Showing posts with label Statistics. Show all posts
Showing posts with label Statistics. Show all posts

Wednesday, August 26, 2026

Third-to-Last Trading Day of August: 90.5% Bullish Record | Jeff Hirsch

August's third-to-last trading day is a calendar favorite for the bulls. Over the past 21 years, the S&P 500 has risen 19 times—a 90.5% win rate—making it one of only two days of the year with 19 gains in 21 years; the other is the first trading day of July.

 Bullish Third-to-Last Trading Day of August (2005-2025).

The Dow Jones Industrial Average has an even stronger claim: its third-to-last trading day of August has been its best-performing day of the entire year, also gaining 19 of 21 times (90.5%).

This unusually strong late-August bias may reflect seasonal positioning: institutions prepare portfolios for the fall, retirement and investment contributions continue, and investors anticipate upcoming earnings, economic data, and Federal Reserve developments. With August ending, markets also begin positioning for the historically active final four months of the year.

Saturday, August 22, 2026

Price Performance vs. Zodiac Signs, Lunar Phase & Mercury Retrograde

S&P 500 (SPX) performance by color-shaded Zodiac Signs (2016–2026),
New Moon, Full Moon and rosa-shaded Mercury Retrograde periods. 
S&P 500 Strategy: Go long during bullish zodiac phases and short during bearish phases; hold through phase end with a 2% stop-loss (1% tighter stops improved results). Starting with $1,000, a 10 year walk-forward case study produced $5,410. The win rate exceeded RSI, Stochastic, and MFI, slightly outperforming Stochastic. Low-win-rate signs (e.g., Gemini at 39%) can be omitted. 

Augmented version: Enter long only when Stochastic (14,1,3) ≤20 during a bullish phase; enter short only when ≥80 during a bearish phase; hold through the full phase. Python backtest: $18,571.79 over two years with a 66.67% win rate. 

Using 10 years of S&P 500, Mercury retrograde periods frequently preceded major pivots, with post-retrograde directional flips.
Upcoming Events (dates and times for New York City):
Jul 29 (Wed), 2026 07:34 EDT — Full Moon (Buck Moon)
Aug 12 (Wed), 2026 12:11 EDT — New Moon
Aug 23 (Sun), 2026 00:19 EDT — enters Virgo (150 deg from 0 deg Aries = vernal equinox)
Aug 27 (Thu), 2026 19:18 EDT — Full Moon (Sturgeon Moon / Lunar Eclipse)
Sep 10 (Thu), 2026 21:12 EDT — New Moon
Sep 22 (Tue), 2026 16:05 EDT — enters Libra (180 deg) (Fall Equinox)
Sep 26 (Sat), 2026 05:49 EDT — Full Moon (Corn / Harvest Moon)
Oct 10 (Sat), 2026 08:51 EDT — New Moon
Oct 22 (Thu), 2026 23:00 EDT — enters Scorpio (210 deg)
Oct 24 (Sat), 2026 03:02 EDT — Mercury Retrograde Begins
Oct 25 (Sun), 2026 15:38 EDT — Full Moon (Hunter's Moon)
Nov 08 (Sun), 2026 23:02 EST — New Moon
Nov 13 (Fri), 2026 11:01 EST — Mercury Direct Resumes
Nov 21 (Sat), 2026 16:00 EST — enters Sagittarius (240 deg)
Nov 24 (Tue), 2026 00:53 EST — Full Moon (Beaver Moon)
Dec 08 (Tue), 2026 15:49 EST — New Moon
Dec 21 (Mon), 2026 10:50 EST — Capricorn (270 deg) (Winter Solstice)
Dec 23 (Wed), 2026 09:28 EST — Full Moon (Cold Moon)
 
Volatility S&P 500 Index (VIX; 2016–2026) 
 
Bitcoin (BTCUSD; 2016–2026) 

Gold (XAUUSD; 
2016–2026) 

Silver (XAGUSD; 
2016–2026)
 
WTI Light Crude Oil (XTIUSD; 
2016–2026)
 
Dollar Index (DXY; 
2016–2026)
 
Reference:
 
Forecast Based on "Moon Synodic + Sun in Virgo" Model | Sergey Tarassov
 
 
 [HERE]
 

Monday, June 29, 2026

25-0 S&P 500 Setup for June 26 to July 15 | Wayne Whaley

After the S&P 500 fell 1.95% in the week of June 19-26, historical analysis identified the 25 closest matching weeks from the past 50 years, where that same period declined between 0.1% and 3.8%. 


