Dean W. Wichern

On the Stable Paretian Behavior of Stock-Market Prices

Abstract In this article we present some empirical evidence which indicates that attempts to represent the probability distribution of the rates of return on common stocks by a member of the stable Paretian family of distributions, with 1 < α < 2, may be misleading and in fact may not produce an adequate fit to observed rates of return. We offer an alternative probability model for describing rates of return based on the hypothesized phenomenon of a changing variance. We test the “goodness of fit” of our model vis-a-vis a stable Paretian model for several series of rates of return. Finally we propose an extension of the stability test of Fama and Roll [6].

A Joint Design Criterion for the Dual Problem of Model Discrimination and Parameter Estimation

Two objectives of much experimentation in science and engineering are (i) to establish the form of an adequate mathematical model for the system being investigated and (ii) to obtain precise estimates of the model parameters. In the past, statistical design procedures have been proposed for tackling either one of these problems separately. Investigators, however, frequently want to perform experiments which will shed light on both questions simultaneously. In this paper, therefore, we present a design criterion which takes both objectives into account. The basic design strategy is to emphasize model discrimination when there is considerable doubt as to which model is best and gradually shifting the emphasis to parameter estimation as experimentation progresses and discrimination is accomplished. It is assumed that experiments can be performed sequentially. The use of the design criterion is illustrated with an example.

A Comparison of Ridge Estimators

Least squares estimates of the parameters in the usual linear regression model are likely to be too large in absolute value and possibly of the wrong sign when the vectors of explanatory variables are multicollinear. Hoer1 and Kennard have demonstrated that these undesirable effects of multicollinearity can be reduced by using “ridge” estimates in place of the least squares estimates. Unfortunately, ordinary ridge estimates depend on a value, k, which, in practice, is determined by the data. Several mechanical rules and a graphical procedure, known as the ridge trace, have been proposed for selecting k. In this paper we evaluate the relative performances of several mechanical selection rules, the ridge trace and the least squares procedure using computer simulation experiments.

Merger and Stockholder Risk

In a world characterized by perfect and complete capital markets, the success (or failure) of a merger is judged by the mergers impact on stockholder wealth. With completeness, the mergers impact on the probability distribution generating stockholder returns is unimportant. The perfect market assumption guarantees that the stockholder not satisfied with the consolidated firms return distribution can frictionlessly sell his shares and reorder his portfolio; hence his only concern is the mergers impact on wealth. However, if we acknowledge the existence of commissions, taxes, and other frictions, or if markets are not complete, the mergers impact on the stockholder return distribution becomes relevant. In this study we will analyze 149 mergers involving large N.Y.S.E. firms. We will examine four different hypotheses related to the impact of merger on attributes of the stockholder return distribution. We focus our analysis on risk-related attributes including beta, total variance, residual variance, and several other risk-related attributes. In a companion paper, mergers impact on wealth is calculated for the same sample but will not be reported here.

Eigenvalue-eigenvector analysis for a class of patterned correlation matrices with an application

General forms for the eigenvalues and eigenvectors of certain patterned correlation matrices are obtained. The pattern considered is one in which the correlation matrix consists of submatrices containing powers of a single correlation coefficient p. The results are discussed in the context of a principal component analysis (or a factor analysis) of observations on a random vector X.

Trading based on forecasts of earnings per share : A test of the efficient market hypothesis

Abstract In this paper the semi-strong form of the efficient market hypothesis is tested with a trading rule based on Box-Jenkins forecasts of earnings per share numbers. The quarterly earnings per share series are modeled for a number of firms. The models are updated quarter by quarter and investments are made in the stocks with the largest forecasted growth rates for the next quarter. The risk-adjusted performance of such a strategy is shown to be inconsistant with semi-strong market efficiency.

Modeling and forecasting discrete univariate time series with applications

Abstract A class of time series models suitable for representing discrete univariate time series is introduced. These models are capable of representing both stationary and nonstationary series and can be easily generalized to allow for seasonality and to accommodate a leading indicator. In addition a model building strategy is discussed and the problem of forecasting is considered. Finally, the methodology is illustrated with several examples.

The Effect of Estimation Error On A Geometric Moving Average

The geometric moving average (G.M.A.) is an optimal predictor for time dependent variables whose first difference follows a first order moving average model. The G.M.A. depends upon a single parameter which in general must be estimated from the available data. In this paper, the effect of parameter estimation error on inferences about a future observation from the process described above is investigated from a Bayesian viewpoint.

Forecasting in Business and Economics.

Describes the major techniques of forecasting used in economics and business. This book focuses on the forecasting of economic data and covers a range of topics, including the description of the Box-Jenkins single series modeling techniques; forecasts from purely statistical and econometric models; nonstationary and nonlinear models; and more.

The Term of a Risk-Free Security

In the late 1930s, Macaulay [7] and Hicks [6] independently introduced the concept of duration as a measure of the length of a stream of cash flows and a measure of the elasticity of the present value of the stream with respect to a change in the rate of discount, respectively. Approximately 15 years later, Reddington [8] and Heynes and Kirton [5] used the concept to develop interest rate immunization rules for the portfolio management of insurance companies. More recently, Fisher and Weil [1] have developed duration based rules to help investors find investments that will insure them of having some fixed amount of money available at a specific future point in time. In [2], Grove uses duration to link the investors decision to speculate or immunize with his subjective forecast of future interest rate movements. Finally, Haugen and Wichern [3, 4] show the relationship between duration and the characteristics of bonds and stocks. Also, in analyzing the effect of financial leverage on interest rate risk, they demonstrate how the financial manager can manipulate the capital structure of his firm, so as to render the present value of the common stock insensitive to changes in the rate of interest.