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.

This paper examines the multiperiod capital allocation problem of a corporate division that is subject to ex post financial scrutiny by the parent corporation based upon meeting a specified target rate of return on investment. Using a zero-order decision rule, a deterministic equivalent linear programming model is developed to solve for the division's optimal mix of productive assets and the maturity structure of its debt.

Recent studies of mutual funds have all arrived at the same conclusion: mutual fund performance has been inferior to the performance of the market indices. One of the most prominent of these studies was conducted by William F. Sharpe. He showed that if his measure of mutual fund performance, the reward-to-variability ratio, is calculated net of management expenses for each fund in his sample of thirty-four, then the average value of this ratio over the thirty-four funds is significantly less than the same measure applied to the Dow Jones Industrials over the 1954–1963 period. From this evidence, Sharpe concluded that average mutual fund performance was distinctly inferior to an investment in the Dow Jones Industrial Average. It is the intent of this paper to show that if another variable, namely the third moment of the fund's annual rate of return, is introduced into the investor's decision process, Sharpe's conclusion must be altered.

Most portfolio analysis is based on the use of two parameters, the mean and variance, of the statistical distribution of returns. Exceptions to this practice can be found in an empirical work by Arditti [1] and a theoretical paper by Levy [4], both using the third moment around the mean. It is the purpose of this paper to begin a general extension of the two-parameter analysis to three or more parameters. Accordingly, some problems will be solved, but others will be suggested for further analysis.

Portfolio selection involves the formation of prior beliefs about expected rates of return and risk on available securities and the utilization of these beliefs in the choice of a portfolio. Markowitz has developed a pioneering theory of portfolio choice based on the assumption that the investor has formed prior cardinal beliefs about the expected rates of return, variances of rates of return, and covariances of rates of return among individual securities. Unfortunately, a feasible method of accurately generating the massive information requirements of the Markowitz model has not been developed. Historical measures of mean rates of, return and covariances of rates of return among individual securities have been shown to be unstable over time and to be ineffectual in generating ex ante efficient portfolios.

This article has described a technique for evaluating intercorporate performance using risk, return, and trend. By regressing risk and trend on return for a large number of companies, an average performance plane has been established. A company's performance is measured by determining its position relative to the plane.

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.

The pivotal role of earnings expectations in equity valuation and therefore in certain areas of business finance is widely recognized, yet there is little theoretical or empirical evidence as to the manner in which investors and other groups actually formulate their estimates of future earnings. The resulting necessity to utilize proxy or indirect measures of expected earnings specified largely according to the predispositions of the investigator has led to numerous difficulties in the testing of cost of capital propositions and models of equity valuation.1 This study is intended to supply a preliminary response to the question of how earnings expectations are determined by appraising the extrapolative component of a limited sample of short-term estimates of earnings per common share. More specifically, the issues are the extent to which the earnings estimates (1) are extrapolative in nature and (2) may be approximated by familiar, naive, extrapolative techniques. In this context, “extrapolative” simply means determined by application of a specified weighting scheme to prior observations in the time series.

In recent years we have seen significant progress in the development of models of capital asset pricing and the related models of portfolio selection and performance appraisal. The central focus, in all of these models, has been one of dealing directly with the difficult and perplexing issues of the measurement of risk and the underlying theories of investor choice-making under uncertainty.

“Capital Growth and the Mean-Variance Approach to Portfolio Selection” Nils H. Hakansson Volume VI, No. 1

Three main approaches to the problem of portfolio selection may be discerned in the literature. The first of these is the mean-variance approach, pioneered by Markowitz [21], [22], and Tobin [30]. The second approach is that of chance-constrained programming, apparently initiated by Naslund and Whinston [26]. The third approach, Latané [19] and Breiman [6], [7], has its origin in capital growth considerations. The purpose of this paper is to contrast the mean-variance model, by far the most well-known and most developed model of portfolio selection, with the capital growth model, undoubtedly the least known. In so doing, we shall find the mean-variance model to be severely compromised by the capital growth model in several significant respects.

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.

An attempt was made in this paper to build time-series models with strong structural relationships with various maturity-bond, holding period yields. The relative strength of several groups of key macroeconomic variables with bond returns was specified and tested.

The most useful regressor with regard to short maturity issues was the monetary policy ratio which had a strong association with the dependent variable in the intermediate and short maturities. The rate of change of wholesale prices was also important in the explanation of capital market yields. The rate of change in the English bank rate added still to the explanatory power of the model, particularly in the longer maturities; the combination of these three variables produced the most effective model. The regression coefficients were frequently many times their respective standard errors, and the correlation for every equation for the final model was statistically significant.

