Testing the Significance of Calendar Effects

Abstract

Working Paper 2005-2 January 2005 Abstract: This paper studies tests of calendar effects in equity returns. It is necessary to control for all possible calendar effects to avoid spurious results. The authors contribute to the calendar effects literature and its significance with a test for calendar-specific anomalies that conditions on the nuisance of possible calendar effects. Thus, their approach to test for calendar effects produces robust data-mining results. Unfortunately, attempts to control for a large number of possible calendar effects have the downside of diminishing the power of the test, making it more difficult to detect actual anomalies. The authors show that our test achieves good power properties because it exploits the correlation structure of (excess) returns specific to the calendar effect being studied. We implement the test with bootstrap methods and apply it to stock indices from Denmark, France, Germany, Hong Kong, Italy, Japan, Norway, Sweden, the United Kingdom, and the United States. Bootstrap p- values reveal that calendar effects are significant for returns in most of these equity markets, but end-of-the-year effects are predominant. It also appears that, beginning in the late 1980s, calendar effects have diminished except in small-cap stock indices. JEL classification: C12, C22, G14 Key words: calendar effects, data mining, significance test 1. Introduction Calendar effects are anomalies in stock returns that relate to the calendar, such as the day-of-the-week, the month-of-the-year, or holidays. Two leading examples are the Monday effect and the January effect. Economically small calendar specific anomalies need not violate no-arbitrage conditions, but the reason for their existence, if they are indeed real, is intriguing. Much effort continues to be devoted to research on calendar effects. Yet, the literature remains open about the significance of these effects for asset markets. One reason is that the of specific calendar effects could be a result of data mining. Even if there are no calendar anomalies, an extensive search - or data mining - exercise across a large number of possible calendar effects can yield significant results of an by pure chance. (1) Another reason data mining is a plausible explanation is that theoretical explanations have been suggested only subsequent to the empirical discovery of the anomalies. The universe of possible calendar effects is not given ex ante from economic theory. Rather, the number of different calendar effects that potentially could be analyzed is only bounded by the creativity of interested researchers. Since an extensive empirical analysis of calendar effects is likely to suffer from data mining problems, it is therefore surprising that there is little work that aims to limit the problem. The reason might be that an explicit control for data mining is costly because it is less likely that a true anomaly will be found to be significant. The best remedy for preserving the ability to detect true anomalies, is to employ a test for calendar effects that is as powerful as possible. A robust test for a specific calendar effect needs to condition on the nuisance of all conceivable effects, unless one is willing to violate basic principles for inference. We construct a powerful test to evaluate the significance of calendar effects in this paper. This test combines and incorporates the information from all calendar anomalies to achieve good power properties without compromising test size by exploiting the correlation structure that is specific to this testing problem. The new test is asymptotically F-distributed. However, we implement a bootstrap version of the test that diminishes possible small sample problems. Our new test of calendar effects can be interpreted as a generalized-F test. It is related to some recent methods for comparing forecasting models that have been proposed byWhite (2000) and Hansen (2001), who builds on results of Diebold & Mariano (1995) and West (1996). …