In every one of those 25 cases, the index rose over the following 19 days (June 26–July 15), averaging +3.33% gains. Most showed only minor pullbacks, and in 12 cases the June 26 low held as the bottom. 

This pattern suggests a strong bullish tendency for the next couple of weeks based on history. 

 
Key Turning Dates of the Solar Cycle vs. the DJIA, 1885-2015.
 
See also:

Monday, May 25, 2026

May 24 to June 5: Fifth-Ranked Bullish S&P Seasonal Period | Wayne Whaley

My Top Ten Seasonal Model evaluates the performance of every time frame in the year, from 7 to 35 calendar days, and identifies the top 10 mutually exclusive periods.

May 24 to June 5, S&P positive in 37 of 50 years with 1.21% average return
and only one 3%+ loss, while Nasdaq averaged 1.77% with 38 up periods.

May 24 to June 5, which I refer to as the Post-Memorial Day Rally, is my 5th-ranked S&P seasonal trade of the year for both the S&P and the Nasdaq when comparing all time frames across the year. 
 
Notably, over the last 50 years, the S&P experienced only one 3% loss (1981) during this period, versus ten different years that recorded 3% gains. The last ten cases have been positive.
 
 
See also:

Saturday, May 23, 2026

S&P 500 Four-Year Election Cycle: Ranking All 48 Months | Wayne Whaley

If you are into Election Cycle tendencies, you might possibly find this study of interest. I have S&P data back to its origin in 1957 and S&P proxy data, via Dow analog, back to 1930. Dating back to 1930, I took the time to calculate my personal performance rating for each of the 48 months of the Four-Year Election Cycle, which is based on an average with outliers underweighted. The rating measure ranges from -100 to +100 in -3 to +3 standard deviation fashion.

Pre-election Januarys lead, midterm election Junes lag, with 2026 resilience challenging weak June seasonals. 
 
Reasonable chance of posting a win this year?

The left side of the table above contains the top 24 rated months through April of 2026 of the Four-Year Election Cycle in the sample set, while the right side contains the bottom 24 months. The 3% column is the performance in those months which had a 3% move in either direction. Likewise for the 5% column.

Four of the top ten months in this study occur in Pre-Election years, with Januarys (20-4) at the top. While four of the bottom ten occur in Midterm Election years. Owing largely to the seven Junes of those 24 in the test set which incurred 5% losses, June of Midterm Election years brings up the rear.

The S&P has exhibited a resilience to many a headwind in 2026 which, in my humble opinion, merits respect, and the weak June midterm election seasonals should be weighed against many a traditional momentum-based seasonal study that gives June a reasonable chance of posting a win this year. Tis your call.

 
See also:

Thursday, May 21, 2026

The 32-Day Cycle: High-Accuracy Edge in S&P 500 First-Hour Structure

This 32-calendar-day cycle is a fixed periodicity in the S&P 500 cash index (SPX), in which ‘Early Highs’ and ‘Early Lows’ during the first 90 minutes (10:00 to 10:55 a.m., center time: 10:30 a.m. ET) of the New York regular trading session follow a precise pattern.
 
Projected Early Highs and Lows, Daily Bias, and Day-of-Week notes for the SPX (May and June 2026). 
 
Empirically derived from Jeffrey Tennant's daily forecasts, this cycle demonstrates a 99.3% repeat rate (136/137 valid pairs) across a 13-month sample from late April 2025 through May 2026, spanning a full spectrum of typical market conditions.
 
Jef
frey Tennant forecast for May 22, 2026
[Note: The scope here excludes the MEJT system and focuses solely on the 32-day cycle (dates in blue).
 
Early Low days exhibit a strong bullish bias, with Close > Open in 69.5% of cases (average return: +0.34%). Tennant frequently characterizes these sessions as 'typically bullish, with a final-hour high.' By contrast, Early High days show a mild negative-to-neutral bias over the sample period (average: −0.09%). This edge is materially amplified on specific weekdays: Monday Early Low stands out as the highest-conviction setup, with a 74.1% bullish close rate, an average gain of +0.45%, and the strongest asymmetry in the dataset. Conversely, Friday Early High represents the clearest cautionary signal (41% bullish, average: −0.17%).
 
