For 125 years, mathematicians and physicists have chased after a single solution to a very difficult problem in fluid mechanics.

That problem arises because the math needed to accurately describe the flow of a fluid depends very much on the scale of the physical world being modeled. There's one set of fluid math equations that works at the microscopic level, where individual atoms and molecules of fluids interact. There's another set at the macroscopic level, which involves the combined interactions of millions and billions of fluid particles. And there's a third set at the mesoscopic level, which falls in between the two other scales and demands its own set of equations to describe.

The following video by brain truffle is one of the better introductions we found to the challenges of using math to describe how fluids behave at each of these scales. If you want to skip over some of the foundational discussion, jump ahead to the 16:48 mark.

The challenge lies mathematically unifying the physical theories behind the fluid mechanics at the microscopic, mesoscopic, and macroscopic levels. It was originally proposed in 1900 by mathematician David Hilbert as the sixth of twenty-three problems he identified as worthwhile endeavors in which to pursue mathematically rigorous solutions.

The benefits of establishing such a rigorous solution would mean much greater confidence in the computational analysis supporting how fluids behave in the real world, no matter the scale of the application.

In the twelve full decades since, progress toward establishing that rigorous math to the different scales of fluid mechanics has come in several different waves. The latest wave however could represent the biggest math story of the year because it potentially achieves a substantial portion of Hilbert's goal for this particular problem.

In March mathematicians Yu Deng of the University of Chicago and Zaher Hani and Xiao Ma of the University of Michigan posted a new paper to the preprint server arXiv.org that claims to have cracked one of these goals. If their work withstands scrutiny, it will mark a major stride toward grounding physics in math and may open the door to analogous breakthroughs in other areas of physics....

The new proof broadly consists of three steps: derive the macroscopic theory from the mesoscopic one; derive the mesoscopic theory from the microscopic one; and then stitch them together in a single derivation of the macroscopic laws all the way from the microscopic ones.

The first step was previously understood, and even Hilbert himself contributed to it. Deriving the mesoscopic from the microscopic, on the other hand, has been much more mathematically challenging. Remember, the mesoscopic setting is about the collective behavior of vast numbers of particles. So Deng, Hani and Ma looked at what happens to Newton’s equations as the number of individual particles colliding and ricocheting grows to infinity and their size shrinks to zero. They proved that when you stretch Newton’s equations to these extremes, the statistical behavior of the system—or the likely behavior of a “typical” particle in the fluid—converges to the solution of the Boltzmann equation. This step forms a bridge by deriving the mesoscopic math from the extremal behavior of the microscopic math.

The major hurdle in this step concerned the length of time that the equations were modeling. It was already known how to derive the Boltzmann equation from Newton’s laws on very short timescales, but that doesn’t suffice for Hilbert’s program, because real-world fluids can flow for any stretch of time. With longer timescales comes more complexity: more collisions take place, and the whole history of a particle’s interactions might bear on its current behavior. The authors overcame this by doing careful accounting of just how much a particle’s history affects its present and leveraging new mathematical techniques to argue that the cumulative effects of prior collisions remain small.

Gluing together their long-timescale breakthrough with previous work on deriving the Euler and Navier-Stokes equations from the Boltzmann equation unifies three theories of fluid dynamics.

That's the practical upshot of Deng, Hani and Ma's work, which is now being put to peer review. If you want to know more about the technical aspects of what they did, they spoke about their work in the following video from a Mathematics Colloquium at the University of Chicago in April 2025:

Finally, if you'd like more background into the governing equations of fluid dynamics at the mesoscopic and macroscopic scales, we'll recommend Mojtaba Maali Amiri's 42-minute discussion of them:

If Deng, Hani and Ma's work holds, successfully connecting the math of Newton, Boltzmann, Navier, and Stokes across these three scales of reality represents a massive achievement in mathematical theory, one with practical benefit.

Reference

Yu Deng, Zaher Hani, and Xiao Ma. Hilbert's Sixth Problem: Derivation of Fluid Equations via Boltzmann's Kinetic Theory. Preprint: arXiv:2053.01800v1. [PDF Document]. 3 March 2025.

