Academic journal article Quarterly Journal of Business and Economics

The Detection of Nonstationarity in the Market Model

Academic journal article Quarterly Journal of Business and Economics

The Detection of Nonstationarity in the Market Model

Article excerpt

INTRODUCTION

Financial theorists and practitioners for many years have used the well-known market model for the development and use of financial theories. As a return-generating equation, the market model has found extensive application in portfolio theory, the capital asset pricing model (CAPM), and event study methodology. Because of its importance, considerable investigation has centered on issues related to the estimation and behavior of the model, especially the systematic risk parameter, beta. In particular, a series of studies by Blume (1971, 1975) and Levy (1971) concludes that the systematic risk measure of individual securities is not stationary, but has a tendency to change over time. Since then there has been additional evidence to support the conclusion that the market model parameters of individual securities are nonstationary.

This nonstationarity of the market model parameters is important when one considers the informational as well as the methodological implications for applications of the model. In the first case, assuming that the market model parameters define the return-generating process for an individual firm, then it stands to reason that a change in the parameters may indicate a change in the fundamental factors influencing a firm's stock price. Research has shown that certain fundamental factors may influence a firm's systematic risk. For example, Hamada (1972) and Lev (1974) show that a firm's systematic risk is related to its degree of financial and operating leverage. Since a theoretical basis exists for the contention that fundamental firm characteristics may influence systematic risk, it naturally follows that changes, or announcements of changes, in these factors may engender changes in the market model parameters. Hence, an empirically identified parameter change may be associated with a change in a fundamental firm characteristic. In other words, given that a parameter change has been observed, there should be a fundamental reason for observing the change. As Bey (1983b, p. 286) suggests, "the ability simply to identify nonstationarity in individual securities in a given period may serve as a viable starting point for identifying the economic factors causing the structural change in the generating process and developing a superior model to describe the stochastic process generating security returns."

In the second case, the important role played by beta and its normative implications in capital market theory highlight the importance of the impact of nonstationarity on the accurate and valid estimation of the systematic risk parameter (Sunder, 1980; Lee and Chen, 1982; Howe and Upton, 1992). In addition, because nonstationarity can bias the true measure of abnormal returns, the detection of stationarity violations calls into question previous tests of market efficiency and event studies that rely on the assumption of a stationary market model (Brown, Lockwood, and Lummer, 1982; McDonald and Nichols, 1984).

The purpose of this study is to reexamine the problem of detecting nonstationarity in the market model parameters using a more general detection scheme and to make a closer examination of the nature and extent of the problem in the daily stock returns of individual firms. In the first objective, a Bayesian shifting regimes (BSR) model presented by Mehta and Beranek (1982) is used to detect nonstationarity in the market model parameters because it provides a general technique for detecting multiple regime shift points. In many studies (e.g., Hsu, 1982; Bey, 1983; McDonald and Nichols, 1984; and Brown, Lockwood, and Lummer, 1985) the technique used or experimental design constrains the number or locations of the shift points, making it difficult to ascertain the extent of the violations. The Bayesian shifting regimes model incorporates the entire time series of returns to determine the number and location of the regimes. While the Bayesian shifting regimes technique has no inherent limitations on the number of shift points, for computational reasons we limit the maximum number of shift points to three. …

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