Following Markowitz's [11] pioneering work on portfolio selection, it is customary to consider an individual's choice among several risky assets as a two-step procedure. First, given some general characteristics concerning his preferences, the decision maker chooses an efficient set of portfolios independent of his specific preference assessment. Secondly, an optimal portfolio is chosen from the efficient set given the individual's specific preferences.

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.

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.

The capital asset pricing model specifies that relative risk is a sufficient descriptor of security risk. This result holds under both the Sharpe-Lintner version,

and the more general Black version of the model,

where

= expected rate of return on asset i,

Rf = riskless rate of interest,

= expected return on the market portfolio,

= expected return on any “zero-beta” asset or portfolio of such assests, and

= relative risk of asset i in the market portfolio of assests.

The recent world-wide increase in consumer prices has created an intense interest in inflation on the part of both the academic and the financial communities. For example, in his American Financial Association presidential address, Professor Lintner [4, p. 259] states “few matters are of more serious concern to students of finance and to members of the financial community than the impacts of inflation on our financial institutions and markets and its implication for investment policy.”

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, .

Two methods for deriving efficient sets involve either the Markowitz [3] approach, where every security can be viewed as being related to an index unique to itself, or the Sharpe [4] single-index model, where every security is related to the same index. Given the extreme differences between these models, Cohen and Pogue [1] developed two intermediate models. They found that the efficient set derived from the Sharpe single-index model came closer to approximating the Markowitz model's efficient set than their models when empirically tested on a sample of common stocks. Subsequently a similar test was performed by Wallingford [6] which yielded contradictory conclusions.

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.

Indexes are frequently used for a basis of comparison of the performance of different types of assets, such as mutual funds and common stocks. Sharpe [6] studied the performance of mutual funds over the period 1944 to 1963 and compared their performance to the Dow-Jones Industrial Average (DJIA) using the capital-asset pricing model. For this period he concluded that mutual funds were relatively inferior investments. Joy and Porter [2], using the stochastic dominance approach, reached conclusions similar to those of Sharpe for the 1954–1963 period.

After Markowitz [14, p. 100] and Sharpe [19, 20] suggested estimating the beta systematic risk coefficient for market assets, finance professors, stock brokers, investment managers, and others began expending large quantities of resources each year on estimating betas. Unfortunately however, it appears that the ordinary least-squares (OLS) regressions used in nearly every instance may be inappropriate. This paper suggests that many stocks' beta coefficients move randomly through time rather than remain stable as the OLS model presumes.

Diversification and capital market theory in conjunction with investors' desire to quantify risk have caused the beta coefficient to receive considerable attention in recent finance literature. Results of empirical investigations of the stationarity of beta over time have been reported by Altman, Jacquillat, and Levasseur [1], Baesel [2], Blume [3], Levitz [5], and Levy [6]. Blume examined the longer-term stability of the beta coefficient, using monthly prices and successive seven-year periods, concluding that portfolio betas are very stable but individual security betas are highly unstable. Levy reported similar conclusions using weekly data and shorter-term estimates of beta; 52-week base periods; and 52-, 26-, and 13-week subsequent periods. Levitz also found portfolio betas to be stable using three-year base periods and one-year subsequent periods.

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 purpose of this paper is to provide evidence that the Bureau of the Census' X–ll program for seasonal adjustment [3] overstates the incidence of seasonality in some forms of times series data. This problem arises in a recent study by Bonin and Moses [1] (hereafter B-M) indicating that 7 of the 30 Dow Jones Industrial stocks exhibited persistent seasonal patterns during the period July 1962 through June 1971.

This study presents theory and some exploratory empirical work on several separate strands of monetarism in an international context and reports the results of tests of the two interrelated hypotheses: (a) the United States' monetary expansion was responsible forthe exportation of inflation to the rest of the world during the period of generally fixed exchange rates that lasted from the end of World War II until August 1971 (followed by the Smithsonian revaluations and generalized floating in March 1973), and (b) foreign nations could not control their money supplies, even in the short run, to prevent importing inflation. Succinctly stated, the monetarist approach to macroeconomic phenomena holds that money is preeminent in determining the short-run shocks to real output and the long-run price level of an economy. However, received theory is simply not clear as to whose money is most important in an international context. Is it the domestic money stock which is kept relativelyindependent of foreign forces under fixed exchange rates through astute central bank policy, at least in the short run? Is it the rest of the world money stock which, under fixed exchange rates, is a close substitute for domestic money? Or is it the money stock of the so-called world's banker, the United States, which drives foreign economies? We address these issues and others in our empirical analysis.

The purpose of this paper is to investigate the performance of propertyliability insurance companies' stock portfolios from 1952 to 1968, and to show how that performance compared to the general stock market and investment company performance.

In a series of recent articles ([2], [3], [4], [5]) R. B. Porter and his associates have conducted empirical comparisons of the Mean-Variance (EV) and Stochastic Dominance portfolio choice criteria. The basic methodology of all these studies was first to compute the set of EV-efficient portfolios by an optimizing algorithm, then to find through heuristic methods “stochastically dominant” portfolios, and finally to compare the two. A major finding of these studies was that most EV-efficient portfolios survived the second-degree stochastic dominance (SSD) test against the randomly generated portfolios. The purpose of this note is to show that, for all cases of practical interest, a portion of the EV frontier is a subset of the SSD-efficient set. In other words, we offer here an exact theoretical justification of some empirical results of the aforementioned studies.

Evaluating investments by discounting anticipated future benefits at an exogenously determined risk-adjusted discount rate (hereafter referred to as the RADR approach) is well accepted in the canon of finance. If benefits (Dt) are to be received for T periods and if k, the discount rate, is constant over each of the t periods, then the discrete time net present value (NPV) is defined as:

A positive NPV characterizes a desirable investment.

In a recent article appearing in this journal [2] Jonathan Ingersoll developed a normative multidimensional security pricing model for the individual investor in which he corrected errors in an earlier attempt by William Jean [3] [4] [5] at developing such a model. The purpose of this correction is to clarify and correct certain parts of Ingersoll's correction of Jean's work.

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.

In response to the many issues raised by Altman and Eisenbeis (A&E) [2], we will use their three-part outline. Before turning to their comments, however, we would like to take this opportunity to correct a typo in footnote 10 from our original paper [4]. The denominator of the formula is incorrect as shown, and should be .