to your HTML Add class="sortable" to any table you'd like to make sortable Click on the headers to sort Thanks to many, many people for contributions and suggestions. Licenced as X11: http://www.kryogenix.org/code/browser/licence.html This basically means: do what you want with it. */ var stIsIE = /*@cc_on!@*/false; sorttable = { init: function() { // quit if this function has already been called if (arguments.callee.done) return; // flag this function so we don't do the same thing twice arguments.callee.done = true; // kill the timer if (_timer) clearInterval(_timer); if (!document.createElement || !document.getElementsByTagName) return; sorttable.DATE_RE = /^(\d\d?)[\/\.-](\d\d?)[\/\.-]((\d\d)?\d\d)$/; forEach(document.getElementsByTagName('table'), function(table) { if (table.className.search(/\bsortable\b/) != -1) { sorttable.makeSortable(table); } }); }, makeSortable: function(table) { if (table.getElementsByTagName('thead').length == 0) { // table doesn't have a tHead. Since it should have, create one and // put the first table row in it. the = document.createElement('thead'); the.appendChild(table.rows[0]); table.insertBefore(the,table.firstChild); } // Safari doesn't support table.tHead, sigh if (table.tHead == null) table.tHead = table.getElementsByTagName('thead')[0]; if (table.tHead.rows.length != 1) return; // can't cope with two header rows // Sorttable v1 put rows with a class of "sortbottom" at the bottom (as // "total" rows, for example). This is B&R, since what you're supposed // to do is put them in a tfoot. So, if there are sortbottom rows, // for backwards compatibility, move them to tfoot (creating it if needed). sortbottomrows = []; for (var i=0; i
April 2026 saw positive changes for the ten worst performing stocks the S&P 500 (Index: INX) served up for Thanksgiving 2025.
Since 28 November 2025, the 503 stocks that make up the market-capitalization weighted S&P 500 index have collectively risen to 104.2% of their value on the day after Thanksgiving Day in 2025.
But when similarly weighted by their market caps into their own index, the ten worst performing stocks of the S&P 500 in 2025, a.k.a. the Thanksgiving Leftover stocks, have collectively fallen to 95.5% of their value on the day after Thanksgiving 2025. Still, that's quite an improvement over where there were almost a month ago when they bottomed at 90.3% of their post-Thanksgiving Day level, even though it would have been outperformed by the entire S&P 500 index.
It could even be much worse. Over the same five month interval, an equal-weighted index of the same ten Thanksgiving Leftover stocks have fallen to be worth just 89.1% of their recorded value at the close of trading on 29 April 2026. Together, they had plunged as low as 80.5% of their day after Thanksgiving Day level on 27 March 2026 before proceeding to stage a recovery through April 2026.
The following chart shows how each of these groupings of stocks, the S&P 500 index and the ten Thanksgiving Leftover stocks, both market cap-weighted and equal-weighted, have fared since 28 November 2025.
As a group, the Thanksgiving Leftover stocks are clearly still losers with respect to the whole S&P 500 index. But individually, three of these ten stocks have outperformed the entire index in the five months since 28 November 2025.
The next chart tracks how each of the ten Thanksgiving Leftover stocks have performed over this period, showing their value on 29 April 2026 as a percentage of their value on 28 November 2025:
In previous editions of this series, we've focused on the worst of 2025's ten worst S&P 500 stocks. But the gains of three stocks are clearly putting the whole index' performance to shame.
Dow Inc. (NYSE: DOW) has done the best of the bunch through 29 April 2026, increasing to 165.8% of its value on 28 November 2025. The chemical company's stock has benefited from the restructuring of its business to focus on growth opportunities, which led its stock to rise from $23.85 on 28 November 2025 to $32.65 on 13 February 2026. Since then however, the company has seen its forecast earnings soar along with other publicly-traded chemical companies as a result of the Iran war because the geopolitical event has disrupted the operations of their largest international competitors in the Middle East.
The second-best performing Thanksgiving Leftover stock is Molina Healthcare (NYSE: MOH). The health insurer has seen quite a lot of volatility in 2026, but in the last few weeks, its stock has sharply risen because it beat its earnings expectations for the first quarter of 2026 by a wide margin. Molina Healthcare accomplished this result by focusing on controlling its costs, while the company has benefited from the escalation of Medicare reimbursement rates that were announced earlier in the month.
The third Leftover stock doing better than the S&P 500 is Deckers Outdoor (NYSE: DECK). On 29 April 2026, the shoe company's stock was 115.1% of its 28 November 2025 level. Deckers Outdoor has fallen since peaking after it announced strong earnings near the end of January 2026, but still remains above the S&P 500's level.