 
Early Low and Early High Days Performance by Weekday.
Early Low has the strongest bullish edge on Mondays (74.1% positive days).
Early High on Fridays shows the clearest negative bias (only 41% bullish days, largest average loss).
Validated via direct sequence matching and daily OHLC backtesting (with 30-minute or lower timeframes being optimal), this cycle enables consistent projection of high-probability intraday structures and daily directional bias. The sequence, or similar 32-day patterns, likely extends to other trading sessions and instruments.
 
S&P 500 Average Open-to-Close Change & Average Daily Range by Weekday (June 2025 to May 2026):
Monday Strongest: +12.66 points (+0.19%).
Monday Calmest: 56.30-point daily range.
Thursday Weakest: -10.65 points (-0.15%).
Thursday most Volatile: 69.73-point daily range. 

See also:
 

Tuesday, May 19, 2026

Pre- and Post-Memorial Day Seasonal Patterns in US Stock Indexes

Memorial Day weekend (May 23-25, 2026) has become the unofficial start of summer for many Americans, marking a notable transition in financial markets. In recent years, trading activity typically begins a gradual decline shortly afterward—barring major external events—toward a later summer low. 
 
Over the past 20 years, the Thursday before Memorial Day has delivered the strongest average gains across major indices (DJIA +0.07%, S&P 500 +0.18%, NASDAQ +0.34%, Russell 2000 +0.32%). Friday shows a solid percentage of up days—particularly for the NASDAQ (66.7%, +0.38% average)—but with more mixed overall performance. Wednesday is the weakest, with negative average returns. The dataset includes 2025; both median returns and win rates also tend to favor Thursday in several cases.
Market participants refer to this summertime slowdown as the summer doldrums, characterized by anemic volume and often uninspired, range-bound trading on Wall Street. Seasonal volume patterns since the 1960s for the NYSE and 1970s for the NASDAQ show this typical lull, with daily trading volumes frequently dropping 20-40% from winter peaks, reaching troughs particularly in late July and August as vacations reduce institutional participation.

In the lead-up to the holiday, historical performance presents mixed yet distinctive results. Thursday before Memorial Day has consistently delivered the strongest average gains across the DJIA, S&P 500, and Russell 2000 in 21-year analyses. Friday, the last trading day before the long weekend, records a higher proportion of advancing sessions for most major indexes, with the NASDAQ standing out at a 66.7% win rate, an average gain of 0.38%, and nine up closes in the last ten years. That said, this Friday session also tends to feature lackluster, light-volume trading. For the DJIA, results have been essentially neutral over extended periods, with an even split of up and down closes and a modest average decline of approximately 0.05%.
 
 May Stock Market Performance in Midterm Election Years:
Early May Strength Turns to Chop Until Late Month Pop.

Following the holiday, market behavior often turns more muted and, in recent decades, weaker. The Tuesday after Memorial Day has shown notable softness, with the DJIA and S&P 500 declining in seven of the last nine observed years, alongside more frequent losses in the NASDAQ and Russell 2000. Broader post-holiday windows, including the full trading week after Memorial Day, performed robustly from the early 1970s through the mid-1990s but have since weakened considerably, with reduced frequency of positive returns and smaller average gains, especially since the late 1990s and after 2010. An event study of returns spanning three days before to three days after the holiday generally aligns with long-term daily averages, showing no pronounced anomaly.

Beyond the immediate sessions, the broader period from Memorial Day to Labor Day (September 7, 2026) has historically produced net positive, albeit modest, results for the S&P 500. The index has advanced in roughly 70% of periods since the early 1970s, with average gains typically ranging from 1.6% to 2.8%. This summer window fits within the broader “Sell in May and Go Away” tendency, during which overall returns tend to be softer than in the November-to-April period, even as the Memorial Day-to-Labor Day segment itself often contributes positively amid the lighter volumes of the doldrums.
 
 
In midterm-election years such as 2026, these summer patterns can intersect with the broader presidential cycle, which historically features heightened volatility and often subdued returns. Midterm years frequently see notable market lows forming between late July and mid-August, aligning with the depth of the summer doldrums, reduced liquidity, and pre-election political uncertainty. Such periods have at times served as bottoming phases, setting the stage for stronger recoveries later in the year or into the following pre-election period, though outcomes vary with prevailing economic and geopolitical conditions.
 
