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.

Although the importance of evaluating the risk of potential investments has long been recognized, only recently have formulations been developed to include risk as an explicit variable in the decision-making process. The considerable progress being made in this area, both in theory and in application, is attested to by the number and variety of contributions to the literature.

Analysts and investment advisors have long searched for investment tools that would either furnish predictive probabilities for future security price movements, or would aid in minimizing losses. One such tool, often recommended by market practitioners, is the Moving Average. This article describes a series of experiments that were performed upon actual market data, using Moving Averages of different lengths and weights, and presents results of the experiments. Conclusions derived from these experiments are suggested.

The recent literature in the field of commercial banking has centered to a considerable extent around the branch banking controversy and bank merger activities, particularly as regards their economic effects on banking structure and performance. Much has been said, moreover, about the effects of branching on the “public interest,” whether such branching is carried out through merger or de novo branching. Public interest is usually defined as including deposit safety, adequate compensation by banks to depositors for the use of their money, availability of credit for borrowers at competitive rates of interest, and, in more general terms, increased competition in banking without sacrificing safety.

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.

“The Dynamic Characteristics of Chow's Model,” by E. R. Arzac, appeared in the December 1967 issue of this Journal.

P. 385, line 14: “lagged dependent variables” should be omitted.

P. 390: The last line on the page was ommitted. It should read:

“can generate a set of random vectors that would correspond to the distri-”

Recent literature has witnessed the emergence of an impressive body of empirical evidence relating to the relationship which exists between successive security price changes. The great majority of this evidence has tended to support what has come to be known as the theory of random walks in security prices—that is, the theory that successive security price changes behave as independent random variables, which implies that knowledge of “the past history of a series of price changes cannot be used to predict future changes in any ‘meaningful’ way.”

Corporations tender for their own shares for a variety of reasons. Some stock tenders are made for strategic purposes—to prevent a take-over, to raise the market price of the stock, or simply because the stock represents ‘a good investment.’ For discussion of tendering in these situations, see the articles of Ellis [2] and Guthart [1]. In addition, there may be tactical reasons for a stock tender; one such reason is to reduce bookkeeping and shareholder servicing costs. In this instance, the argument runs roughly as follows: “The annual cost of servicing a holding is independent of the number of shares; consequently, the cost per share of servicing small holdings is relatively great. Let us reduce these high per-share costs by buying up small holdings.” Typical procedure is to then mail out an offer to buy holdings of less than a certain size directly, thus permitting the shareholder to dispose of his holding without paying the usual brokerage and odd-lot fees. Frequently no premium is offered except for the avoidance of brokerage fees. If one were to consider the premium offered as a controllable variable, it would be surprising to discover that its optimal value were exactly zero. One also recognizes that the maximum shareholding tendered for may be another decision variable available for optimization. See the appendix for data on tenders of this sort made in recent years. The variety of policies seems to indicate an almost complete absence of systematic application of the ideas presented here.

Professor Solow's article, “Technical Change and the Aggregate Production Function,” now virtually classic, has made a great impact on economists generally and in the last few years the subject has received unprecedented attention in economic literature. The reason for this extraordinary emphasis on “Technical Change” has been the conclusion—in Solow's above-mentioned article—based on statistical evidence, that gross output per man-hour in the United States nonfarm economy doubled over the period 1909–1949, “with 87.5 percent of the increase attributable to technical change and the remaining 12.5 percent to increased use of capital.”

We shall investigate the problem of optimal exercising strategy for option holders for the case in which option holders are averse to risk. A model of stock price changes incorporating the Lognormal random walk assumption will be combined with a class of utility functions containing diminishing marginal utility of money. In general, the strategy of waiting until the last possible day to exercise an option, which maximizes expected value, will not maximize expected utility. The strategy which maximizes expected utility is obtained by a dynamic programming formulation of the decision problem. At each day (or decision stage), the option holder may choose to act (exercise) or wait until the next day. Working backwards from the last day, a series of critical prices are obtained, with the optimal strategy being as follows: act if the stock price on any day is greater than the critical price for that day; otherwise, wait. Using the concept of proportional risk aversion developed by Pratt, we will demonstrate that, under certain conditions, a utility function which exhibits increasing proportional risk aversion is sufficient to create a series of finite critical prices. Moreover, once an option is exercised, the option holder continually faces a tactical decision to hold the stock and wait for capital gains or sell and take profits as ordinary income, thereby avoiding further risk. This decision may also be optimized by a dynamic programming scheme similar to the approach used above.

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.

In “Valuation Under Uncertainty,” which recently appeared in this Journal (September 1967), Houng-Yhi Chen argues [1, pp. 313–314] that “Robichek and Myers' criticism [2, 3] of the use of the risk-adjusted discount rate is unfounded,” and suggests that our “conclusions must be based in part on a misunderstanding of the risk-adjusted discount rate method.” These charges are without foundation, as we will show here.

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.