Test the claim that U.S. Treasury rates rise during September, known as the “September Effect.” 1
Rather than relying on market rumors or media narratives, the goal was to quantitatively assess whether the historical data supports this seasonal effect.
Assets: U.S. Treasury rates (1-month, 2-year, 10-year, 30-year).2
Time Span: Multi-decade historical series. The actual length depends on what was available of FRED.3But we are limiting the number of years to the last 10 before current.
Frequency: Daily closing rates
Processing: For each year, and month by month, we calculated the monthly change of rates: last-day rate minus first-day rate. Data reshaped so each month could be analyzed independently.
Visualization: Created box plots for each Treasury maturity to display distribution of monthly changes over the years, each box represents one month of the year.
Median highlighted in red; outliers shown as orange circles.
Quantitative Comparison: For all series (durations), years and months, "delta" was calculated as the difference between the last day of the month rate and the first day of the month rate. Then we calculate D (per series per year) as the difference of September delta and the mean of the other 11 months deltas for that year.
If (i) represents the number of years we have data for, and (j) is the month index (1-12), then:
δi,j = rate of last day of month j - rat of first date of month j, for year i
D = mean(δi,j, where j ≠ 9)
μ9 = mean(δi,j, where j = 9)
The values of D are used to do:
- hypothesis with H0: μ9 = D and H1: μ9 > D.
- calculate the Cohen ratio per each series.
The results are shown in the table below or 1 month, 2 years, 10 years and 30 years.
| series | t_stat | p_vlaue | Cohen ratio |
|---|---|---|---|
| DGS1MO | -1.1975 | 0.8706 | -0.0001 |
| DGS2 | 1.1489 | 0.1387 | 0.0001 |
| DGS10 | 2.0835 | 0.0319 | 0.0002 |
| DGS30 | 1.8412 | 0.0477 | 0.0002 |
Rationale: We limited the calculations to 10 years. So to use the t-test we needed to ascertain or assume normality.4 The Cohen ratio was added to provide additional insight. 5
Assuming significance level of 0.05, we see that the 10 and 30 years p-value are below that. That means we have enough evidence to reject the null hypothesis. I.e. the September effect does exist. The orange bar in each plot, show this year, 2026, change in September rates (last day - first day). In 2026, there was a huge spike in all rates, and the latter was attributed to war, inflation expectation, FED rate hike, etc.
1 - The phenomenon is notice over the last 10 years or so, we we are limiting the data to the last 10 years, so we can test the claim as is.
(2) - The 20 year treasury data was missing a "chunk" from 1986 till 1993. Never the less, we have 45 years of whole year data.
(3) - FRED
(4) - I will soon be adding a study to show the "normality", or lack of, the for the above data sets include more than 10 year.
(5) - Cohen'h