Stable distributions are becoming increasingly popular as appropriate models for stock price changes and other economic phenomena. As a result, there is an expanding body of literature on inferential procedures for this family of distributions. Computationally simple estimators for the parameters of symmetric stable distributions have been provided by Fama and Roll. Little attention, though, has been given to goodness-of-fit tests for members of this family other than the normal.

It is the purpose of this paper to discuss simple goodness-of-fit hypothesis tests using kurtosis, b2, to distinguish among members of the stable family. The b2 tests of hypothesis comprise: 1) a null normal versus a nonnormal symmetric stable alternative; 2) a null nonnormal symmetric stable versus a normal alternative; and 3) a null nonnormal stable versus another nonnormal stable alternative. Tables that give the percentage points of b2 and that are necessary for these tests of hypothesis are given. Apart from providing critical values for the tests, the tables allow the researcher to calculate the power. It will be seen that the b2 test exhibits excellent power.

It is then hoped that computational convenience will make b2 an important tool for researchers and practitioners in finance. It is also hoped that the procedures we provide will aid these researchers and practitioners in the construction of appropriate financial models.

The work of Black and Scholes [2] and Merton [4] suggests that analysis of hedged positions in a continuous time random walk model yields powerful insights into the valuation of financial securities. The present paper extends this methodology in a straightforward fashion to foreign exchange transactions. By adopting the device of hedging in a secondary market for forward currency contracts against a long position in spot currency, a simple statement of boundary conditions for the forward position can be detailed. This allows a direct solution of the continuous time valuation problem that yields the interest rate parity theory.

The relationship between an investor's attitude toward risk and the shape of his preference functions has long been recognized in both the general portfolio problem and the mean-variance model. By contrast, the literature has largely ignored the connection between general measures of an investor's attitude toward risk and the shape of his mean-variance or mean-standard deviation indifference curves. Yet this relationship is significant. Through general measures of risk aversion, assumptions about an investor's behavior under uncertainty imply restrictions on indifference curves. Conversely, assumptions about indifference curves impose restrictions on an investor's behavior under uncertainty. The development of this relationship and its implications is the objective of this note.

International finance has developed into a recognized field of study within the broader discipline of international business. This has occurred because increasing commitments of companies to international operations have forced more and more financial managers to face a number of problems and issues not found in a strictly domestic setting. Foreign currency exchange risks, exchange controls, restrictions on the flow of funds, diverse accounting and taxation systems, host government interference, and the effects of worldwide inflation on enterprise assets, earnings, and capital costs are just a sample of the variables calling for specialized knowledge.

In recent years intensive work has been done applying the Sharpe-Lintner-Mossin Capital Asset Pricing Model to the multiperiod investment decision under uncertainty. The purpose of this paper is to develop a practical working procedure for use by the financial manager. We first develop the multiperiod capital budgeting decision criterion in a form that lends itself to application. Second, we propose a method of implementation, one that we have made operational in computer programs currently on the Columbia University computer system. This makes it possible to extend the evaluation to encompass typical capital budgeting problems which, until now, have been discussed only under certainty. In particular we deal with the case of capital rationing. We employ programming techniques for this analysis and interpret the meanings of the dual variables.

I was interested to read Meyer and Kim [5], where I learned a little about sugar futures, but regret to say that I found the attempted Box-Jenkins analysis singularly lacking in expertise. It is my intention, here, to discuss a few of its most obvious shortcomings. My list will not be exhaustive, but will include just five points.

The focus of this study is the role of default risk in capital market theory. The impact of default risk on the value of securities has been a major concern of investors and academics alike. Several authors have examined the relationship between bond ratings, the probability of default, and security value [5, 12]. In this context, the ability to avoid or reduce expected bankruptcy costs and thereby increase value has been suggested as a reason for mergers and consolidations [16, 18]. In other studies, models have been developed for predicting ratings [17, 20, 21, 28], for predicting bankruptcy using accounting and other financial variables [1, 6, 7], and for approximating default premiums in the credit markets [22]. Finally a question which has received considerable attention is the effect of bankruptcy on a company's cost of capital. When bankruptcy is possible and there exists a positive bankruptcy transaction cost, it has been argued that there is an optimal capital structure [24, 26].

The academic research has produced a series of contributions on optimal portfolio strategies (Bradley and Crane [1], Crane [4], Cheng [3], Fisher and Weil [5], Watson [9], Wolf [10]). Several of these studies--Bradley and Crane, Watson, and Wolf--conclude that an optimal strategy for bank portfolios would be a “dumbbell” strategy. Such a dumbbell strategy invests only in the shortest and longest maturities, ignoring the intermediate maturities. The logic is straightforward: liquidity risk is lowest in the shortest maturities and yield is generally highest in the longest maturities. The risk/return superiority of such a strategy was empirically verified by Watson, with subsequent confirmation by the Bradley and Crane tests via a stochastic dynamic programming formulation.

In this paper we have extended the Bierman-Hass model to include the effect of a second parameter, the terms of settlement in the event of default. The addition of this second factor was found to not alter the independence between a bond's risk differential and its maturity. Our analysis of the required risk differential for various borrower credit characteristics demonstrates the tradeoff between p and γ. Throughout, we have assumed the loan size does not affect p or γ.

Studies of returns on common stocks have observed positive market index autocorrelation (see Fisher [10] and Dimson [6]), negative autocorrelation of market model residuals (see Fisher [10] and Fama, Fisher, Jensen, and Roll [9]), and a deterioration in the market model R2 as the returns measurement period is shortened (see Pogue and Solnik [17], Altman, Jacquillat, and Levasseur [1], and Schwartz and Whitcomb [19]). We present further evidence on the strength of these findings and show that they are concurrent events. That is, common factors can explain both positive index and negative residual autocorrelation, and these correlation patterns in turn cause R2 to fall as the differencing interval is shortened.