The total market capitalization of new homes sold in the United States dipped slightly in April 2025. Political Calculations initial estimate of the time-shifted trailing twelve month average of the total value of new homes sold during the month is $28.22 billion.

This figure is down just 0.4% from our revised estimate of $28.36 billion in new homes sales in March 2025. The March 2025 data was revised upward from the initial estimate of $27.87 billion we reported last month.

The following charts present the U.S. new home market capitalization, the number of new home sales, and their sale prices as measured by their time-shifted, trailing twelve month averages from January 1976 through April 2025. The trends they show suggest the new home market is starting to reverse its general downtrend since July 2024.

Flattening new home sales trend:

Flattening trend for home prices:

The transition from a falling to a flat trendline in the trailing twelve month averages comes as the reported number of new home sales surged in April 2025. Seeking Alpha summarized April 2025's underlying monthly data that fed into our overall estimate of the market cap for new homes:

U.S. new home sales jumped 10.9% M/M to 743K in April, rising from 724K in March and surging past the 700K consensus estimate, according to data released by the U.S. Census Bureau on Friday. The increased sales rate led to an increase in the median sales price and a reduction in inventory.

On a Y/Y basis, new home sales rose 3.3%.

The median sales price of new houses was $407.2K, up 0.8% from March's $403.7K and below April 2024's price of $415.3K. The average sales price of new houses, though, was $518.4K, 3.7% higher than the previous month and 3.6% above April 2024's level.

If the numbers hold, April 2025's new home sales will be the highest recorded since February 2022. New home sales data is subject to frequent revisions before being finalized, where the size of revisions can be significant.

References

U.S. Census Bureau. New Residential Sales Historical Data. Houses Sold. [Excel Spreadsheet]. Accessed 23 May 2025. 

U.S. Census Bureau. New Residential Sales Historical Data. Median and Average Sale Price of Houses Sold. [Excel Spreadsheet]. Accessed 23 May 2025. 

Image credit: Photo by Ironman on Unsplash.

"Liberation Day". Otherwise known as 2 April 2025, that was the day U.S. President Donald Trump waited until after the nation's stock markets had closed before announcing the tariffs the United States government would impose on the value of goods produced in other countries to the U.S. that he had campaigned for in the 2024 election.

During his announcement, President Trump displayed several charts indicating the size of the tariffs imposed by foreign governments on U.S.-produced goods and the reciprocal tariff rates the U.S. government would soon impose. The list was stunning, both for the magnitude of tariffs that would be imposed and number of countries and foreign territories that would be affected.

There was just one problem. The numbers didn't make sense, either from a mathematical standpoint or an economic one.

That wouldn't have been a problem if the foreign tariff rates presented on the charts matched the tariff rates those nations and regions impose on U.S. goods. Because they didn't, the reciprocal tariff rates being announced by President Trump also didn't make sense for how the administration described they were arrived at.

The numbers were strange enough that many mathematicians and economists went to the trouble of digging into where they were really coming from. In the following video, Matt Parker, the author of Humble Pi: When Math Goes Wrong in the Real World, presents in the following video explainer:

Since there's no direct connection to actual tariff rates imposed by foreign countries on U.S. goods, the results of this reciprocal tariff math is instead signaling what the Trump administration really cares about. What that is boils down to the following list:

• The size of the trade deficit the United States has with other nations.
• Generating tariff revenue from all nations exporting goods to the U.S.

These things are much more about politics than they are about either maths or economics. The results of the reciprocal tariff math seems it was developed to produce a big, but not too big tariff number to negotiate around for the nations with which the U.S. has its biggest trade deficits, which is almost certainly the point of the exercise. Combined with the scope and scale of the "Liberation Day" tariffs, which even apply to foreign territories mainly inhabited by penguins, the real political message being sent by the Trump administration is there will be no escape for any nation from the newly announced minimum tariff of 10% and nations with whom the U.S. has large trade deficits will pay higher tariffs.

How those higher tariffs might be set however is up for negotiation and likely will be for quite some time.

