A convertible bond is a hybrid financial instrument that incorporates features of a bond (fixed income security) and an equity claim (usually common stock). In most instances the convertible can be exchanged, at the holder's option, for the common shares of the corporation issuing the convertible. The conversion value, or stock value, is the market value of the common shares for which the convertible can be exchanged. The bond value or floor price is the market value of an equivalent bond that does not include a conversion feature. The market price of a convertible will be the conversion value or the bond value, whichever is higher, plus a premium. The purpose of this paper is to develop and test a model which estimates the premium. The premium estimated is defined as the difference between the market price of the convertible and the bond value or conversion value, whichever is larger. No consideration will be given to convertible preferreds.

In response to the suggestions of the editorial and reviewing staff of this journal, some additional explanation and extensions of the model presented in an earlier paper [4] seem desirable at this time. In that paper the investor in securities was assumed to have a utility function that depended on the first n moments of the statistical distribution of returns rather than just on the mean and variance. When the borrowing-lending possibility was introduced as in the Sharpe-Lintner model, the investor's perceived risk premium could be expressed in the higher moments' dimensions as well as in terms of the variance.

Solving capital budgeting problems with linear and integer programming has been part of the finance literature for some time [21, 22, 23, 7, 14, and 18]. Capital budgeting problems have unique properties that distinguish them from other integer linear problems discussed in the mathematical programming literature. Capital budgeting problems generally have the following characteristics: (1) the matrix tends to be rectangular with more variables than constraints; (2) they are all maximization problems with ≤ constraints and nonnegativity conditions in the general form 0≤xi≤1 in the case of linear programming and xi = 0, 1 in the case of integer problems; and (3) there are often mutually exclusive projects among the variables. The purposes of this note are to illustrate some computational experience using existing integer algorithms to solve a set of capital budgeting problems and to begin to catalog the performance of integer codes on financial problems.

Unfortunately Professors Arditti and Levy (A-L) in their comment published in this issue of this journal did not realize that the determination of the investor optimum in my paper [1] was simultaneous with respect to the three parameters, the mean and the variance and the third moment of portfolio returns. When the nth moment was introduced, it was assumed that the investor chooses on the basis of all n parameters — the mean, second moment, third moment, etc. — through the nth moment.

Michael H. Hopewell, Comment: A Model of Capital Asset Risk, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 2, Supplement: Outlook for the Securities Industry (Mar., 1972), pp. 1673-1677

Despite the enormous attention received by the single-period mean-variance model in the literature, its structural relationship to the empirical world is still largely unexplored. The purpose of this note is to show that when certain consistency requirements and equilibrium conditions in the financial markets are taken into account, the collective judgment of the present literature concerning the mean-variance approach is in some respects too lenient and in other respects too harsh. In addition, it will be noted that the mean-variance model can only achieve consistency with the von Neumann-Morgenstern postulates and absolute preference (also known as first-order stochastic dominance) at the price of a severe upper bound on the risk aversion that can be possessed by the decision maker.

This paper is a selective review of the received theory of financial institutions with some suggestions regarding future research on this topic. The major emphasis is placed on the positive economic theory of these firms. Financial institutions are considered to be firms that supply financial securities and contracts held as assets by other sectors of the economy and that use the proceeds of these sales to finance the purchase of financial securities and contracts which are the liabilities of other economic units. The theory discussed here is stripped of much of the regulatory and legal framework surrounding financial institutions. The primary reason for so limiting the scope of this paper is a conviction that a reasonably complete model of a simple financial institution is a necessary precursor to useful models of the positive economic behavior of financial institutions in any specific legal, regulatory, and operational framework. While recognizing that no tractable model of a financial institution is likely to be so general as to avoid the problem of model specificity, I take the view that many of the questions asked in the literature would be better answered in less specific models, i.e., in models capable of explaining additional important aspects of the behavior of the financial institution in question.

Some recent empirical studies have concluded that the common stock investor can virtually eliminate diversifiable risk with a portfolio that contains a “small” number of separate common stock issues [5, 6, 10, 11, 13]. The conclusion has several important implications. One of the inherent limitations of a portfolio manager is his inability to evaluate an infinite number of securities. The seriousness of this problem is directly related to the risks associated with a “small” portfolio. The economic function of a mutual fund industry is to provide diversification and professional management. If it is assured that a “small” portfolio can virtually eliminate diversifiable risk, the necessity of these functions may be questioned. In addition, the strategy of concentration may be less “risky” than is commonly supposed. Finally, the modern portfolio models generally assume that portfolio additions are costless.

In a recent paper by Lusztig and Schwab, a sensitivity analysis was performed on a linear programming capital budgeting problem where selection of projects is based on the criterion of present values. Their model is typical of current practice in the literature, and it is the point of this paper to indicate that a better model exists which allows more flexibility of assumptions and will yield the same results as a present value criterion. The model to be presented here uses a terminal value (horizon value) criterion for selection of the optimum set of investment projects.