The relationship between capital market equilibrium and firm financial policy has received extensive attention in recent years. Until recently, accepted theory was generally consistent in its view that the diversification effect of new investment on firm earnings is a necessary consideration in project selection. In arguing this position, no distinction was made between the perfect market situation exemplified by the models of Modigliani and Miller (M-M) [9, 10, 11] and those of Sharpe [19], Lintner [6, 7] and Mossin [12] (LSM model) and the traditional case in which firm value is not independent of debt policy, e.g., as might be the case if individual investors cannot lever on terms comparable to those available to firms. In a recent article, Mossin [13] examines the implications of the former case of perfect markets. Using a single period model with riskless rate borrowing and lending by individuals and firms, homogeneous expectations, mean-variance portfolio selection, and no taxes, Mossin shows that the effect on the investing firm's value of a new project is independent of the stochastic properties of the other income earned by the firm. This conclusion and the M-M [10] Proposition I follow from the statistical property of Mossin's model that any income stream has the same value regardless of how that stream is divided into the equity or debt streams of one or more firms; or, equivalently, firm value and financial structure are independent. Schall [18] presents a general proof that firm value and financial structure are independent and that firm investment diversification effects are irrelevant in perfect capital markets.

When measures such as the average or the midrange are used to report a typical value for the price series in each interval, the stochastic character of the underlying price process is subtly transformed. Fortunately, the spurious serial dependence introduced by averaging measures is sufficiently well understood to allow direct tests of many hypotheses to be made from averaged data. Moreover, a simple autoregressive transformation of the averaged data can be used to unscramble the effects of averaging on the lower-frequency components of the spectrum of the underlying process. These statistical devices are presented and are then illustrated by applications to the Cowles Commission Common- Stock Indexes, a massive collection of New York Stock Exchange price indexes tabulated in the form of monthly midranges.

After integrating risky debt instruments into the generalized asset pricing model developed by Sharpe and Lintner, we have demonstrated that the required return-to-equity capital in this model is a linear function of the debt-to-equity ratio with a slope equal to the difference between the unlevered cost of equity and the direct cost of debt. Consequently, we take the average cost of capital to be invariant with respect to leverage. The particular nature of the debt instrument issued by the firm does not affect this result.

Our analysis supporting the net operating income valuation construct is of interest in that it takes into account not only the variance of the probability distribution of equity returns but also the covariance relationships between these returns and all other returns in the system. Further, we need not rely on assumptions of “equivalent return” classes or arbitrage possibilities to arrive at our solution. More important, our conclusion is quite general in that we demonstrate indifference toward finance with any instrument regardless of its inherent risk characteristics.

This paper has reported on an investigation of the relationship between the external industrial classification of corporations and the statistical groupings that can be found in their corporate financial measurements. It appears that utilities and industrials are quite different in their financial characteristics. Five industrial classes also appear to be quite distinct, although somewhat less distinct than the industrial-versus-utility comparisons. Consequently, it appears that financial variables do tend to distinguish the various industrial classifications and that, with only a corporation's financial characteristics known, its industrial classification may be reliably determined.

The approach of selecting a portfolio of stocks on the basis of expected return and variance was introduced by Markowitz [18] in 1952 and subsequently was more fully developed by him [19] in 1959. Since this time, there has been considerable research either directly concerned with, or related to, the Markowitz model. The utility implications of his assumption that an investor chooses a portfolio solely on the basis of expected return and variance (where variance is identified with risk) have been studied, [1], [A], [22], and [31]. A simplified method of solving for the efficient set of portfolios under the assumption of a regression structure has been developed by Sharpe [26], and approximation methods have been suggested [25] and [29]. Empirical tests (with partially contradictory conclusions) of portfolio selection theory are described in [5], [7], [8], [20], and [27]. Studies of economic questions (such as liquidity preference, equilibrium stock prices, substitutability of risky assets, etc.), as formulated within the portfolio model, can be found in [10], [11], [13], [14], [16], [23], and [28]. A related portfolio selection approach, based on the assumption of a Pareto underlying distribution, has been suggested by Fama [6]. A modification by Baumol [2] introduced a confidence limit criterion. Also, some initial attempts have been made at deriving related adaptive models of portfolio selection, [21], [30].

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.

As the authors, Donald L. Tuttle and William L. Wilbur, indicate in footnote 1 of their article, “A Multivariate Time-Series Investigation of Annual Returns on Highest Grade Corporate Bonds,” the equations tested in this paper seem to me to be ad hoc. The problem is not that I think the authors should have estimated a general equilibrium model of the economy, but rather that they have not provided a satisfactory explanation of the single equation they have tested. The use of a technique to choose among alternative variables on the basis of their ability to shrink the coefficient of multiple correlation could be taken as further evidence of the absence of a well-articulated theoretical relationship explaining annual returns on corporate bonds.