We debated about whether to present a tool to do President Trump's reciprocal tariff math, but ultimately decided against doing so at this time because it's not a high value-added calculation. If you want to see which countries the U.S. has the biggest trade deficits with, you can get that information from official resources like the U.S. Census Bureau's Excel spreadsheet or sites that visualize that data like Brilliant Maps.

We'll close by presenting the video of President Trump's "Liberation Day" announcement, which we've queued to start from the beginning of his remarks.

The reciprocal tariff charts are brought out at about the 32-minute mark.

Image credit: Microsoft Copilot Designer. Prompts: "An editorial cartoon of a confused mathematician standing with their back to a classroom looking at a blank green chalkboard" and "Change the mathematician to an economist". We grafted the two images together to make the final cartoon.

The upward momentum of the S&P 500 (Index: SPX) reversed in the previous week. The index fell 2.6% to close out the trading week ending on Friday, 23 May 2025 at 5,802.82.

Figuratively speaking, Wall Street bears clubbed the index lower because of a politics-oriented event. The stage for that action was set late in the preceding week after Moody's Investor Service finally got around to stripping the U.S. government of its AAA credit rating, becoming the third of the three major firms that rate the creditworthiness of governments to do so. Standard and Poor took that action in August 2011 and Fitch Ratings did the same in August 2023. Moody's action was long-expected because outlook on the U.S. government's fiscal health turned negative in November 2023.

With investors' nerves sensitized to the prospect for higher interest rates that come from the U.S. government getting a lower credit rating, the progress of the "One Big Beautiful Bill" toward passage on Wednesday, 21 May 2025 jolted them. Interest rates jumped and stock prices fell as the projected deficit associated with the spending package was larger than expected. The bill would go on to pass in the narrowly divided House of Representative early in the morning of Friday, 23 May 2025.

But the bigger news was President Trump's threatened 25% tariff on goods imported to the U.S. by Apple (NASDAQ: AAPL), which knocked the S&P 500's largest component stock lower on the day, taking the index lower by a smaller percentage along with it.

The total negative change in stock prices however wasn't large enough to move the trajectory of the S&P 500 outside the redzone forecast range on the alternative futures chart. Here's the latest update of the chart:

We're continuing to monitor the S&P 500's trajectory with respect to the dividend futures-based model's projections to see if we might be on the cusp of a new market-regime-changing volatility event.

All in all, it's very rare to see a political event outside a change in tax rates produce a noticeable effect in stock prices, but an event that changes interest rates would be capable of the feat. Even so, the magnitude of the effects observed on each of the days they occurred don't even qualify as interesting in the context of the market's typical day-to-day volatility.

Here are the week's market-moving headlines.

Monday, 19 May 2025

• Signs and portents for the U.S. economy:
• Moody's cuts America's pristine credit rating, citing rising debt
• Moody's downgrade intensifies investor worry about US fiscal path
• Oil edges lower as US and China growth concerns weigh
• Trump tells Walmart to 'eat the tariffs' instead of raising prices
• Fed minions say their monetary policy is "in good place":
• Fed's Williams says no significant move out of US assets seen so far, monetary policy in good place
• Bigger trouble developing in China:
• China April industrial output, retail sales growth slow
• China struggles to lift home prices as April shows no growth
• BOJ minions say they'll keep hike Japan's interest rates if economy grows:
• BOJ to keep hiking rates if economy rebounds from tariff hit, deputy governor says
• Nasdaq, S&P, Dow finished mostly flat after Moody’s downgraded U.S. credit rating