In any case, we now have an answer to the question we raised at the end of our previous edition of this series: If you were going to place a bet on the outcome, would you take the over or the under for the Thanksgiving Leftover Stocks given where they were at a month ago? Readers who took the over would be winners.
But what about now? If you were offered a new chance to place a bet for where the Thanksgiving Leftover stocks will be at the end of May 2026, compared to their level at the close of trading on 29 April 2026, would you take the over or the under?
Not that it's much help, but there's a reason why so many commercials for trading firms carry the disclaimer: "Past performance is not indicative of future results". With that in mind, if you won the last time around, would you go for double or nothing?
Labels: SP 500, stock prices, thanksgiving
From Our World In Data, here's an interactive chart showing how life expectancy for Americans who have reached the indicated age has changed from birth (for Americans born from 1880 through 2023) and for those who have reached the indicated age (from 1933 through 2023):
As of 2023, U.S. life expectancy for all age groups has more than fully recovered from 2020's Coronavirus Pandemic. Here is a static version of the chart that we created after creating an alternate interactive version of the chart using Datawrapper's data visualization tools.
Labels: data visualization
Going by Mars' calendar, the third quarter of Mars Year 38 (MY38) ended on Friday, 24 April 2026. Sadly, the Red Planet's nascent economy remained stalled with no new rock samples either drilled or stored for future export by the Mars Perseverance rover during the 146 (Earth) days of the quarter. Mars GDP' for the quarter is therefore $0.
The following video provides a very brief introduction to the work the Mars Perseverance rover has done that counts as Mars' only economic activity at its current phase of exploration.
At present, there is no feasible path for the export of the collected samples either stored on the rover or stored at a depot location on the Martian surface. Even the least costly proposals for a sample return mission were determined to be too expensive to execute with available technologies, resulting in the funding for continued development for it being cancelled in January 2026.
The following chart shows the economic activity generated by the Mars Perseverance rover since it has been on Mars, by Martian year and quarter:
The lack of a viable means to return the Perseverance samples doesn't mean those samples won't ever be collected and exported to Earth, but it underscores the failure in the original planning that left the sample return portion of the mission too poorly defined. The first missions that do return samples from Mars will almost certainly return the samples they collect using return launch capabilities they specifically transport with them.
For example, Japan's Space Agency plans to launch a probe to Mars' moon Phobos to collect and return a sample, building on the experience the gained from retrieving samples from asteroids. Meanwhile, fabrication has begun on China's probe that will return samples from the surface of Mars.
In other news, we may need to revisit our estimates of the value of the Mars' rock samples currently stocked in the Perseverance inventory and the "Three Forks" sample depot. An experiment conducted on the older Mars Curiosity rover on its drilled rock samples provided evidence of some very interesting organic chemistry:
NASA's Curiosity Mars rover has uncovered a diverse mix of organic molecules on Mars, including chemicals widely considered building blocks for the origin of life on Earth.
The findings, which come from a chemical experiment performed for the first time on another world, reveal that the Martian surface can preserve the kinds of molecules that could serve as signs of ancient life. However, this experiment cannot distinguish between organic compounds from potential past life on Mars and those formed through geologic processes or delivered by meteorites.
Definitively identifying signs of past life would require returning rock samples to Earth.
Here's the paper where the findings were reported on 21 April 2026.
Our Mars GDP estimates are based on the estimated value of the rock samples collected for export by the Mars Perseverance rover, which are in turn based on the value of Martian meteorites that have been found on Earth that have not had similar evidence of organic compounds. Samples that do have these compounds will be substantially more valuable. Should any of the Perseverance samples have such a chemical signature, we will likely need to revise our GDP estimates upward to capture their greater value.
What that value might be has yet to be determined.
Labels: gdp, ideas, technology
The second-longest ever winning streak for the S&P 500 (Index: SPX) was broken on Monday, 20 April 2026. The streak had endured for 13 days, one short of the all time record.
While the streak was broken, all was not bad for Wall Street bulls, who could celebrate the index hitting a new all-time record high closing value of 7,165.08 on Friday, 24 April 2026.
The streak largely came about as a result of the cease fire in the Iran War, which was at risk of ending before President Trump announced an extension during the past week. The markets new highs came in response to that event, the prospect of diplomatic talks between the U.S. and Iran soon resuming, and the strength of earnings out of the market's technology sector.
All these things kept the trajectory of the S&P 500 running along the bottom end of the redzone forecast range we added to the alternative futures chart back in February, as shown in its latest update. That range assumes investors would be focused on the current quarter of 2026-Q2, which they certainly have been, even with the disruption of the Iran war geopolitical event.
