Consider the following linear programming problem, which is denoted by (S):The various vectors and matrices have the following dimensions:a = an m-vectorAj = (j = 1 … n), an m by njmatrix,bj = (j = 1 … n), an mj-vector,Bj = (j = 1 … n), an mj by nj matrix,Cj = (j = 1 … n), an nj-vector, andxj = (j = 1 … n), a variable nj-vector.

Problems with this decomposable structure have been extensively studied in economics and management science literature, because they arise in several economic contexts and situations. Therefore, (S) lends itself to more than one economic interpretation, but the following one is hereby adopted for the purposes of this paper: (S) models a two-level manufacturing organization, consisting of headquarters and n producing divisions. Let this organization be called simply “the company”. The company can produce and sell a number of different products, thereby obtaining fixed unit contributions. These contributions are given by the vectors c1, c2, … cn. The products are produced by the different divisions. The variable vector xj (j = 1 … n) gives the production program for the jth division.

This study has addressed itself to that group most immediately affected in corporate acquisition, the stockholders of acquired companies. We find that in the years observed, acquired company stockholders seem to have benefited from the acquisitions. This study differs from other studies of post-merger performance of the common stock of acquirors and not the performance of securities received by acquirees in exchange for their common stock. It should also be noted that most of the financial gain resulting from the acquisitions accrued at the time of merger because of substantial premiums paid by acquirors. While the stockholders of the acquired companies have, on average, benefited, these results tell us little of the effect of mergers on the welfare of society or, for that matter, of their effect on the stockholders of the acquiring firm. If the merger cannot be justified on the basis of some economy of scale or synergistic advantage, the newcomers reap their lucrative returns only at the expense of the old guard. If the acquiring firm pays a premium in acquisition on the basis of justifiably sound expectations of increased profits, social welfare is not necessarily enhanced. Increased profitability may not reflect increased efficiency; it may, for example, be a manifestation of decay in the competitive environment.

If a firm is considering replacing part of its productive facility because of obsolescence rather than wear-and-tear (e.g., purchasing a new model machine), it weighs the expected gains against the expected costs. A problem may arise when the rate of technological innovation for the type of machinery is extremely rapid. Such replacement may yield a gain if made today, but because innovations are so rapid, a year's delay in replacement may yield a greater net gain, and it would seem wiser to wait the year. But each year the same reasoning seems to hold; the more rapidly innovations seem likely to occur, the more likely a firm is to delay. If technology is advancing quickly enough, a firm may never consider any time a good time for replacement.

One of the most vexing areas of business finance is empirical validation of theory. Many problems arise that the investigator cannot avoid. The purpose of this paper is to define a class of problems that can be avoided but that have caused many previous investigators difficulty, even though they may not have realized it. In what follows, the concept of dimensional analysis, borrowed from the physical sciences, is introduced. Then dimensional analysis is extended to the interpretation of estimated regression coefficients.

By examining the annual data from 1937-1967, we found that odd-lot volume has become loss important in the market in recent years. Although the odd-lot trading volume has increased steadily in the absolute term since the end of World War II, the share of odd-lot trading in relation to total round-lot volume has been declining. By 1967, the percentage of odd-lot volume to round-lot total sales was down to 11.6 percent. The same data also indicate that odd-lot short sales have increased moderately since 1962; however, the volume is quite insignificant. The average of odd-lot short sales to total round-lot short sales for the 31-year period is only 1.9 percent. Odd-lotters were also found to be net purchasers during this period (1937-1967); however, odd-lotters have turned into net sellers in recent years. The total net sales from 1961 to 1967 amounted to 22.2 million shares, which is approximately 25 percent of the total net purchases of the entire period (1937-1967).

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.

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.

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.

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.

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.

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.

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.

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.