 
 
 
See also: 

Saturday, May 2, 2026

Seasonal Odds Favor S&P 500 Gains Next Week (May 2–9) | Wayne Whaley

The S&P 500’s performance during the week of May 2–9 (Sat-Sat) has historically been fairly neutral over the past 51 years, posting 28 advances and 23 declines for an average gain of just 0.09%. 
 
» Seasonal evidence alongside recent momentum points modestly in favor of higher prices over the coming week. «
 
51-year May 2–9 performance: mostly neutral (+0.09% avg; 28 up / 23 down)
Overall seasonal and momentum bias: modestly bullish for next week
First half of May often mirrors first half of April behavior
2026 April (Apr 1–16): strong +7.09% advance
Strong April (>1.68%) historically: 15 up / 2 down in following week
Weak April (<-0.45%) historically: 6 up / 11 down in following week
Closest strong April cases (2009, 2020) saw +5.89% and +3.50% gains
 
However, a broader set of seasonal studies suggests that stronger recent price trends tend to support continuation, implying a bias toward further gains in the coming week. Notably, the first half of May has often behaved similarly to the first half of April, reinforcing the relevance of the recent April setup.

In the data breakdown, May 2–9 returns are grouped into three 17-year categories based on the S&P’s performance from April 1–16 over the same 51-year history. In 2026, the index rose 7.09% during that April window. In the 17 prior instances where April 1–16 gains exceeded 1.68%, the S&P advanced in 15 of the following May 2–9 periods versus only 2 declines. By contrast, when April 1–16 was weaker than –0.45%, the next-week record flipped to 6 up and 11 down. More specifically, in the two historical cases most comparable to 2026—2009 and 2020, both with April gains above 5%—the S&P followed with strong May 2–9 advances of 5.89% and 3.50%, respectively.

The accompanying ratings system scales outcomes into -3 to +3 standard deviation bands on a -100 to +100 framework, with outliers down-weighted to better reflect typical behavior; readings below -50 or above +50 are treated as trade-alert conditions. While multiple non-seasonal factors can certainly influence market behavior, the combined seasonal evidence alongside recent momentum points modestly in favor of higher prices over the coming week.

Reference:
 
S&P performance after a 10% calendar month: "For me, from a directional signal perspective, it is a bull friendly development but more so because it occurred in the barometrically important month of April than the fact that it was a rare double digit month.
"

See also:

Monday, April 20, 2026

DJIA 2026 vs Top Three Midterm Correlated Years Since 1886 | @Fiorente2

Plotting all 35 midterm-election years for the DJIA since 1886, the spread of outcomes is enormous: In difficult midterm years, the DJIA has fallen by as much as 25% (1966), while in stronger years it has gained up to 45%. The average of ±2% is likely the most realistic expectation right now, given the current environment.
 
Chart 1: DJIA 2026 versus the Top Three Midterm Correlated Years:
1898 = approx. +20% (correlation 0.764)1926 = ended the year flat (0.716)1966 = approx. -20% (0.826)

However, to get a sharper view, the three midterm years with the highest correlation to 2026 DJIA performance (from January through last week) were selected and charted: 1966, 1926, and 1898 (Chart 1).  
  • 1966 has the strongest correlation (0.826).  
  • 1898 (0.764) is the bullish outlier: if 2026 follows that path, the market could go bazooka from here.  
  • 1926 (0.716) sits in the middle, and curiously, its path aligns with the average of the top three.
 
Chart 2: DJIA 2026 vs 1966 and Top Three Composites. In 1966, the DJIA printed its yearly low in early October.
  
Each of these years carries its own resonance: 
  • In 1898, the US was just emerging as a global power through victory in the Spanish-American War. 
  • In 1926, an industrial revolution was reshaping the economy. 
  • In 1966, tariffs, war, inflation, and a punishing midterm election defined the landscape.  
The bias points toward 1966 (Chart 2): The correlation is the strongest, and the themes are too close to ignore: tariffs, a costly overseas conflict with no clear exit, inflation concerns, and a midterm election that may punish the incumbent party. 
 
