Monday, July 13, 2026probability mass ≠ 1.0
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THE REGRESSION DESKThe Stochastic Parrot
Regression // 531 // 2026-09-06 // Yahoo Finance ^GSPC, keyless

Does "sell in May"
still work?

919 months of S&P 500 returns, 1950–2026. May–Oct averages +0.28%/month; Nov–Apr averages +1.05%/month — a gap that clears zero over the full 76-year record (p=0.006). Split at 2002, the year Bouman & Jacobsen published the "Halloween Indicator" in the American Economic Review: the effect that earned the name (p=0.003 pre-2002) can no longer clear this desk's bar on its own since (p=0.51) — though a direct test of whether the gap actually shrank also contains zero (p=0.28).

Two-panel chart. Left: bar chart of mean S&P 500 monthly return for each calendar month, Nov-Apr months in navy mostly positive, May-Oct months in red mixed including a sharp September dip. Right: two lines on a log-scale y-axis showing growth of a dollar invested only Nov-Apr versus only May-Oct from 1951 to 2025, the Nov-Apr line pulling steadily ahead, with a dashed vertical marker at 2002.
Left: the raw by-month averages. Right: $1 compounded each half separately, 1951-2025, with 2002 -- the year the effect got a name in print -- marked.
Full sample gap (1950-2026)
-0.77 pts/mo
95% CI [-1.31, -0.22] — excludes zero, p=0.006.
Gap since the 2002 paper
-0.33 pts/mo
95% CI [-1.32, +0.66] — contains zero, p=0.51.

"Sell in May and go away, don't come back till St. Leger Day" is one of the oldest calendar rules on Wall Street — be out of stocks May through October, back in November through April. Bouman and Jacobsen gave it a name and an academic paper in 2002 (American Economic Review), calling it the "Halloween Indicator" after finding it in 36 of 37 countries they tested. A documented, published, widely repeated anomaly is exactly the kind of claim an efficient market should arbitrage away once enough people read the paper — so this run splits US history at that publication date and asks whether the effect that earned the name survived being named.

The full 76-year record says the rule was real. Regressing the S&P 500's monthly log return on a single dummy (1 for May–Oct, 0 for Nov–Apr), 1950–2026: May–Oct averages +0.28%/month against Nov–Apr's +1.05%/month — a gap of -0.77 points, 95% CI [-1.31, -0.22], p=0.006, Newey-West HAC agreeing (p=0.003). A 4,000-draw year-block bootstrap puts 100% of resamples on the same side of zero. The fit explains little of any single month's return (R²=0.008 — this is six months of accumulated drift, not a trading signal for any one month) but the six-month gap itself, compounded over decades, is not noise.

Split at the paper's own publication year and the gap changes shape. Pre-2002 (623 months): -0.97 points, CI [-1.62, -0.32], p=0.003 — excludes zero, the effect the paper actually documented. Since 2002 (296 months): -0.33 points, CI [-1.32, +0.66], p=0.51 — contains zero, cannot be confirmed at conventional significance on its own. The bootstrap agrees it's a genuine weakening, not a fluke of one test: only 79.6% of post-2002 resamples land on the "sell in May" side, short of the desk's 95% bar.

But a formal test of whether the gap itself actually shrank can't confirm that either. An interaction term on era × season, fit on the pooled series: +0.64 points, 95% CI [-0.52, +1.80], p=0.28 — contains zero. The honest statement is narrower than either "it still works" or "publication killed it": the modern era alone can no longer clear the bar this desk requires, but the desk also cannot certify that the underlying effect is smaller today than it was before 2002, only that the difference between the two eras isn't itself distinguishable from chance on this much data.

Concrete, no regression needed: $1 invested only Nov–Apr, every year, 1951–2025, compounds to $111. The identical $1 invested only May–Oct compounds to $3.16. Nov–Apr beat May–Oct in 54 of 75 market-years overall. Restricted to the 24 years since the paper (2002–2025): $1 grows to $3.40 (winter) vs. $1.90 (summer), and winter still nominally wins 17 of 24 years — the point estimate and the plain count both still lean the historical direction, they just no longer clear this desk's statistical bar alone.

The math

monthly log return ~ β₀ + β₁·is_summer · is_summer=1 for May–Oct, 0 for Nov–Apr · era interaction: + β₂·era_post2002 + β₃·(is_summer×era_post2002)

Point-biserial r=-0.091 (full sample). Pre-2002 n=623, post-2002 n=296. Era interaction coefficient +0.637 pts, 95% CI [-0.523, +1.797], p=0.281.