Tuesday, 20 May 2025

• Signs and portents for the U.S. economy:
• Oil steadies as market assesses US-Iran talks, demand signals
• Fed minion speculates big inflation wave will soon arrive, others think they're doing the right thing with monetary policy given their uncertainty:
• US economy may be on the brink of price-hike wave, Fed's Bostic says
• Fed's Musalem: current policy remains appropriate if trade tensions are durably de-escalated
• Fed's Musalem: policy uncertainty has 'meaningful' impact on economic outlook
• Fed officials take cautious view on US markets amid downgrade
• Bigger stimulus developing in China, Australia:
• China cuts key rates to aid economy as trade war simmers
• Australia's central bank cuts rates to two-year low of 3.85%
• Australia central bank warns global trade war a major downside risk to economy
• BOJ minions thinking about bigger bailouts:
• Japan's super-long bond yields soar to records as market frets about demand
• Reaction to Japanese super-long bond yields hitting record highs
• ECB minion suddenly gripped by the obvious:
• ECB's Escriva sees risks to global financial sector from U.S. trade policies
• Wall Street rally stalls near overbought levels, S&P snaps six-day winning run

Wednesday, 21 May 2025

• Signs and portents for the U.S. economy:
• Moody's downgrade ripples through bond market, causes worries for stocks
• Tepid demand for US Treasury auction shows investor jitters about tax bill, deficit
• Oil prices fall on news that US-Iran will hold nuclear talks
• Fed minions keep looking for tariffs to make inflation much higher:
• Fed officials expect tariffs to boost prices; White House downplays risk
• Bigger trouble developing in Japan:
• Japan's super-long yields rise to all-time highs on fiscal, auction concerns
• Japan's exports rise 2% on year in April, shipments to US slump
• Japan's super-long yields rise to all-time highs on fiscal, auction concerns
• Is Japan About To Hike Rates AND Restart Yield Curve Control?
• ECB minions don't believe markets, but do believe Fed will continue delivering dollars to prop up Eurozone economy; thinking about next rate cut:
• ECB warns buoyant markets 'out of sync' with uncertain world
• ECB has no doubt Fed will continue to supply dollars abroad
• US Withdrawal: ECB Warns Of Dollar Shortage
• ECB's Centeno: rate cuts below neutral level may be needed to keep inflation on target
• Wall Street slides, Dow falls 800 points as bond sell-off & fiscal fears batter sentiment
• Wall Street stocks tumble as worries mount about US debt

Thursday, 22 May 2025

• Signs and portents for the U.S. economy:
• House narrowly passes Trump's tax-cut bill
• The One, Big, Beautiful Bill
• New US tax bill will 'stabilise things' but increase deficit, JPMorgan's Dimon says
• US real earnings stalled across age, income groups in past year, study shows
• US existing home sales unexpectedly fall in April
• Oil prices settle down on potential further increase in OPEC+ output
• Fed minions say they'll get around to resuming rate cuts later in 2025, argue about whether to make their economics forecasts available:
• Fed's Waller sees path to rate cuts later this year, Fox Business reports
• Plan to beef up Fed forecasts hits hurdle among its regional presidents
• BOJ minions say they they'll let Japanese government's bond yields continue spike for now:
• BOJ policymaker rules out intervention to stem bond yield spike
• Japan's possible response to rise in super-long bond yields
• ECB minions starting to think they may need to back off their rate cut excitement:
• Case growing for summer pause in ECB easing cycle
• With inflation nearly tamed, ECB keen to project stability, accounts show
• Wall Street stocks end flat in choppy trading as Treasury yields ease
• Wall Street closes little changed as U.S. bond sell-off eases up

Friday, 23 May 2025

• Signs and portents for the U.S. economy:
• Trump threatens new tariffs on European Union and Apple, reigniting trade fears
• Trump signs executive orders aiming to expand nuclear power, speed up reactor construction
• Oil gains on short-covering, nuclear talks
• Fed minions to use April 2025's market volatility as model for future stress tests:
• Fed's Cook: April market volatility will help hone financial stability assessment
• Bigger stimulus/subsidies developing in China:
• CATL Received More Chinese Subsidies In 6 Months Than BYD, Great Wall And SAIC Did All Year
• BOJ minions standing by to maybe hike Japan's interest rates later this year:
• Japan's core inflation hits more than 2-year high, could force year-end BOJ hike
• BOJ vigilant on markets as super-long yields soar
• Japanese bonds rally after fiscal concerns send super-long yields to records
• Eurozone minions not happy with being in Trump crosshairs, ECB minions think they've beaten Eurozone inflation:
• EU urges respect not threats as Trump pushes for 50% tariff
• ECB confident that services inflation will moderate, Lane says
• Wall Street sheds nearly 3% for the week on fiscal concerns, Trump's tariff threats
• Apple dives as Trump says tariffs must be paid on iPhones not made in US

