It is well known that present institutional arrangements do not permit investors to use the proceeds of short sales to finance the purchase of other stocks. On the contrary, investors must place the proceeds of short sales in escrow, and they must also affirmatively invest (deposit) an additional amount equal to margin requirements (which may be as much as 100 percent) of the “proceeds” of the short sales. These escrowing and depositing requirements together will be referred to as “short-sales escrowing requirements.” These escrowing requirements not only involve forced or “by-product” holdings of the (nominally) riskless asset, they also change the structure of the investor's wealth constraint by requiring the substitution of absolute values for the natural number of shares when short sales are made.

The Capital Asset Pricing Model of Sharpe [10, 1964], Lintner [8, 1965], and Mossin [9, 1966] showed how it was possible to derive under fairly stringent assumptions the conditions for equilibrium in a market for risky assets. Recent work has been directed at relaxing these assumptions, and this paper extends the progress made thus far by deriving some properties of capital market equilibrium when investors are faced with divergent borrowing and lending rates and when these rates may vary among investors.

A portfolio frontier superior to the Markowitz one-period buy-and hold efficient frontier does exist. Such a superior frontier can be generated by pursuing a rebalancing policy, even under the conditions of random walk. By rebalancing we mean that an investor maintains a fixed but optimal set of weights among the securities in a portfolio throughout an investment period by buying and selling securities at the end of some predetermined intervals.

The purpose of this paper is to consider some problems arising in several applications of the theory of portfolio analysis pioneered by Markowitz [8] and Tobin [13]. This theory of asset choice under uncertainty has been applied to a large and growing set of problems beyond the original application to the selection of the investor's optimal portfolio, e.g., the capital budgeting decision of the firm (Lintner [7]), international capital flows (Grubel [5]), the choice of an export mix for a country (Brainard and Cooper [1] and the flow of direct investment (Stevens [12] and Prachowny [10]). In all applications a common element is the set of efficient portfolios which, in turn, is determined. by the set of moments—means, variances, and covariances—of the returns from the different assets that are. Considered for inclusion in the portfolio.

Present models for selecting portfolios according to the mean-variance criteria do not account for the simultaneous effect of error in estimating means, variances, and covariances of security returns. This paper describes an experiment in which the impact of estimation error is so strong that the usefulness of present mean-variance approaches to portfolio selection is brought into question.

Almost twenty years ago, Markowitz [4] first suggested that portfolio selection be regarded as a parametric quadratic programming problem. Risk is stated in terms of the predicted variance of portfolio return — a function that is quadratic in the decision variables (the proportions of the portfolio invested in various securities). All other functions (e.g., expected return) and constraints are assumed to be linear. The objective is to find the set of efficient feasible portfolios. A portfolio is feasible if it satisfies a set of relevant linear constraints; it is efficient if it provides (1) less variance than any other feasible portfolio with the same expected return and (2) more expected return than any other feasible portfolio with the same variance.

This note examines the positive implications of the Latané-Tuttle [5, 6] geometric mean portfolio selection criteria for the determination of stock prices. Recently, Mossin [9] and Lintner [10] have derived the market prices of equities under the respective assumptions that investors have quadratic and exponential utility functions. While it would be presumptuous to suggest that all investors are “long-run wealth” maximizers, this criterion has a certain amount of intuitive appeal. The geometric mean criterion is equivalent to the maximization of a Bernoulli or logarithmic utility function and displays the desirable characteristic of decreasing absolute (i.e., as the investor's wealth increases, he becomes less averse to risk). This contrasts with the exponential utility function which displays constant absolute risk aversion and the quadratic utility function which displays the undesirable characteristic of increasing absolute risk aversion. Another suggested desirable characteristic of the geometric mean criterion is that it emphasizes the avoidance of bankruptcy while maximizing the asymptotic rate of growth of wealth [4, 5] and maximizing the probability of exceeding a given wealth level within a fixed time [3]. This note analyzes the aggregate effect on stock prices of investors using the geometric mean portfolio selection criterion.

We have discussed some of the effects of rate regulation in the property and casualty insurance industry. One consequence of the regulatory environment is that an optimal capital structure may clearly exist in this industry. If the rate of return to the insureds is generally deficient, we would expect that property and casualty stock companies would have an incentive to lever themselves to the maximum extent permissible by selling insurance. The classic monopoly of the economic literature finances its lucrative investment opportunities in a competitive capital market. The stock insurance company invests in that market, but the relative distribution of the return earned there may be less than equitable due to the process and standards of rate regulation.