The centerline of the redzone forecast range provides a reasonable estimate of where the S&P 500 would have gone in the absence of the Iran war. From Friday, 17 April 2026 through Friday, 24 April 2026, the index has ranged between 2.5 and 3.0% below that trajectory, which is to say the geopolitical event is keeping the S&P 500 from rising even higher.
What happens next for the S&P 500 will be determined by investor reactions to the random onset of new information. Here are the market-moving headlines that affected the trajectory of the index during the week that was.
The CME Group's FedWatch Tool continued to anticipate no Federal Reserve rate cuts in 2026, though with a growing bias toward a quarter point rate cut over time.
The Atlanta Fed's GDPNow tool forecast of real GDP growth in 2026-Q1 ticked down to +1.2%, dipping from its projection of +1.3% growth a week earlier.
Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull who is excited the S&P 500 closed at a new record high of 7,165.08 on Friday, 24 April 2026".
Increasingly capable Artificial Intelligence (AI) technologies are gaining steam in proving long-standing mathematical conjectures. The latest development involves a proof of another one of prolific mathematician Paul Erdős' 1,135 unsolved problems, but unlike AI's previous accomplishments in tackling part of Erdős' legacy, GPT-5.4's proof of Erdős #1196 appears to be genuinely novel.
The previous proofs by AI systems of other Erdős problems did not answer the question of whether the technology was bringing anything new to the table. The problems themselves could be considered "low-hanging fruit", whose unsolved status had more to do with the obscurity of the conjectures within the Erdős collection than their difficulty. When AI developed proofs for them, it more or less followed the playbook that mathematicians had established in proving other Erdős conjectures.
But Erdős' 1196th conjecture is not in that category. Mathematicians had previously taken on the challenge of developing a proof for it, largely turning to the tools of probability and statistics in the process. But instead of copying that approach, GPT-5.4 Pro found the path for proving the conjecture differently. Mathematician Terrence Tao offered this observation:
I had previously stated the opinion that the AI-generated proof had inadvertently highlighted a tighter connection between the anatomy of integers and the theory of Markov chains than had previously been explicitly noted in the literature. Based on further developments, I would like to update that opinion to the following: the AI-generated proof artefact, when combined with subsequent (and mostly human-generated) analysis, has revealed a tight connection between the anatomy of integers and flow network theory that does not, to my knowledge, have any explicit precursor in the literature (although related uses of Markov chains in adjacent settings do appear in that literature).
The development of the proof was verified using the Lean proof assistant, which we would argue is the secret sauce behind why AI technologies are making such rapid progress in advancing proofs to unsolved problems in the field. The pairing of the technologies is key to the advancement.
Getting back to the novelty of the proof, here's a comment by Jared Duker Lichtman, who developed the first proof of the related Erdős primitive set conjecture as part of his doctoral thesis in 2024.
In my doctorate, I proved the Erdős Primitive Set Conjecture, showing that the primes themselves are maximal among all primitive sets.
This problem will always be in my heart: I worked on it for 4 years (even when my mentors recommended against it!) and loved every minute of it.
[Primitive sets are a vast generalization of the prime numbers: A set S is called primitive if no number in S divides another.]
Now Erdős#1196 is an asymptotic version of Erdős' conjecture, for primitive sets of "large" numbers. It was posed in 1966 by the Hungarian legends Paul Erdős, András Sárközy, and Endre Szemerédi.
I'd been working on it for many years, and consulted/badgered many experts about it, including my mentors Carl Pomerance and James Maynard.
The proof produced by GPT5.4 Pro was quite surprising, since it rejected the "gambit" that was implicit in all works on the subject since Erdős' original 1935 paper. The idea to pass from analysis to probability was so natural & tempting from a human-conceptual point of view, that it obscured a technical possibility to retain (efficient, yet counter-intuitve) analytic terminology throughout, by use of the von Mangoldt function \Lambda(n).
The closest analogy I would give would be that the main openings in chess were well-studied, but AI discovers a new opening line that had been overlooked based on human aesthetics and convention.
In fact, the von Mangoldt function itself is celebrated for it's connection to primes and the Riemann zeta function--but its piecewise definition appears to be odd and unmotivated to students seeing it for the first time. By the same token, in Erdős#1196, the von Mangoldt weights seem odd and unmotivated but turn out to cleverly encode a fundamental identity \sum_{q|n}\Lambda(q) = \log n, which is equivalent to unique factorization of n into primes. This is the exact trick that breaks the analytic issues arising in the "usual opening".