The CME Group's FedWatch Tool showed no meaningful change from last week. It projects the Fed will avoid cutting the Federal Funds Rate until the conclusion of its 17 September (2025-Q3) meeting, at which time, it will cut rates by a quarter percent to a target range of 4.00-4.25%. After that, the FedWatch Tool forecasts the Fed will reduce U.S. interest rates a quarter point at a time at twelve-week intervals, coming after it meets on 10 December (2025-Q4) and 18 March (2026-Q1).

The Atlanta Fed's GDPNow tool projection of real GDP growth in the U.S. during the current quarter of 2025-Q2 remained steady at +2.4%, with no updates in the past week. The next update will come on 27 May 2025.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bear who is pushing stock prices down with a stick labeled 'Bigger National Debt'."

Yesterday marked the end of an era that has lasted over 232 years. 22 May 2025 is the day the U.S. penny died.

Or rather, it is the day the United States Mint ordered the coin blanks it will use to make pennies for the last time. When that final supply runs out later this year, no more U.S. pennies will be made, per an order issued by President Trump on 9 February 2025.

The cause of the penny's death is inflation. According to the U.S. Mint's 2024 annual report, it cost about 3.69 cents to make and distribute each one-cent penny produced in 2024.

From a cost perspective, the writing has been on the wall for the U.S. one-cent coin for a long time. Just the metal alone in the modern copper-plated, 97.5%-zinc Lincoln pennies minted since 1982 was worth 71% of their one-cent face value on 22 May 2025.

It could be worse. The value of the metal in the 95%-copper pennies minted from 1909 through 1982 is worth 284% more than their face value.

Unlike previous episodes when the cost of the metal needed to make a penny surged, today's labor costs have increased substantially, which add on top of the value of the metal needed to make the penny.

Even so, it would be possible to justify continuing to mint pennies at a loss if the demand for pennies was high enough. The increasing volume of electronic transactions however has put an effective cap on the needed supply of pennies. The combination of factors justifies the decision to stop making U.S. pennies.

There are benefits to be realized in stopping penny production. The U.S. Treasury Department anticipates "an immediate annual savings of $56 million in reduced material costs". And that doesn't include the related labor savings and environmental benefits.

The United States is finally applying something from the lessons of Doc Palmer, the "godfather" of Canada's "Ban-the-Penny" movement. Only about 13 years later than it should have.

Image credit: U.S. Mint. Learn > Coin & Medal Archive > Circulating Coins > Penny. The obverse and reverse images of the 2025 Lincoln Penny are United States Government works and are therefore public domain, which we've animated to show off both sides of the same coin. If you look very closely and are wondering about those very tiny letters tucked in bottom of the designs on the 'heads' and 'tails' sides of the penny, they are the initials of the artists who created them (VDB is Victor D. Brenner, LB is Lyndall Bass, and JM is Joseph Menna).

The Chief Executive Office, or CEO, of a business comes with a lot of responsibility. For better or worse, CEOs are the faces of the companies they lead. They not only set the direction for what the company does and will do, they also function as its main representative, both to the public and to the company's owners.

For publicly-traded companies, the owners are shareholders. Shareholders can be anyone from people who liked the company's prospects and bought a handful of shares of its stock to the institutions that manage multi-billion dollar retirement funds for millions of people who buy thousands of shares for the same reason. Shareholders have a vital interest in the success of the business because the future value of their investments depend upon it.

So what then are investors supposed to make of the situation when the CEO of a company in which they have staked their future starts prioritizing partisan politics in their public communications? Especially when that activity suggests they're not putting the shareholders' interests in the success and growth of the business first and foremost in their role as CEO?

Or to get straight to the bottom line, are politically partisan CEOs good for stock prices?

