The arithmetic formulas appearing in the mathematics of finance are practically useless unless one has available either excellent tables and infinite patience, or working computer programs, a machine, and a budget. The present article shows how a number of useful topics in this area can be dealt with effectively by the more tractable mathematics of continuous processes. The methods yield approximate answers of high quality, and in some cases exact answers as well, with small effort, and have obvious applications in “truth in lending” investigations.

If all urban renewal projects were perfectly divisible and completely independent of one another, and if the urban renewal authority had perfect foresight as well as unlimited funds, the investment decision would be ideally simplified. There would be no need to choose between competing projects, and the urban renewal authority could evaluate each project on its own merits, without reference to any other project. Its decisions would be merely decisions to accept or reject single projects, uncomplicated by portfolio considerations.

It is well known that different combinations of investments involve different risks. In recent years the analysis of risk has tended to focus on two moments of the probability distribution of returns, the mean and variance. This paper considers the effect on the variance of an investment fund of adding dependent investments.

The purpose of this paper is to estimate empirically the effect of the deferred call provisions on corporate bond yields using the conceptual framework of callable and call-free yields developed by Jen and Wert [3]. After reviewing briefly the above-mentioned study in Section I, Section II presents patterns of callable and call-free yields of deferred issues from January 1956 to June 1961 by grades, months of offering, and coupon rates and contrasts them with those of the freely callable issues. Section III further contrasts yields of deferred issues with those of freely-callable ones on a pair comparison basis, while Section IV discusses the implication of the study for both the issuers and the investors.

This paper is another step in an attempt at unification, through generalization, of existing theories in various areas of finance. The subject treated here is the valuation of equity shares.

Money, conventionally defined as demand deposits and currency held by the nonbank public, has two principal functions. It serves as a medium of exchange and as an asset conferring perfect liquidity on the holder.

Savings deposits in commercial banks, savings and loan associations, mutual savings banks, credit unions, and the postal savings system are almost like money. For all practical purposes, they are perfectly liquid assets, or at least considered as such by depositors, and therefore substitutable for asset money. Because interest is paid on savings deposits, and not on demand deposits (except for an implicit return received through checking services provided below cost), it can be reasonably argued that the long-term asset demand for money (money that people expect to hold over six months) is considerably less than it would be in the absence of savings deposits. This does not mean, however, that the sum of currency, demand deposits, and savings deposits measures what the demand for money would be if savings deposits did not exist. Some savings deposits are certainly held in lieu of nonmonetary assets.

The most conspicuous deficiency of my study of underwriting compensation is my failure to examine the determinants of underwriting spreads on tax-exempt bond issues. That deficiency has now been remedied by Richard West. Unfortunately, my study was not published very long before West's and there was little opportunity for him to compare his results and speculation with my own. Although a few of the comments below are critical of West, and I point out some alternative interpretations of his statistical findings, this note should be considered a supplement to, rather than a critique of, West's paper.

In a recent article in this journal, Harold Bierman, Jr. takes me to task for an alleged incompleteness and insufficiency of my “Elements of a Theory of Stock-Option Value.” The criticism consists of an insistence that option (call) values are relative to alternative long positions in common stock, rather than of “absolute” and independent value as options per se.

A. James Boness is correct in stating that the orientation of my paper “Elements of a Theory of Stock-Option Value” is more oriented to valuation problems for executive stock options than to valuations arising in the New York put and call market. However, Boness, in his earlier article, stated that “its generality suggests that it is equally appropriate to an analysis of the values of stock warrants, convertible issues, and with modification, executive (non-negotiable) stock-options.” My article is an attempt to define one modification that is necessary.