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

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.

Sunday, July 6, 2025

The S&P 500 Jumps 26% in 86 Calendar Days: What's Next? | Wayne Whaley

The S&P finished the 4th of July week at 6,279.35 and is now up 6.76% for 2025 and 13.4% over the last 12 rolling months (July 4 - July 4), currently residing at an All Time High for at least the three day weekend. 
 
You may recall that the S&P experienced an 18.9% selloff from the February 19th Close of 6,144.15 to the April 8th Close of 4,982.77, exceeding 20% if measured vs the April 8th intraday Low of 4,910.42. From that 4,982.77 Closing Low on April 8th, the S&P has now advanced 26.0%, doing so in less than a Quarter, 86 calendar days (April 8 - July 3) to be precise.  

The S&P surged 26% in just 86 days, reaching another all-time high, and has now risen 6.76% in 2025. 
Historical data shows similar rallies led to gains of 19.2%+ over the next year.
 
Looking back through post 1950 history, I can only find five prior occasions in which the S&P has advanced 25% in less than a Quarter and none of those five occasions were anywhere near an impending top. 

Certainly, one would prefer to have more than five data points from which to draw conclusions upon which to base one's market exposure but the magnitude and uniformity of the advances across the following 12 months in those five cases appears worthy of our respect. All five cases were positive over the following 1 to 12 months, up at least 19.2% one year later, 31.7% on average. None of the five cases experienced a 4% drawdown as measured from the signal Date.
 
July 5, 2025
 

Saturday, June 28, 2025

What the S&P Historically Did After Similar V-Shaped Rallies | SubuTrade

@SubuTrade highlights a rare V-shaped recovery in the S&P 500, surging 18% from a low on April 7, 2025 to a new high by June 27, 2025, a pattern historically linked to strong gains, with data from 11 past instances showing an average 1-month gain of 2.0% and a 3-month gain of 6.9%, though outcomes vary widely (e.g., -8.1% to +17.7%).

S&P 500 after it rallies 18% to a 1 year high within 3 months (1927-present).

This rebound aligns with unexpected US-China trade talks resuming in May 2025, reducing tariffs from 145% to 30% and lifting export restrictions on rare earth minerals, a move that boosted market confidence despite initial fears of a recession, as reported by Reuters on June 27, 2025.

Historical analysis of similar recoveries suggests caution, as a 2020 study in the Journal of Financial Economics found V-shaped rallies often precede volatility, with a 30% chance of a correction within 6 months, challenging the bullish optimism.

 

See also: 

Saturday, May 17, 2025

"Three Day Whaley" Predicting 20% Average Annual Return | Wayne Whaley

When the S&P 500 experiences a one-day upside move of three standard deviations or more, there is often a tendency for the index to undergo some level of profit-taking (consolidation) over the next couple of days. However, if the index defies this tendency and follows the initial surge with two consecutive positive days, it signals strength. This pattern, known as the "Three Day Whaley," is a notable market move deserving of attention.

 The "Three Day Whaley" signal has a perfect 30-0 record since 1950
for predicting positive annual returns averaging 20.2%.

Volatility has increased over the past 75 years. The setup for this pattern requires the S&P to post a move on Day 1 that reflects the volatility during that specific period, followed by two consecutive positive days. The threshold for that initial move has evolved from around 2.25% in 1950 to 3.25% in 2025.

On May 12-14, the S&P met the criteria for this setup with a three-day sequence of 3.25%, 0.76%, and 0.10%—its first occurrence since March 26, 2020, which was followed by a 50.55% annual gain.

Since 1950, the S&P has gone 30-0 in the year following this setup, with an average annual gain of 20.2%. All 30 instances have seen at least a 7.5% gain, and only four of the 30 cases experienced a double-digit drawdown. The first-day threshold requirement can be found in column 3 (DAY1 THHLD) in the table above.

Sunday, March 24, 2024

S&P 500 March-April 2024 Seasonality │ Jeff Hirsch & Wayne Whaley

After 5 months of solid gains, are markets ready for a pause? Bullish Presidential Cycle Sitting President Pattern flattens out the mid-February to late-March seasonal retreat considerably without 2020 in the average.

 'Best Six Months' ends in April.

April is the final month of the “Best Six Months” for DJIA and the S&P 500. From our Seasonal MACD Buy Signal on October 9, 2023, through (March 21, 2024), DJIA is up 18.4% and S&P 500 is up 20.9%. Fueled by interest rate cut expectations and AI speculation, these gains are approximately double the historical average already and could continue to increase before the “Best Months” come to an end.


This AI-fueled bull market has enjoyed solid gains since last October and will likely continue to push higher in the near-term, but momentum does appear to be waning with the pace of gains slowing. With April and the end of DJIA’s and S&P 500’s “Best Six Months” quickly approaching we are going to begin shifting to a more cautious stance. We maintain our bullish stance for 2024, but that does not preclude the possibility of some weakness during spring and summer.
 
 
 
THE CORRELATION MODEL SEES A NEGATIVE LAST WEEK OF MARCH FOR THE S&P. Provided a time frame of interest, my correlation model calculates the Correlation Coefficients (-1 to +1) for the past performance of 4165 different time frames over the prior 3 months vs the performance for the time frame of interest in search of the period which has demonstrated the most barometric acumen in predicting the performance of the upcoming time frame of interest. 
 
This week I ask the model for it’s prognosis for the S&P in the last week of March. It responded that the prior ten calendar days (Mar10-24) had a very uncanny track record of forecasting the last week of March with those 2 time frames having a very strong NEGATIVE correlation which doesn’t bode well for next week given that March 10-24 was up 1.63% this year.  
 
Note the 3-10, March 24-31 performance in the far right category below in those 13 prior years where March 10-24 was greater than 1.2% for an avg wkly loss of 0.74% with 1% moves 1-7 to the downside.  This contrasts dramatically to the 11-2 performance when March 10-24 was less than -0.5%.  Fingers crossed that it is wrong this year. 
 
The outlook for April is much brighter. 
 
  
Reference: 
 
[ oftentimes true: ]
 
In Bull Markets, New Moons are Bottoms, and Full Moons are Tops. 
In Bear Markets, New Moons are Tops, and Full Moons are Bottoms.
 
The SoLunar Rhythm in March 2024.