A new working paper by William Cassidy and Elisabeth Kempf of the Harvard Business School strongly indicates the answer is no. Political CEOs are not good for stock prices.

The way they came to that conclusion is pretty novel. They focused on corporate Twitter posts made during the period from 2012 through 2022, using natural language analysis to determine which contained partisan political content. They then looked at how various firms' stock prices behaved in the 10 days before a partisan tweet was issued with how they behaved in the 10 days after. The following figure from the paper shows what they found:

Cassidy and Kempf describe what the panels of the chart illustrate:

Figure 6, Panel A plots the average cumulative abnormal return around partisan tweets. On the day of the tweet itself, the average stock return is close to zero. However, a noticeable decline in the stock price occurs over the ten days following the average partisan tweet, reaching approximately –20 basis points (bps) on event day +10, statistically significant at the 5% level. When we extend the post-event window to 30 days after the tweet, we find that stock prices continue to decline until about 13 trading days after the tweet before leveling off, reaching a CAR of almost negative 30 bps (see Internet Appendix Figure IA.11). In other words, the full stock-price impact takes time to materialize, consistent with the delayed stock-price impact of legislation documented in previous work (e.g., Cohen et al. (2013)). We do not observe a significant trend in the stock price prior to the tweet event.

In Panel B of Figure 6, we separate tweets into those whose partisan slant is more versus less surprising given the company’s past tweet history. Specifically, we compute a tweet’s partisan-slant surprise as the absolute difference between the tweet’s P SI-value and the average P SI-value of the company’s tweets in the 36 months prior to the event. Tweets with a high surprise are those in the top quartile of partisan-slant surprises across all partisan tweets in a given calendar month. All other tweets are considered “low surprise.” Consistent with the news content of partisan-slant surprises being higher, we observe a stronger decline in the stock price in the high-surprise subsample.

The period from 2012 through 2022 saw a sharp rise in partisan tweets made by CEOs of U.S. corporations starting in 2017, particularly in support of policies associated with the left-leaning portion of the political spectrum in the U.S., which greatly outnumbered conservative-leaning tweets. Their results indicate that shift in CEO and corporate communications in favor of partisan politics hurt stock prices.

If you think about it, that makes a lot of sense. Whenever corporate leaders like CEOs turn their attention away from their chief fiduciary duties in running their businesses, it diminishes the outlook for their business' prospects. To put it into sports terms, it signals they're taking their eyes off the ball, which is not good for investors.

That's the best case scenario. A focus on partisan politics can also provide a distraction away from poor business performance, which in the very worse case scenarios, tries to cover up a series of bad decisions that actively hurt both the business and the interests of investors.

Here are Cassidy and Kempf's main conclusions, in which they also identify the main driver behind the shift in CEO and corporate communication practices:

This paper provides one of the first large-scale empirical analyses of partisan corporate speech, using a novel measure based on natural language processing of corporate social media communication. We use this measure to establish three key stylized facts. First, partisan corporate speech has increased significantly over the past decade, with a particularly sharp rise after 2017. Second, this increase has been disproportionately driven by Democratic-leaning statements, a trend that spans industries, geographies, and firms led by both Democratic and Republican CEOs. Third, partisan corporate statements are, on average, followed by negative abnormal stock returns, with significant heterogeneity depending on the political alignment of the firm’s investor base.

To explain these patterns, we explore potential drivers of the rise in Democratic-sounding speech. While employee and consumer preferences may play a role, we also find novel empirical support for an investor-demand channel. The surge in Democratic corporate speech coincides with the rapid expansion of sustainable investing, and firms with high BlackRock ownership exhibit a particularly strong shift toward Democratic language following Larry Fink’s 2019 letter to CEOs, which urged CEOs to engage more in contentious social and political debates. Our theoretical model formalizes this mechanism, demonstrating how shifts in investors’ nonpecuniary preferences can lead firms to adopt partisan positions, even when doing so negatively impacts stock prices.

Since 2022, BlackRock's Larry Fink has systematically backed away from supporting the left-leaning "Environmental, Social, and corporate Governance" (ESG) standards he previously championed. It wasn't good for his influential company's investments. Or for the investors who own shares in the companies whose CEOs put politics ahead of running the business.

