Academic journal article Quarterly Journal of Business and Economics

International Evidence on Mean Reversion in Stock Prices

Academic journal article Quarterly Journal of Business and Economics

International Evidence on Mean Reversion in Stock Prices

Article excerpt

INTRODUCTION

This paper examines whether international stock price indexes contain slowly mean-reverting components. This issue has generated substantial debate in recent years and has significant implications for stock market efficiency. The study employs the regression-based tests of Fama and French (1988) that focus on the autocorrelations of stock returns for increasing holding periods. The results show that a majority of the 18 country indexes studied exhibit variations during the past two decades inconsistent with mean-reversion in long-horizon returns. Evidence also is provided that suggests that any apparent mean-reversion is due largely to country-specific factors.

Previous studies have found predictability in return data, but most have relied on short-horizon data and found only a small degree of systematic change in prices (Lo and MacKinlay, 1988; French and Roll, 1986; O'Brien, 1987; Poterba and Summers, 1988; and Cochrane and Sbordone, 1988). But stock prices may mean revert very slowly as Summers (1986) argues; hence, predictability may be evident only at longer return horizons. The tests of Fama and French (1988) explicitly capture Summers' (1986) insight. Their evidence, based on U.S. data for industry and decile price indexes, implies considerable predictability for the 1926 to 1985 period, especially for smaller firms. They find much less predictability, however, in the 1940 to 1985 subperiod. Because the present study covers the 1970 to 1989 period, the results are broadly consistent with those of Fama and French (1988).

The present study's application of the Fama/French test to international data is important both for practical and scientific reasons. On a practical level, interest in worldwide investing is growing rapidly. Worldwide investors are interested in whether patterns observed in the United States apply to foreign markets with their differing institutional arrangements. On a scientific level, results from a wide range of countries provide new evidence on time-series properties of returns and allow more general inferences than do results based on a single country. In addition, any apparent cross-country differences may provide insights into the sources of predictability, which are still the subject of debate.

A TEST OF MEAN-REVERSION IN STOCK PRICES

Fama and French (1988) develop their test from a simple model of stock price behavior.(1) The log of a stock's price, p(t), is the sum of a random walk component, q(t), and a slowly decaying stationary component, z(t) = az(t-1) + e(t), where e(t) is white noise and a is close to, but less than, unity. The continuously compounded return from t to t+T is:

(1) r(t, t+t) = |q(t+T) - q(t-1)~ + |z(t+T) - z(t)~.

The random walk component produces white noise in returns while the stationary component induces negative autocorrelation. Two results based on equation (1) are of particular interest. First, the first order autocorrelation of T-period changes in z(t), that is,

(2) |Rho~(T) = cov|z(t+T) - z(t),z(t)- z(t-T)~/||Sigma~.sup.2~|z(t+T) - z(t)

approaches -0.5 for large T. Second, the slope in the regression of r(t, t+T) on r(t-T, t), |Beta~(T), equals

(3) |Beta~(T) = |Rho~(T)||Sigma~.sup.2~|z(t+T) - z(t)~/||Sigma~.sup.2~|z(t+T) - z(t)~ + ||Sigma~.sup.2~|q(t+T) - q(t)~

The test centers on predictions about changes in the magnitude of |Beta~(T) as the return horizon, T, increases. Three cases can be considered, each reflecting the relative importance of q(t) and z(t) in the variance of p(t). Assume first that q(t) is nonexistent. In this case p(t) is stationary, and mean reversion pushes the slope, |Beta~(T), toward -0.5 as T increases. Recall from equation (3) that if no random walk component exists, |Beta~(T) = |Rho~(T) which approaches -0.5 as T becomes large. If p(t) is a pure random walk, |Beta~(T) will equal zero regardless of T because r(t+T, t) is white noise. Finally, assume that p(t) has both random walk and stationary components. …

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