Joshua Zelinsky offers perhaps the best framing of the accomplishment and what it could mean for additional progress:
Four things to note: #1196 is a decently well known problem. It wasn’t like Erdős-Straus level fame, but it is well known enough that I was familiar with it. Second, this is not a problem where no one had worked on it; there was a lot of prior work on it and closely related problems. Third, this is not example where the AI made small modifications to things in the literature or recognized that large parts of the problem were in an obscure paper. The approach the AI used is largely a different direction than the literature on this problem went. Fourth, and closely related to three, this proof does look like parts of it will inspire subsequent proofs because it really is going in a different direction which now looks likely to be a productive line of investigation for similar problems.
If this kind of progress continues, the productivity of AI technology in cracking unsolved math problems will be the biggest math story of the year. AI was already the biggest math story of 2025, but 2026 is shaping up to be even more so.
Labels: math, technology
The rolling twelve-month average price of a 10.75 fluid ounce can of Campbell's Condensed Tomato Soup continued falling in the three months since our last monthly price history update.
In that January 2026 snapshot, the rolling average was $1.21 per can, which was down from an average of $1.29 per can in September 2025. In mid-April 2026, that twelve-month average has fallen further, dropping to $1.15 per can.
The falling prices during this period, which coincides with peak "soup season" in the United States, also coincide with deep discounts for consumers at major grocery selling retailers. Here are the prices available to U.S. consumers in April 2026 at ten of the nation's largest grocery-selling retailers and how they've changed since our January 2026 snapshot:
Not all these prices carry equal weight. It would not surprise us to learn that Walmart is the largest single purveyor of Campbell's tomato soup in the U.S., followed by Kroger-affiliated grocery stores. The dominance in sales of these "Big Two" gives more weight to their prices as being more representative of what most Americans pay on average for a can of Campbell's tomato soup.
The falling rolling average price of Campbell's tomato soup is the result of substantial discounts at these major retailers since September 2025. During this period, an iconic 10.75 fluid ounce "Number 1" size can of Campbell's Condensed Tomato Soup has been priced at just $1.00 per can at these biggest sellers.
The following chart presents the price history of Campbell's Condensed Tomato Soup in the 21st century, from January 2000 through April 2026. If you want to see more history, you can find our collected price data extending back to January 1898 here:
Before 2022, it was rare to ever find a can of Campbell's tomato soup priced higher than $1.00 per can. However, because of the high inflation unleashed by the Biden administration, it has been rare since 2022 to find a Campbell's tomato soup on sale for less than $1.00 per can.
But will this sale price hold now that soup season is ending? We'll check back in on the latest prices for our next update in three months.
Image Credit: Campbell's Tomato Soup at Walmart on 20 February 2026 with digital shelf price tags photo by Iron Man on Unsplash.
The climbing limo method of forecasting future GDP in the United States projects the nation's economic output in the recently finished first quarter of 2026 will be around $31.5 trillion.
This estimate assumes the momentum the U.S. economy recorded in growing between 2024-Q4 and 2025-Q2 will be sustained through the recently ended quarter of 2026-Q1. Since the U.S. economy's momentum has come in stronger than expected over the intervening quarters since our last snapshot, it's likely 2026-Q1's will come in above that value, which is not adjusted for inflation.
These projections have been delayed because the Senate Democrats' government shutdown disrupted U.S. economic data reporting. It took until earlier this month to get finalized GDP data for both 2025-Q3 and Q4, which means we can now generate the climbing limo method's momentum-based projections for both 2026-Q2 and 2026-Q3. The following chart visually presents those projections while showing how actual non-inflation adjusted GDP tracked with the model's previous projections:
For the now current quarter of 2026-Q2, the climbing limo GDP forecasting method projects GDP will potentially rise to almost $32.8 trillion. Since that projection was generated with finalized GDP figures for 2025-Q1 and 2025-Q3, long before any impact from the Iran war would be felt, it will be interesting to see how well that forecast tracks with 2026-Q2's actual GDP.
That's because the climbing limo forecasting method is a momentum-based projection. As such, even when recorded GDP deviates considerably from the forecast values that are projected three quarters ahead in time, it provides valuable information in confirming the economy's underlying momentum has changed. We should get a good reading on how big the Iran war's impact has been on the U.S. economy after the actual GDP data for 2026-Q2 is reported.
Meanwhile, the most distant future projection we can make with available finalized GDP data is for 2026-Q3, where the climbing limo forecasting method anticipates the nation's nominal GDP will rise to about $32.9 trillion.
U.S. Bureau of Economic Analysis. National Income and Product Accounts. Table 1.1.5. Gross Domestic Product. [Online Database]. Accessed 9 April 2026.
