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David Zaitzeff, a futures broker at Peregrine Financial Group, Inc. follows up on our review of possible three-day weekend anomalies:
"For regular five-day weeks, does Thursday tend to yield poor returns; and Tuesday, good returns? Also, there is conventional wisdom among traders about reversal Tuesdays. If Monday is up (down), what percentage of Tuesdays are down (up) and by how much?"
To investigate these questions, we examine returns and volatilities for the five trading days of the week during normal trading weeks, which we define as those having five trading days. In other words, we exclude abnormal weeks which have at least one day during which U.S. stock exchanges are closed all day. We do not exclude normal weeks adjacent to abnormal weeks. so a normal week occasionally follows or precedes a three-day weekend. Using daily closing prices for the S&P 500 index since the beginning of 1990, we find that:
The following chart shows the average daily returns for the S&P 500 index during the five trading days of normal weeks since the beginning of 1990, with one standard deviation error bars to indicate volatility. Sample size is 758 weeks. The average daily return for all days during normal weeks since the beginning of 1990 (red line) is 0.032%. Average returns for specific days of the week range from -0.003% for Friday to 0.063% for Wednesday. In order of decreasing returns, the ranking is Wednesday, Tuesday, Monday, Thursday and Friday. Standard deviations of returns are close to 1% for all five days. In general, variability swamps the slight differences in average returns by day of the week. (To answer David's question explicitly, Tuesday's average return of 0.036% is a little better than Thursday's average return of 0.016%.)
If we consider data only since the beginning of 2000, average returns for days of the week range from -0.07% for Friday to 0.082% for Thursday. In order of decreasing returns, the order is Thursday, Wednesday, Monday, Tuesday and Friday. The difference between the total sample and this large subsample in the order of average returns by day emphasizes the insignificance of any day-of-the-week effect for traders.
What about Tuesday reversals?
Of the 758 Mondays in the sample, 55% have positive returns and 45% have negative returns. When returns for Monday are positive (negative), 54% (48%) of the returns for Tuesday of the same week are positive, and 46% (52%) are negative. When returns for Monday are positive (negative), the average return for Tuesday of the same week is -0.013% (0.095%). Does these results represent a significant reversal?
The following scatter plot compares returns for Monday and Tuesday of the same week (for normal weeks) across the entire sample period. The Pearson correlation between the two series is -0.13, suggesting a slight tendency for Monday and Tuesday returns to move in opposite directions. However, the R-squared statistic for the two series is just 0.0167, indicating that variation in Monday returns explains less than 2% of the variation in Tuesday returns.
In fact, if we exclude the two outlier points in the far upper left of the plot, the Pearson correlation shrinks to -0.05 and the R-squared statistic to 0.003. This lack of explanatory power means no Monday-to-Tuesday trading signal.
In summary, there are no tradable differences in returns by day of the week evident in recent broad stock market data, and there is no reliable Monday-Tuesday reversal.
For related research, see Blog Synthesis: Calendar Effects.
