According to a now classic study of stock market price behavior by Fama [6], the empirical distributions of daily log price relatives are usually stable Paretian, non-Gaussian. However, there appears to have been substantial reluctance to accept Fama's [6] research results as indicative of a fundamental return generating process which is stable Paretian, non-Gaussian. Blattberg and Gonedes [1], Clarke [4], Officer [18], Praetz [19], and Press [20] have each in their own way questioned the Fama [6] results. Most recently Hsu, Miller, and Wichern (HMW) [13] have suggested that in periods of homogeneous activity for a firm the empirical distribution of rates of return on a common share may be Gaussian, in other words, that the fundamental return generating process may be normal.

In a recent article in this Journal Joy and Tollefson [10] (hereafter J&T) critically analyzed discriminant analysis and its application to bankruptcy analysis. The authors make several interesting points and provide a useful discussion of the application of this statistical technique in finance. There are, however, three aspects of their presentation which need further elaboration. These relate to their discussions of (1) the difference between the stability of the discriminant model and its predictive ability, (2) the alternative methods of making inferences about the relative discriminatory power of variables, and (3) the reference statistics to use in assessing classification efficiency. In commenting on these points we will make use of the data from the Altman [1] study as did J&T.

Since call option trading started on the Chicago Board Options Exchange (CBOE) in April 1973, the interest shown by both the investment and academic communities has grown as rapidly as the volume of option trading. In May 1973, the first full month of trading on the CBOE, a total of 34,599 contracts were traded; during 1976, the monthly volume reached 1.5 million contracts on the CBOE and 800,000 contracts on the American Stock Exchange. At present the New York Stock Exchange and certain regional exchanges are evaluating the feasibility of adapting option trading for their respective exchanges.

In this paper we confront two well-known models for pricing options. It shows how the two models, one derived in a discrete time framework by Boness, the other derived in a continuous time framework by Black and Scholes, can be made consistent. In doing so, we find the implicit, discrete period, discount factor for the call option. Several characteristics of the discount factor are analyzed and compared to the characteristics of the instantaneous expected rate of return on the call.

In a timely, comprehensive article in this journal, Joy and Tollefson (J & T hereafter) treated design and interpretation problems for linear multiple discriminant analysis (LMDA). Although the article is generally correct in treating a complex topic, it has two problems:

1. The (widely-used) split-sample validation technique that J & T used is an inappropriate method for establishing the efficacy of the estimated discriminant function.

2. J & T reach erroneous conclusions on the correctness of two methods for assessing the discriminatory power of individual variables.

This comment addresses these two problems.

Much of the applied work in finance, for instance the literature on capital budgeting, assumes that a firm's management has an accurate estimate of the firm's beta. This estimate is presumably derived by running a regression of the form:

where:

Ri = rate of return on equity for firm i,

Rf = the risk-free rate, and

u = a white noise random variable.

The following proof of Modigliani and Miller's (MM) [2] famous propositions concerning the valuation of the firm and the cost of capital does not require the usual risk-class or arbitrage assumptions; the proof depends only on the Fundamental Theorem of Parameter-preference, which states that the riskpremium for security A is a linear combination of its comoments with the market index, .