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

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:

Saturday, September 27, 2025

S&P After 10%+ First Three Quarters and Positive September | Wayne Whaley

Since 1950, whenever the S&P 500 gained 10% or more in the first three quarters and September was positive, the fourth quarter has historically been positive 80% of the time (16 out of 20 years). The average gain for the fourth quarter during these years is 4.42%. The best performance observed was +11.36%, while the worst was a loss of -1.26%.

Looking at 2025, as of September 27, with only two trading days left in the month, the first three quarters of the year have seen a total gain of 12.96%, with 2.84% of that gain coming from September alone.
 
Since 1950, after the S&P 500 had gained 10%+ in first three quarters and with a positive September, the fourth-quarter performance was positive 80% of the time (16-4 up-down) with an average gain of 4.42%.

October: The market has been negative in October 55% of the time (9 years up, 11 down) with an average loss of -0.44%. The best performance was +4.46%, while the worst was -6.86%.

October 20–27: During this specific period, the market has been down 80% of the time (4 years up, 16 down), with an average decline of -1.29%. The best performance was +1.22%, and the worst was -8.23%.

November: In contrast, November has been positive 80% of the time (16 years up, 4 down), with an average gain of +3.41%. The best was a gain of +10.24%, while the worst was a decline of -1.89%.

December: December has been positive 75% of the time (15 years up, 5 down), with an average gain of +1.47%. The best performance was +5.25%, and the worst was -3.39%.

Combining November and December, the performance has been positive 90% of the time (18 years up, 2 down), with an average gain of 4.81%. The best combined performance was +13.57%, while the worst was a modest -0.45%.

The average absolute drawdown in the fourth quarter was -2.66%. The worst was -8.64%, though the period also saw potential upside gains of up to +12.00%.
  
Reference:
 
 
 

See also:

Tuesday, September 16, 2025

“Sell Rosh Hashanah, Buy Yom Kippur” | Hurst Cycles Suggest Otherwise

The Wall Street adage “Sell Rosh Hashanah, Buy Yom Kippur” suggests that traders can profit by shorting the S&P 500 at the start of Rosh Hashanah (Monday, September 22, 2025) and covering to go long on Yom Kippur (Wednesday, October 1, 2025), capitalizing on a historical tendency for market declines during this period. And statistics bear this out. 
 
"Sell Rosh Hashanah at the high of the day, and cover on Yom Kippur at the low" 
vs. "Buy Rosh Hashanah at the low of the day, and cover on Yom Kippur at the high." 

The table above examines the performance of the S&P 500 from 1970 to 2024, analyzing extreme prices ("Sell Rosh Hashanah at the day's high and cover at Yom Kippur's low" vs. "Buy at Rosh Hashanah at the day's low and cover at Yom Kippur's high") and calculates percentage returns for each year, averages, medians, and counts positive/negative years to evaluate the profitability of each strategy:  

Sell Rosh Hashanah, Buy Yom Kippur: Average profit 2.31% (median 2.10%), positive in 51/55 years (92.73%).
Buy Rosh Hashanah, Sell Yom Kippur: Average loss 1.42% (median 0.79%), negative in 41/55 years (74.55%). 
 
However, will this year be different, and, contrary to negative seasonality, ‘Buy Rosh Hashanah, Sell Yom Kippur’ be the better option?  
 
Statistically, clearly not—but Hurst cycles analysis suggests otherwise: The 20-week, 80-day, and 40-day cycles bottomed on Monday, September 1, and are pushing higher into early October. The S&P 500 may have already peaked today or could top around tomorrow’s FOMC press conference, before declining into a 20-day cycle trough later this week (New Moon/Fall Equinox) or early next week, and then resuming the uptrend into the major 40-week cycle top around October 6 (±2-3 days)(see also David Hickson’s Bitcoin cycle analysis).
 

Saturday, August 2, 2025

17-0 Turn-of-Year S&P 500 Setup with 7.1% Average Gain | Wayne Whaley

After the 20% pullback in the S&P 500 that occurred from February 19 to April 8, May, June, and July each posted positive returns of 6.2%, 5.0%, and 2.1%, respectively. In the 75 years following 1950, there have only been 17 instances in which the traditional "Sell in May and Go Away" period was marked by three consecutive positive months (May, June, and July): 

 From October 12 to October 27, the performance was 2 wins to 15 losses, with an average loss of 3.0%.
From October 27 to January 18, the record was 17-0, with an average gain of 7.1%.
 
Looking at the following 12 months, from August through July, the outcome was favorable, with a record of 14 wins and 3 losses in this setup. The average gain over this period was 12.6%, compared to a more typical yearly gain of 9.5%.

Interestingly, the only negative month during the following year was October. Specifically, from October 12 to October 27, the performance was 2 wins to 15 losses, with an average loss of 3.0%. However, from October 27 to January 18, the trend reversed dramatically, posting a perfect 17-0 record with an average gain of 7.1% over 11.7 weeks.

Tuesday, July 15, 2025

S&P 500 Rally Returns to Midpoint of Long-Term Channel | Deutsche Bank

The S&P 500 has rallied about 25% in 3 months to hit record highs, which seems impressive. But it is only 2% above the February peak; i.e., over the last 5 months, it is up 5% at an annualized rate. And year-to-date, it is up 6.5%, or 12.5% at an annualized rate. In historical context, these numbers do not stand out.

The S&P 500 has just caught back up to the middle of its post Global Financial Crisis channel, 
and price gain so far this year is in line with the long-run median outside of recessions.
 
The median annual gain for the S&P 500 over the last 100 years is about 11.5%. And if one were to look only at years without recessions, it is 13%; for those with positive returns, the median is a whopping 19.5%. Indeed, the S&P 500 trends upward over time with occasional selloffs, and over the last 15 years—i.e., since the Global Financial Crisis (2007–2009)—it has been in a strong but wide channel rising at an annual rate of 12.5%. The rally has just taken it back to the middle of this channel, where it was at the February peak. 
 
 
  » Volatility is the toll we pay to invest. «
 
Since 1980 the median annual drawdown of the S&P 500 is 11% for all years,
and it's the same for election years (red boxes). 
 
»
US stock market is among the three most overvalued in 100 years. « 
 
 Dow Industrials Four-Year Presidential Cycle 2024-2027, Ned Davis Research, 2024.