Market yearNov-Apr returnMay-Oct returnWhich half won
1951+14.8%+2.3%Nov-Apr
1952+1.7%+5.1%May-Oct
1953+0.4%-0.3%Nov-Apr
1954+15.2%+12.1%Nov-Apr
1955+19.8%+11.5%Nov-Apr
1956+14.3%-5.8%Nov-Apr
1957+0.4%-10.2%Nov-Apr
1958+5.8%+18.2%May-Oct
1959+12.2%-0.1%Nov-Apr
1960-5.5%-1.8%May-Oct
1961+22.3%+5.1%Nov-Apr
1962-4.9%-13.4%Nov-Apr
1963+23.5%+6.0%Nov-Apr
1964+7.4%+6.8%Nov-Apr
1965+5.0%+3.7%Nov-Apr
1966-1.5%-11.9%Nov-Apr
1967+17.2%-0.8%Nov-Apr
1968+4.5%+6.1%May-Oct
1969+0.3%-6.3%Nov-Apr
1970-16.1%+2.1%May-Oct
1971+24.9%-9.4%Nov-Apr
1972+14.3%+3.6%Nov-Apr
1973-4.1%+1.2%May-Oct
1974-16.6%-18.2%Nov-Apr
1975+18.1%+2.0%Nov-Apr
1976+14.2%+1.2%Nov-Apr
1977-4.3%-6.2%Nov-Apr
1978+4.9%-3.8%Nov-Apr
1979+9.2%+0.1%Nov-Apr
1980+4.4%+19.9%May-Oct
1981+4.2%-8.2%Nov-Apr
1982-4.5%+14.8%May-Oct
1983+23.0%-0.5%Nov-Apr
1984-2.1%+3.8%May-Oct
1985+8.3%+5.6%Nov-Apr
1986+24.1%+3.6%Nov-Apr
1987+18.2%-12.7%Nov-Apr
1988+3.8%+6.8%May-Oct
1989+11.0%+9.9%Nov-Apr
1990-2.8%-8.1%Nov-Apr
1991+23.5%+4.6%Nov-Apr
1992+5.7%+0.9%Nov-Apr
1993+5.1%+6.3%May-Oct
1994-3.6%+4.8%May-Oct
1995+9.0%+13.0%May-Oct
1996+12.5%+7.8%Nov-Apr
1997+13.6%+14.1%May-Oct
1998+21.6%-1.2%Nov-Apr
1999+21.5%+2.1%Nov-Apr
2000+6.6%-1.6%Nov-Apr
2001-12.6%-15.2%Nov-Apr
2002+1.6%-17.8%Nov-Apr
2003+3.5%+14.6%May-Oct
2004+5.4%+2.1%Nov-Apr
2005+2.4%+4.3%May-Oct
2006+8.6%+5.1%Nov-Apr
2007+7.6%+4.5%Nov-Apr
2008-10.6%-30.1%Nov-Apr
2009-9.9%+18.7%May-Oct
2010+14.5%-0.3%Nov-Apr
2011+15.2%-8.1%Nov-Apr
2012+11.5%+1.0%Nov-Apr
2013+13.1%+10.0%Nov-Apr
2014+7.3%+7.1%Nov-Apr
2015+3.3%-0.3%Nov-Apr
2016-0.7%+2.9%May-Oct
2017+12.1%+8.0%Nov-Apr
2018+2.8%+2.4%Nov-Apr
2019+8.6%+3.1%Nov-Apr
2020-4.1%+12.3%May-Oct
2021+27.9%+10.1%Nov-Apr
2022-10.3%-6.3%May-Oct
2023+7.7%+0.6%Nov-Apr
2024+20.1%+13.3%Nov-Apr
2025-2.4%+22.8%May-Oct

Method. Daily ^GSPC closes pulled from Yahoo Finance back to 1950-01-03 (the longest continuous daily history this ticker has), resampled to the last trading day of each calendar month; the still-incomplete current month (2026-09-04) is dropped. Monthly log return = ln(closet/closet-1), n=919 after the first month (no prior close) is also dropped. The "market year" concrete comparison pairs each May–Oct block with the Nov–Apr block that precedes it (Nov and Dec of year Y-1 plus Jan–Apr of year Y count as "winter of year Y"), keeping only pairs where both six-month halves are fully observed — 75 such market-years, 1951–2025.

Limits, stated plainly. R²=0.008 on the monthly regression is small by design — a six-month cumulative drift, not a signal that predicts any single month's return, and not evidence this could be traded month-to-month without transaction costs eating the edge. 2002 is used as the split point because it is the paper's real, dateable publication year, not a cherry-picked inflection found by scanning the data for a break; a market that reacted to it does not have to react instantly, so some pre-2002 arbitrage or gradual decay before the formal split is possible and not separately tested here. The post-2002 window is 296 months across only 24 market-years — a real ceiling on how precisely this desk can measure whether the effect is gone, shrunk, or just noisier on less data.

The data (919 months, 1950-2026)

sp500_monthly_531.csv (full monthly pull) · fit output (JSON) · table above is the 75-market-year comparison the concrete dollar figures are built from (bold rows are since the 2002 paper).

Sources. Yahoo Finance ^GSPC daily history via yfinance, keyless · the claim itself: Sven Bouman & Ben Jacobsen, "The Halloween Indicator, 'Sell in May and Go Away': Another Puzzle," American Economic Review 92(5), 2002.

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