Reference

Cassidy, William, and Elisabeth Kempf. "Partisan Corporate Speech." Harvard Business School Working Paper, No. 05-056, May 2025. [PDF Document]. DOI: 10.2139/ssrn.5249915.

Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a group of investors attending a company's annual meeting who are horrified that the CEO is tweeting about politics".

The outlook for the S&P 500's dividends in upcoming quarters has improved considerably over the month since our previous snapshot of the future.

Each of 2025's remaining quarters to be completed showed improvement. Here's the short summary of how they changed and what the expectations are as of the close of trading on Tuesday, 15 May 2025.

• 2025-Q2: Increase of $0.02, rising to $19.07 per share
• 2025-Q3: Increase of $0.14, rising to $19.10 per share
• 2025-Q4: Increase of $0.46, rising to $19.30 per share

The following animated chart shows how expectations for the S&P 500's quarterly dividends per share changed in the month from 15 April 2025 to 15 May 2025. If you're reading this article on a site that republishes our RSS news feed, you may need to click through to our site to see the animation.

The picture changes a little when we compare our May 2025 snapshot with our 14 March 2025 snapshot, which was taken before President Trump's 2 April 2025 'Liberation Day' tariff announcement. That action knocked the dividend outlook lower in its immediate aftermath, which bottomed about a week before our 15 April 2025 snapshot before beginning to recover.

As of 15 May 2025, the outlook for dividends in the current quarter of 2025-Q2 has surpassed its mid-March 2025 level by $0.22 per share. Meanwhile, expected dividends in 2025-Q3 has recovered all but $0.05 per share of its value, but 2025-Q4 remains some $0.30 per share short of its projected level from 14 March 2025.

How changes in the outlook for dividends at specific points of time in the future contribute to changes in stock prices is described by this math.

More About Dividend Futures Data

For this series, we have been taking a snapshot of the CME Group's S&P 500 quarterly dividend futures data shortly after the second or third week of each month.

Dividend futures indicate the amount of dividends per share to be paid out over the period covered by each quarter's dividend futures contracts, which start on the day after the preceding quarter's dividend futures contracts expire and end on the third Friday of the month ending the indicated quarter. So for example, as determined by dividend futures contracts, the now "current" quarter of 2025-Q2 began on Saturday, 22 March 2025 and will end on Friday, 20 June 2025.

That makes these figures different from the quarterly dividends per share figures reported by Standard and Poor. S&P reports the amount of dividends per share paid out during regular calendar quarters after the end of each quarter. This term mismatch accounts for the differences in dividends reported by both sources, with the biggest differences between the two typically seen in the first and fourth quarters of each year.

Image Credit: Microsoft Copilot Designer. Prompt: "A crystal ball with the word 'SP 500' written inside it". And 'Dividends' written above it, which we added.

Every three months, we take a snapshot of the expectations for future earnings in the S&P 500 (Index: SPX) at approximately the midpoint of the current quarter, shortly after most U.S. firms have announced their previous quarter's earnings.

The latest snapshot comes 87 days after the Winter 2025 snapshot. Since that snapshot, the outlook for earnings has dimmed, with significantly lower growth anticipated in the quarters ahead.

The change over the past three months is larger than the typical pattern that earnings forecasts follow. Here, expectations for future earnings tend to erode with each later snapshot, usually by relatively small amounts from quarter to quarter. It is unusual for the earnings forecast to improve from snapshot to snapshot.

Two major events have occurred during the last three months that have knocked the earnings forecast lower. First, a deflation phase for the AI-bubble got underway, starting on 21 February 2025 when the company behind China's DeepSeek Artificial Intelligence (AI) system announced they would make its code open source. That serious new competition put a cap on the potential earnings of the "Big Tech" firms making big AI-related investments.

Second, President Trump's 'Liberation Day' tariff announcement after the market closed on 2 April 2025 knocked the earnings outlook for many other firms lower, at least through the time of this snapshot. This snapshot only captures a little over a week's worth of the recent surge of deal-making momentum that's driven stock prices higher in recent weeks.

