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Random freezes, missing sound and display glitches usually trace back to one bad driver. Find and replace yours safely.Free scan · under a minuteA preregistered test of a turn-of-month strategy on SPY produced a positive return difference—but failed its prespecified decision rule. The reported estimate was +3.95 basis points per day, yet its 95% confidence interval included zero, a calendar-rotation test returned p = 0.212, and matched-exposure comparisons fell short of the required threshold. That is inconclusive evidence for this particular test, not proof that the effect is gone.
What was tested—and what “turn of month” means here
The turn-of-month effect is the historical claim that equity returns tend to cluster around the transition between calendar months. This test used one specific SPY window: the final trading day of one month plus the first three trading days of the next. It did not test every possible definition of a turn-of-month strategy.
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The author reports daily SPY returns from January 29, 1993, through September 24, 2026: 8,470 return bars in total. The four-bar window accounted for 1,616 bars, or 19.1% of the sample. These figures and the calculations below are reported by the article’s author and were not independently reproduced. Read the author’s account and methods.
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Before analyzing the returns, the author says they froze the hypothesis, statistic, inference methods, decision criteria, and one-run stopping rule in a preregistration file. The author reports the file’s SHA-256 hash as 04396d92f6a45d2ffebff0faff7c4e31cfde983e11d3bdfd5b5bc9f8e7d8cba2. The file itself and the calculations were not independently checked for this article, so the preregistration and hash should be understood as author-reported.
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Why the positive estimate still failed
The window’s reported mean return was +7.28 basis points per day, compared with +3.33 basis points on other days. The difference was therefore +3.95 basis points per day. A positive point estimate is not, by itself, evidence that the rule reliably outperforms the comparison.
The reported stationary-bootstrap 95% confidence interval for the difference ran from −2.02 to +9.80 basis points per day. Because it spans zero, the result is compatible with a negative difference as well as a positive one. A circular-rotation null test returned p = 0.212, which did not meet the preregistered cutoff. The test’s interval used a mean block length of 20 trading days and 10,000 resamples, according to the author.
The preregistered decision required all five clauses to pass. The author reports that the rule failed because the confidence interval included zero, the rotation test missed its cutoff, net returns did not exceed the matched-exposure null’s 95th percentile at the tested costs, and the late-half interval included zero. The five-clause bar was conjunctive: a favorable point estimate could not compensate for a failed clause.
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How the comparison was designed
A calendar-alignment test
The circular-rotation test preserved the return series while rotating the labels that identify the calendar window. The stated rationale was to retain the return series and the count and spacing of labeled days while testing whether the observed calendar alignment was unusual under that null. Its p-value of 0.212 did not clear the preregistered threshold.
A baseline with comparable exposure
Comparing a strategy invested about one-fifth of the time only with cash would confound the timing rule with how often it is invested. The author instead compared it with randomly positioned sets of four contiguous bars within each month, matching the strategy’s exposure. The rule’s results came close to, but did not reach, the specified 95th-percentile benchmark.
Costs and delayed execution
At a reported round-trip cost of 2 basis points, the rule’s annualized return was 3.25%, versus 3.38% for the matched-exposure null’s 95th percentile; the rule ranked at the 93.8th percentile. At 5 basis points, it returned 2.88%, versus 3.02% for that benchmark, ranking at the 93.7th percentile. Both comparisons missed the preregistered 95th-percentile bar. The author also reports that delaying execution by one bar reduced gross return from 3.50% to 3.01%. These are backtest figures reported by the author, not independently reproduced results.
What the sample split says
The author reports positive differences in both halves: +5.84 basis points per day for 1993–2009 and +2.03 basis points per day for 2010–2026. Neither half was individually significant, and the late-half confidence interval included zero, so the split-sample requirement failed. Matching signs are not enough to establish a repeatable effect when the required evidence is absent.
Why an alternative window is not a successful result
The article reports one alternative window with a larger difference, +8.35 basis points per day, and p = 0.020. But the author says it did not pass the Holm-corrected threshold of 0.0167 set for three alternatives. The author also notes that the plausible search space extended beyond those three windows, which would make selection concerns more serious, not less.
That result is best treated as a hypothesis for a separately designed follow-up. Selecting a promising window after seeing results and presenting it as though it were the preregistered winner would weaken the protection that preregistration is meant to provide.
How this result fits older calendar-pattern evidence
The failed test does not erase earlier findings, which studied different samples and definitions. Robert A. Ariel’s 1987 paper, A monthly effect in stock returns, reported that mean stock returns were positive immediately before and during the first half of calendar months and indistinguishable from zero during the second half in that paper’s sample. Ariel’s finding is historical context, not a direct test of this article’s four-trading-day SPY rule. See Ariel’s paper.
A J.P. Morgan summary reproduced in an SEC-hosted filing gives historical annualized S&P 500 returns through October 2022 of 26.06% for the first four trading days of a month, 1.53% for middle days, and 18.72% for the last two trading days. The corresponding shares of positive-return days were 56%, 52%, and 54%. Those grouped historical statistics use different bins from the SPY test and are not a forecast or proof that a trading rule can capture the pattern after costs. See the SEC-hosted filing.
Calendar patterns have been attributed to possible mechanisms such as institutional portfolio adjustments, pension reinvestments, or systematic retail mutual-fund investments. The filing cautions that other factors may be responsible and that persistence is not assured; these explanations should not be treated as established causes. For broader historical context on calendar effects, see Richard Thaler’s overview for the American Economic Association.
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What the failed test can and cannot establish
What it establishes about this test
- Under the author’s stated SPY window, sample, methods, and preregistered decision rule, the reported evidence did not pass.
- The point estimate was positive, but the interval and rotation test did not distinguish the difference from zero under the stated criteria.
- The matched-exposure results at the reported costs were near the required benchmark but below it.
What it does not establish
- It does not prove that the turn-of-month effect is absent or has disappeared.
- It does not establish that other window definitions, assets, indices, or countries behave the same way. The analysis covers SPY only and reports no cross-instrument replication.
- It does not show that a different strategy is profitable, or that this rule is a trade recommendation.
The author estimates that roughly 2.2 times the sample—about 75 years at the stated volatility—would be needed to resolve an effect of the estimated size. That is the author’s power estimate, not an independently evaluated calculation. The practical implication is limited but important: the available test was not precise enough to settle whether a small effect of this size exists.
Transparency and data caveats
The author says adjusted historical data can be revised retroactively and that the result is tied to a hashed data snapshot. The author also discloses that the first run computed from an in-memory data pull while saving a snapshot rounded to six decimal places; after fixing the I/O behavior, the author reran the same snapshot and reports that the verdict and all five clause outcomes were unchanged. This is a disclosure by the author, not an external audit of the code, snapshot, or calculations.
The useful lesson is methodological: specify the window and decision bar before looking at outcomes, use a null that reflects the question, account for exposure and costs, and report near-misses as near-misses. A preregistration cannot make an estimate precise or guarantee that its assumptions are right, but it makes it harder to quietly change the standard after seeing the result.
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