Since we now have a data base approaching five years of more or less fluctuating exchange rates, there undoubtedly are numerous empirical studies under way comparing the movements of exchange rates with each other and with all sorts of other economic variables. A rather subtle problem with such activities is that the analysis is sensitive to which currency of an exchange rate one chooses to make the numeraire. Specifically, a time series of, say, dollars per pound sterling is not the same thing mathematically as a time series of pounds per dollar although the information content is the same. In particular it can be shown that

Published scholarly research is asserted to be a major criteria used to judge or assess the quality of a university's faculty. This assertion has been supported in many of the academic disciplines by comparing peer ratings of graduate programs and the research productivity of the faculty of those programs. In the economics area, John J. Siegfried [ 7] found a significant relationship between peer ratings of economics departments, using the ratings of the first American Council on Education study by Cartter, and the number of available pages contributed by the department to the leading economic academic journals. A recent study by Klemkosky and Tuttle [6] found the same relationship between an academic institution's published research productivity and the quality of the institution's graduate finance programs as rated by peers, using the survey results of Brooker and Shinoda [3] to determine peer ratings. The importance of published research in turn is recognized by many academic institutions since the relative quality and quantity of published research is one of the major criteria used in making faculty promotion and tenure decisions.

The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A1) The instantaneous (spot) interest rate follows a diffusion process; (A2) the price of a discount bond depends only on the spot rate over its term; and (A3) the market is efficient. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation.

In an earlier paper [1] a model of securities markets was introduced which implies that the ratio of transaction volume to price change is greater for transactions on which price rises than for those on which price falls. Examination of individual transactions data for a sample of corporate bonds showed that price changes and transaction volumes for those securities appears to behave in a manner consistent with the theory. However, the paper raised the question of whether the same is true for stocks. The positive dependence on share price of broker commissions for stocks could easily eliminate, or even reverse the sign of, the predicted positive difference between the absolute values of slopes of buyers' and sellers' reservation demand functions; and it is this difference which leads the model to predict the inequality of the ratios of volume to price change on upticks and downticks. This note records the results of tests of the model with stock data, using volumes and price changes pertaining both to individual transactions and to trading days. The tests indicate that the ratios of volume to price change exhibit the predicted relationship, when one of the two possible measures of volume is employed.

Time series techniques based on autocovariance and spectral analysis methods have often been used for statistical analyses of commodity and stock prices, with the usual conclusion that the prices, zt, are best described by a random walk:

where the errors, ut (alternatively called shocks or residuals), have zero expectation and form a sequence of independent random variables [5 and 8 ].

The API metric, as initially formulated by Ball and Brown [1], has been used to examine the relationship between stock prices and accounting numbers. Its use in this manner has raised at least three difficulties: (1) the metric does not utilize all of the information portentially available from accounting numbers, (2) the statistical significance of the API metric and of differences between API's has not always been satisfactorily considered, and (3) the meaning of the metric has been questioned. This paper will attempt to resolve these difficulties by reformulating the API approach. Two nonparametric statistical procedures are considered, both of which provide a test of the statistical significance of the relationship between accounting income numbers and stock prices. The first procedure is particularly appropriate when alternative accounting income numbers are considered. Both procedures provide a conventional unambiguous interpretation of the results.

Prof. A. Carol examined a replacement problem in a paper published in the January 1972 issue of this journal.

The aim of the author seems to be to obtain a precise insight in the pattern of quantities to be considered to take a rational decision.

In [1, p. 999] I wrongly stated that “the solution locus generated by the chance-constrained problem is efficient (for the class of utility function implied by the expected wealth-probability of ruin criterion) if the assets follow a multinomial distribution with means above the survival level.” In support of this statement footnote 6 of [1] attempted to establish the quasiconcavity of the expected utility function

in the (μ, σ) plane, where F is the normal distribution, z = (s-μ)/σ < 0, s is the survival level, μ is the mean of the portfolio, σ is the standard deviation, and c is a positive constant. The condition

was claimed to hold for any two assets (μ1., σ1) and (μ2., σ2) on any given indifference curve of (1), where zi. = (s-μi.)/σi., i = 1,2, and zγ = (s−μγ)/σγ corresponds to the convex combination μγ = γμ1 + (1−γ) μ2, σγ = γσ1+ (1−γ) σ2, in the (μ, σ) plane. (Note that this is not the same as asserting that F(z) is a convex function of μ and σ, which it is not as an examination of its Hessian determinant would readily show.)

This paper extends the results of previous work by the author in the development of a structure for analysis of rather general two-currency decision problems using an nstage dynamic programming model. After a brief review of the model, the paper provides a characterization of a convertibility scheme as a set function which assigns to each currency portfolio a set of currency portfolios which can be attained from the original portfolio, operating through the convertibility scheme. The concept of a substitutable convertibility scheme is developed; the substitutability property allows the decision maker to substitute a functionally determined single currecy payoff for a given twocurrency payoff. Two tests to determine substitutability in general, and for a particular return function, are developed. The modest reduction in dimensionality of the dynamic programming problem arising from this property is explained. Some specific convertibility schemes are then characterized, including free convertibility, inconvertibility, retention quotas, maximum balance, maximum acquisition, and multiple rate schemes. The substitutability of free convertibility is demonstrated. A retention quota scheme which allows free sale and purchase of retained funds in a parallel market is shown to be equivalent to a free convertibility scheme, and therefore substitutable.