on loans, business volume, and prior probabilities of good and bad customers. Furthermore, since the alternative systems have different initial costs, effectiveness, and investigation costs per application, no one system is optimal for all creditors. Finally, any credit-scoring alternative declines in effectiveness over time. Measurement of the overall effectiveness of a system requires that the optimal time between updating the system be known.

In a past issue of this journal, Carl J. Norstrøm [3] developed a sufficiency condition for the existence of a unique nonnegative internal rate of return for an investment project. His method is appealing because it involves a simple computation using cumulative undiscounted cash flows and because it applies to a wide range of practical situations.