 
Berkshire Hathaway's cash position has risen to a record above $370B, underscoring a scarcity of attractive valuations and ongoing reductions in holdings such as Apple. Warren Buffett has described recent market pullbacks as modest relative to historical downturns, drawing parallels to the elevated cash levels he maintained ahead of the 1999 dot-com crash and the 2007 financial crisis—periods when major equities ultimately fell by 80–90%.
See also:

Thursday, April 16, 2026

S&P 500 After Rapid 10% Gains: +17% Avg One-Year Return | Alex Krainer

Historical S&P 500 data shows that sharp 10% rallies over a 10-day span tend to exhibit strong follow-through. On average, returns have been approximately +0.6% after one week, +2.5% after one month, and +17% over the following year.

Rapid 10%+ bounces in the S&P 500 (weekly candles), 1980 to 2026.

A review of the weekly S&P 500 chart from 1980 to 2026 highlights multiple instances of these "rapid +10% bounces," marked by green and red arrows. In most cases, these moves were followed by continued upside, though there were notable exceptions—such as the period around 2000.
 
Alex Krainer argues that the current setup differs meaningfully from the 2000  episode. He notes the absence of broadly synchronized overbought conditions among megacap stocks today, and emphasizes that the more significant declines in 2000 occurred only after the index had already fallen below its 40-week moving average.
 
S&P 500 RSI readings above 70 have led to pullbacks in 8 of the last 10 cases over two years, with the other two resulting in flat consolidation. The daily chart (May 2024–April 2026) marks these signals with red arrows for pullbacks and one green arrow, alongside recent price action near 7,000. This suggests an 80% likelihood of a near-term pullback, though prior corrections since the 2025 rally have been relatively mild.
 

Jeffrey Hirsch notes that the S&P 500's 7.57% gain in the first 10 trading days of April 2026 ranks as the second-strongest start to April since 1950.

Gains averaged +10.8% for the rest of the year, with full-year returns positive in 91.7% of cases (+16.2% avg.).

Historically, such powerful early-April momentum has been a bullish signal: in 20 of 24 comparable cases (83.3%), the market delivered further gains over the remainder of the year, with an average advance of +10.8%. Full-year returns were positive in 22 of those 24 instances (91.7%), averaging +16.2%. Hirsch’s data also segments April starts into performance tiers, with 2026 firmly in the top group—where subsequent returns have consistently outpaced those seen in the middle and bottom tiers.

Friday, April 10, 2026

DJIA Up in 77.3% of April OpEx Weeks Since 1982 | Jeff Hirsch

April's monthly option expiration is generally bullish across the board, with respectable gains on the last day of the week, the entire week, and the week after. Since 1982, DJIA has advanced 28 times in 44 years on monthly expiration day, with an average gain of 0.20%. 
 
DJIA has risen in 34 of the past 44 April options-expiration weeks (next week), with an average gain of 1.00%. The S&P 500 and NASDAQ also show strong seasonality, averaging weekly gains of 0.77% and 0.76%. Losses in 2022, 2024, and 2025 have tempered the longer-term averages. 
 DJIA Up in 77.3% of April OpEx Weeks since 1982.
 
 
S&P 500 Up in 65.9% of April OpEx Weeks since 1982.

S&P 500 has a similar record, also with 28 advances and an average advance of 0.15% on monthly expiration day. Monthly expiration day was trending solidly bullish after four or five declines from 2014 to 2018, but took hits in the 2022 bear market, 2024, and in 2025 due to Liberation Day tariff uncertainty.

NASDAQ Up in 63.6% of April OpEx Weeks since 1982.
 
Monthly expiration week also has a bullish track record over the past 44 years. Average weekly gains are +1.00% for DJIA, +0.77% for S&P 500, and +0.76% for NASDAQ. The bullish bias of April monthly expiration also persists during the week after, although average gains have not been as strong, with selling pressure rising (from 2018 to 2022). However, strength has returned since 2023. NASDAQ jumped 6.73% in the week after in 2025.
 April seasonality strong: 2nd-best month for DJIA and S&P; 4th for NASDAQ.
 April 2026 started solidly (+0.52% DJIA, +1.98% NASDAQ) despite geopolitical tension, rising energy costs, April 15 tax deadline.
 Historically, early April outperformed—since 1994, strength shifted to second half.
 Post–April 15 stronger (especially NASDAQ, Russell 2000).
See also: