The Monthly Effect in Stock Returns and Conditional Heteroscedasticity
Journal article by Menahem Rosenberg; American Economist, Vol. 48, 2004
Journal Article Excerpt
The Monthly Effect in Stock Returns and Conditional Heteroscedasticity. by Menahem Rosenberg I. Introduction Various seasonal anomalies in stock returns have been researched since Rozeff and Kinney (1976) originally presented the January effect. (1) For example, French (1980) documented the weekend (or Monday) effect, (2) and Ariel (1987) presented the end-of-month (or monthly) effect. In addition, documentation of similar phenomena by Lakonishok and Smidt (1988) using a longer time series and by Jaffe and Westerfield (1985) in foreign equity markets has reduced the possibility that these anomalies are due to sampling error. In this paper, we present a possible structural explanation for Ariel's end-of-month effect. Ariel (1987) reports a higher cumulative return for the first-half of the month than the last-half of the month. Lakonishok and Smidt (1988) confirm this finding using an extended daily time series. In contrast, Wang, Li, and Erickson (1997) show that Mondays in the last two weeks of the month are responsible for the previously reported end-of-month effect. After controlling for Mondays in the last two weeks of the month, they find the coefficient for the end of the month to be insignificant. In other words, the end-of-month anomaly is explained as a weekend anomaly. Most of the research cited above uses daily stock returns data. However, French, Schwert, and Stambaugh (1987) suggest that the daily returns on the S&P 500 index exhibit conditional heteroscedasticity, while Engle and Mustafa (1992) show similar characteristics in individual stock returns. Moreover, Connolly (1989) tests the weekend effect in S&P 500 index returns and rejects the constant variance model in favor of a Generalized Autoregressive Heteroscedastic (GARCH) model. Disregarding such changing volatility and applying a constant variance model can lead to an inefficient though unbiased estimator of mean returns. This could in turn lead to acceptance of a false null hypothesis (see Pindyck and Rubinfeld 1998). In this paper, we use a GARCH model to present evidence that end-of-month returns are lower than beginning-of-month returns. Contrary to Wang, Li, and Erickson (1997), we will show that this result holds, even when we control for Mondays and end-of-month Mondays. We will also present evidence that the monthly effect may be associated with the economic business cycle. Ogden (1990) shows that standardization of payments in the U.S. economy leaves investors with additional funds to commit at the turn of the month. When the money supply is tight (which is a result of stringency in monetary policy of the Federal Reserve Bank), funds availability is negatively correlated with turn-of-month stock returns. The implication here is that the difference between the beginning-of-month mean return and the end-of-month mean return should be significant only in an expansion phase of the business cycle, as we will show. The paper is organized as follows: Section II describes the data and methodology used. Empirical results are presented in Section III. Section IV offers the summary. II. Data and Methodology This paper applies a time-varying GARCH model, as initially suggested by Engle (1982) and then generalized by Bollerslev (1986). The GARCH (1,1) model we apply here incorporates one lagged variance term in the conditional variance. The index return regression model is: (1) [r.sub.t] = [mu] + [alpha][D.sub.t] + [[epsilon].sub.t] [r.sub.t] | [I.sub.t=1] ~ N ([mu], [h.sub.t]) where the conditional variance follows: (2) [h.sub.t] = [[beta].sub.0] + [[beta].sub.1][[epsilon].sup.2.sub.t-1] + [[beta].sub.2][h.sub.t-1] In this model, [r.sub.t] is the daily index return, and [mu] is the daily mean return. [D.sub.t] is a vector of dummy variables that will take a value of one to mark various calendar conditions, such as Monday or the last-half of the month, and otherwise will take a value of zero. Variable [alpha] is the corresponding vector measuring the special calendar date's contribution to the mean return. Hypothesis testing is conducted on each of the [alpha] components that are different from zero. An [alpha] component that is significantly different from zero will point to a calendar date that contributes significantly to the overall mean return, [mu]. In the tests to be reported, we employ the Center for Research in Security Prices (CRSP) daily returns for the period from July 1962 through December 1993, which includes a total of 7,927 daily observations. The daily data also contain the daily calendar dates. This information allows us to mark each daily return for both specific calendar dates and the day of the week. We employ three indices in our analyses: the NYSE value-weighted index, the NYSE equally-weighted index, and the S&P 500 index.Monthly data on U.S. business cycle expansion and ... |
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