The stock price literature abounds with applications of the Markowitz [16] – Sharpe [18] market model to American stock price data. There is a lack of corresponding studies for non-American securities, due primarily to the absence of generally available machine readable data bases (see, however, [1], [2], [8, Section 9.5], [11], [17], and [20]. The purpose of this paper is to present the results of some initial tests of the market model for a broad cross-section of the European common stocks. Our data base consists of daily price and dividend data for 229 stocks from seven European countries. In addition, for comparison purposes we have included a sample of 65 American securities.

Stable distributions are suggested as being the underlying distributions for many economic variables. Capital market variables, in particular, are said to follow a member of the symmetric stable class.

The purpose of this article is to produce a conservative estimate of how often traditionally conceived seasonal components are present in prices of individual Dow Jones industrial stocks. A careful estimate is needed to resolve some of the current confusion on the question and to provide basic information along lines suggested by Smidt [27, p. 238]: “… investigations of the random walk hypothesis would be most fruitful if they were conducted in the spirit of attempting to determine the size and extent of systematic tendencies that may exist in price series” (italics added).

Single-period portfolio selection deals with the allocation of an investor's initial wealth to a finite number of risky assets according to his preferences over random final wealth. The purpose of this paper is to study chance-constrained portfolio selection from the point of view of utility theory.

In the past most of the studies whose aim was to explain earnings-to-price ratios (or alternatively, price-earnings ratios) of common stocks attempted to answer the much-debated question raised in both investment and academic circles: Why does a given common stock consistently command a higher price relative to its earnings vis-a-vis other stocks? Success in answering this question has been limited, largely due to (1) researchers' inability to incorporate expected earnings (E) correctly into the empirical measurement of earnings-to-price ratio and/or (2) inadequate treatment of risk variables to explain variability of earnings-to-price ratio.

The traditional valuation framework is unsuited to the task of valuing a growth stock when the capitalization rate is specified in terms of market leverage, simply because it is impossible to maintain a constant ratio of book to market leverage over the growth horizon. This severely limits the usefulness of the traditional model in analyzing the valuation problem. We have proposed a more general form of the model which allows us to show the consistency between M-M's Propositions I and II under growth.

Robert J. Saunders [4] has demonstrated that, because of the high degree of linear interdependence among many of the variables commonly used in banking studies, it may be necessary to interpret explanatory variables in a cross-sectional regression equation, not as representing individual influences but as representing more general factors. He attempted to demonstrate how principal component analysis might be used to isolate and identify some of these general factors.

Marion L. Chiattello [1] has provided additional empirical support for the suggestion that, because of the high degree of linear interdependence between many of the variables commonly used in banking regression studies, it may be necessary to interpret explanatory variables in a cross-sectional regression equation, not as representing individual influences, but as representing more general factors. Further, he has provided more empirical support for the suggestion that principal component analysis might be useful in helping to isolate and identify some of these general factors.

Prior to 1952 there was no analytical theory available that would satisfactorily explain the well-known phenomenon of asset diversification by investors. Although the portfolio selection criteria of Markowitz [3] and that of Roy [5] both explain diversification, they are based on very different objectives. The objective of Markowitz's approach is to select the portfolio of securities that maximizes the expected utility of the investor, i.e., the EV criterion. The objective of Roy's approach is economic survival through selection of the portfolio that minimizes the probability of disaster, i.e., the safety-first (SF) criterion.

We are grateful for the opportunity which Professors Gressis and Remaley's Comment [1] has afforded us to clarify our analysis of the relationship between Roy's Safety First principle and the Mean-Variance expected utility rule, which unfortunately they find misleading. In our original presentation we did not explicitly analyze situations in which Roy's criterion leads to an extreme corner solution; and G-R are perfectly correct in noting that if a riskless asset exists, a “Safety-Firster” will not invest in risky securities at all if the risk-free interest rate, r, exceeds the disaster level d. The reason for this is straightforward: such an investment strategy minimizes the risk of disaster. In fact in this particular instance the investor can reduce the probability of disaster to zero.

In a previous issue of this journal Boot and Frankfurter (hereafter B-F) published the results of their study on the optimal mix of short-and-long-term debt. While interesting, their results appear to be open to question on the following grounds:

1. Use of wrong data: The short-term borrowing data used by B-F in their regression analysis include the following items which do not generally and, rightly so, belong to short-term debt:

(a) Reserve for deferred or future income taxes,

(b) Restricted surplus for deferred taxes,

(c) Insurance reserves,

(d) Surplus reserves,

(e) Unamortised debt premium, and

(f) Contributions for constructions.

In his comment [4], Pashmi Thakkar raises two questions concerning our study [1] in three points. Points 1 and 3 have to do with discrediting the existence or proper measurement of our dependent variable, while point 2 argues for a technically biased regression structure resulting in biased estimates.

The mathematical difficulties encountered when attempting to express the internal rate of return (IRR) of a combination of two or more investments as a weighted algebraic sum of the individual investments' IRRs has been recognized in the financial literature for some time. However, in a recent issue of this journal, Professors Reilly and Wecker (hereafter R-W) [3] apply the well-known mathematical impossibility of expressing the root(s) of a polynomial as an algebraic combination of the roots of related polynomials to question the validity of the weighted cost of capital (kw) concept.

Many important results in the Neoclassical theory of consumer choice are derived from properties of the inverse of the bordered Hessian of a consumer's utility function. It is therefore not surprising that this type of matrix also plays an important part in the theory of portfolio choice. The purpose of this note is to establish a simple property of the inverse of a bordered matrix and to point out its implication for portfolio theory.