Professor Jennings, in his recent article [2], developed a model to estimate convertible bond premiums. The model incorporates the capital asset pricing model to evaluate convertible bonds. The purpose of this comment is not to criticize the general development of the model but to point out flaws in its implementation which influence Jennings' empirical results.

Numerous empirical studies have appeared in recent years concerning the behavior of stock market prices. Cootner's book [2] presents an excellent summary of pre-1964 efforts, while Fama's paper [5] discusses some of the more recent work. While a few writers believe that certain price trends and patterns exist which enable the investor to make better predictions of the expected value of future stock price changes, the majority of these studies conclude that past price data alone cannot form the basis for the prediction of the expected value of price movements in the stock market.

In Gonedes [5], the results of an empirical analysis of accounting-based and market-based estimates of systematic risk were presented. These results suggested that there is, in general, a “statistically significant” relationship between accounting-based and market-based estimates of systematic risk at the level of individual securities, if the accounting-based estimates are conditional upon first-differences or scaled first-differences of the accounting numbers. The differencing transformation seemed to induce relatively better specified models for the accounting numbers.

The Stable (or Pareto-Lévy) distribution has been of considerable interest in describing the behavior of security prices ever since the important work by Mandelbrot [6], [7] and Fama [1]. The aforementioned contributions focused on the empirical hypothesis that security price data are better fitted by theoretical distributions with infinite variance rather than finite variance. Specifically, in the case of Stable distributions, the “characteristic exponent” is less than two, and the data are not adequately fitted by a normal distribution. Remarkably, however, although almost the entire body of literature addressing empirical questions with respect to the distribution of security prices investigages the behavior of the (natural) logarithm of security price relatives, to this author's knowledge no paper exists which analyzes the portfolio choice implications of the assumption that the logarithm of the asset returns has a symmetric Stable distribution with infinite variance. Thus, in Fama [2], Samuelson [10], and Ziemba [12], where the problem of selecting an optimal portfolio in Stable markets is the object of concern, one finds that it is assumed that the price-relatives (returns) have a Stable distribution; this rather than the logarithm of the price relatives. And it should be noted that none of these authors suggests that the untransformed price-relatives are better-fitted by a symmetric Stable distribution as compared with the logarithm of the price-relatives.

The purpose of this paper is to examine the intertemporal relationship between variations in the prices of individual common stocks and variations in the rest of the stock market. Empirical data are analyzed to determine the frequency with which stock prices precede, occur simultaneously, and follow movements in the market average.

The structure and analytical representation of investors' utility-of-wealth functions has long been of interest in portfolio theory. In proposing convenient analytical utility functions most economists have used (i) constant elasticity (power) functions, (ii) the negative exponential function. Both (i) and (ii), of course, restrict the preference structure; Moreover, one may object to (i) because such functions are not uniformly bounded on [0, ∞). And, as has been shown by Arrow [1], this is undesirable in an axiomatic system. The negative exponential function has no such disadvantage, but objections may be raised on empirical grounds. Thus, no simple convenient specification of bounded utility functions on [a, ∞) is available. In fact, even polynomials in wealth of arbitrary order are restrictive since they immediately impose the requirement that moments of wealth are finite. (If the polynomial is of order n, then the nth moment must be finite.)

The comment by Linke and Kim correctly observes that the assumption regarding the maintenance of constant proportional use of capital sources is not appropriate for our argument and should be deleted. As our analysis did not make use of this assumption, the two conclusions hold.

1. The weighted average cost of capital calculated with the usual weights (original capital structure proportions) is not in general equal to the discount rate which equates the current value of the firm to the present value of future cash flows.

2. The above conclusion holds for any weights which can be constructed from the cash flows.

State-preference theory has developed as a choice-theoretic framework through which many problems of finance and economics dealing with time and uncertainty can be analyzed. Hirshleifer [3], [4], [5], [6] has used the approach to provide significant insights to areas such as production and exchange, investment decisions, and speculative behavior. However, the theory has not made progress in attempting to incorporate state-labeled utility functions into the body of the theory. This paper will develop a method of graphically and analytically allowing for differing utility functions across states. As a further step, the impact of belief-deviation upon the tangency optimum will be discussed. Finally, the significance of these findings upon the consideration of risk will be discussed.

The measurement and determination of risk have received considerable attention in recent years. One measure of risk is systematic risk, defined in terms of the covariance of a security's return with the return from the market portfolio. The relationship is often standardized by dividing the covariance by the variance of return from the market portfolio. Hereafter, this measure of standardized systematic risk shall be referred to as beta.

Statistical analyses of price series generated by auction markets has been oriented historically toward the detection of structure (or lack of structure). While the results of such studies have been mixed, insufficient empirical evidence has been obtained on the properties of the measures employed to capture the inherent behavior of the price series. The first differences of the closing price have been shown, theoretically, to be unbiased for a random walk process. The use of averages, particularly the first differences of the midrange, has been shown to introduce spurious serial dependence in mathematical time series. It is the purpose of this article to examine the properties of both the delta close and delta midrange as measures, and to perform a variety of statistical tests and analyses to establish empirically the relationship between them. The predominant effort in seeking this relationship consisted of the spectral analysis of 11 years of May potato futures prices. The results obtained support the contention that the delta midrange amplifies the delta close, and that the amount of amplification is stochastic distortion in the delta midrange.