Image Credit: Microsoft Copilot Designer. Prompt: "A simple sketch of a limousine driving uphill toward the right side of a rising zig zag line chart".
Labels: gdp forecast
Measured by the number of companies announcing they would be lowering their dividend payouts from their previous level, March 2026 was a good month for the dividend paying companies of the U.S. stock market. But then, after the concentrated carnage that swept through the ranks of publicly traded Business Development Companies in February 2026, there aren't many BDCs left in the financial services arena with imminent dividend cuts in their future.
That's not to say there won't be more such firms that will need to face up to the risk of their loans to software firms now facing pressure from AI technologies going bad, but the month of March saw considerably fewer of them.
Overall, the number of dividend decreasing companies in our sampling for the month dropped from a revised total of 27 the month before to just 6 in March 2026. The following chart presents the tally of dividend decreases recorded for each industrial sector within the U.S. stock market.
The oil and gas sector saw the most decreases with four firms announcing decreased dividends in March 2026. Three of which are represented by royalty trusts that pay variable dividends, which directly results from the business conditions for this portion of the industry in the preceding month. While March 2026 saw oil and gas prices surge in response to the Iran war's disruption of the global trade in oil, February had seen falling prices, which reduced the revenue and earnings of many of these firms, which in turn resulted in their reduced distributions to their shareholders for this month.
Even so, the number of these firms falls well below the threshold of ten we use as a rule of thumb for determining whether the industry is facing contractionary conditions.
The financial services sector added two more dividend decreasing firms to the total, both of which pay fixed dividends that required action by their boards of directors to declare.
Here are the sampled dividend decreases for March 2026:
Monroe Capital has a strange situation in that after the company slashed its dividend payout in March, it delivered an outsize dividend payment in April 2026 after its acquisition by Horizon Technology Finance (NASDAQ: HRZN).
The overall number of dividend decreases announced in March 2026 is well below the total of 50 that signifies recessionary conditions are present in the U.S. economy as a whole.
Image credit: Dividends definition. State Savings and Loan Association advertisement on Page 9 of Beatrice, Nebraska's Beatrice Daily Express, 12 December 1921. Chronicling America. [Online Database]. 12 December 1921. Public domain image.
Labels: dividends
The S&P 500 (Index: SPX) continued its bullish run in the trading week ending on Friday, 17 April 2026. The index closed out the week at 7,126.06, a new record high following 13 consecutive days of higher closes.
To put that unlikely event into perspective, since 3 January 1950, the S&P 500 has only seen one winning streak that has exceeded 12 consecutive days. That streak started on 26 March 1971 and ended on 15 April 1971. The index rose from 99.61 at the close of trading on 25 March 1971 to reach 103.52 after 14 trading days, a gain of 3.9%.
The current winning streak, which is still running going into the new trading week, has seen the S&P 500 rise 12.3% after the index bottomed at 6,343.72 on 30 March 2026. The gains have largely come as the U.S. has largely achieved its aims in the Iran war, including an announcement from Iran's government that shipping traffic would resume transiting the Hormuz Strait without harassment on Friday, 17 April 2026.
Investors responded positively, bidding oil prices substantially lower which, in turn, boosted stock prices. The latest update of the alternative futures chart finds the index' trajectory has risen to fall within the redzone forecast range we added several weeks ago before the geopolitical conflict, where it is now just 2.6% below the central trend line of the forecast range.
The positive development also improved the outlook for a Federal Reserve rate cut in 2026, which is a big change after the last few weeks had all but taken that chance off the table. The CME Group's FedWatch Tool projects a rising chance of a single quarter point rate cut in 2026, most likely to be announced after the Fed's Open Market Committee meets on 9 December (2026-Q4).
Of course, whether that happens depends on the course of geopolitical events in the Iran war, which the flow of new information in recent weeks has demonstrated to be subject to change with little notice. To get a sense of what we mean, here are the market moving headlines from just the past week:
We normally cut off our coverage of a trading week's news events with the close of trading each week. Since that's the case, be aware that events that come up afterward can have a material effect on how stock futures trade in the interim between the previous week's market close and the upcoming week's market open.
In other news, the Atlanta Fed's GDPNow tool forecast of real GDP growth in 2026-Q1 was unchanged at +1.3%, the same as at the end of the preceding week.
Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a suit-wearing Wall Street bull and bear celebrating falling oil prices because the Hormuz Strait is open. The bull holds a newspaper with the headline 'HORMUZ STRAIT OPEN! OIL PRICES PLUNGE!' and a champagne glass, while the bear laughs holding dollar bills. A toppled oil barrel and a downward oil price chart sit on the table."
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