Of the two events, the deflation of the AI-bubble has been the bigger force shaping future earnings expectations.

The following chart, covering how earnings expectations have changed from the end of 2021 through 9 May 2025:

The current projection for the S&P 500's earnings per share through the end of 2025 is $241.33, which would represent 14.8% year-over-year earnings growth over December 2024's finalized level of $210.17.

Looking further forward through the index' expected earnings per share through the end of 2026, Standard & Poor projects the S&P 500's earnings per share will be $276.88, down 4.4% from its initial estimate of $289.64 per share.

Reference

Silverblatt, Howard. Standard & Poor. S&P 500 Earnings and Estimates. [Excel Spreadsheet]. 9 May 2025. Accessed 16 May 2025.

Image Credit: Microsoft Copilot Designer. Prompt: "A crystal ball with the word 'SP 500' written inside it". And 'Earnings' written above it, which we added.

The S&P 500 (Index: SPX) continued its upward momentum on the strength of progress toward multiple trade deals in the past week. Combined with strong indications the Trump administration will ultimately set tariffs on goods imported into the U.S. at lower levels than initially announced on 2 April 2025, the index rose nearly 5.3% to end the week at 5,958.38.

That puts the S&P 500 within three percent of its all-time record high close of 6,144.15 set on 19 February 2025. Not uncoincidentally just before the AI-bubble began to deflate just two days later.

Speaking of which, the AI-bubble is showing signs of reflating. A good part of the rise of the index comes as several of its biggest component firms announced major investments from middle-Eastern nations during President Trump's trip to that region during the past week. Most notably, AI-chipmaker Nvidia (Nasdaq: NVDA) jumped 10% in value over where it closed the previous week.

The deals being announced during President Trump's deal-making trip are driving stock prices because it represents a significant export market for the index' big tech firms. The middle-eastern nations are energy-rich, which has become an important consideration for siting power-hungry AI data centers.

All the dealmaking allowed the S&P 500 to continue its upward trajectory of recent weeks. The latest update of the alternative futures chart shows the index continues to track along within the redzone forecast range we modified earlier this month to capture the apparent changes in market regime that have taken place since 9 April 2025.

We don't know how long the current market regime that started on 28 April 2025 might last. We think we're still within the cluster of volatility that makes changes in market regime likely. At least until it ends and the dividend futures-based model's multiplier goes back to being mostly constant.

For signs of such a change, we'll rely on the context provided by the random onset of new information that investors absorb as they make real time investment decisions. Here are the past week's market-moving headlines:

Monday, 12 May 2025

• Signs and portents for the U.S. economy:
• U.S. and China agree to slash tariffs for 90 days
• What have China and the United States agreed to in Geneva?
• Oil prices settle up at 2-week high as US, China ease tariffs
• Trump executive order demands pharma industry price cuts
• Fed minions say inflation risk is lower with tariff pause, still won't commit to cutting US interest rates:
• Fed officials say China-US tariff reprieve lowers risks
• U.S.-China tariff delay gives Fed fresh reason to sit tight on rates
• Exclusive: Fed’s Hammack wants clear data before moving on rates, not much data by June
• Bigger trouble, tariff relief developing in China:
• China's factory-gate deflation deepens
• China's March shipments of foreign-branded cellphones drop almost 50%
• China's official media welcome US tariff deal, others sceptical
• JapanGov calls for end to tariffs with US, BOJ minions talking about interest rate hikes in Japan:
• Japan PM Ishiba reiterates call to eliminate all tariffs with US
• Some in BOJ saw scope to resume rate hikes, March summary shows
• Wall Street equity indexes close higher after US-China tariff truce
• Dow jumps more than 1100 points, Nasdaq soars 4% on U.S.-China trade deal
• Coinbase to join S&P 500 index, shares surge 9% after hours

Tuesday, 13 May 2025

• Signs and portents for the U.S. economy:
• US inflation falls to 2.3% in April as tariff effect looms
• CPI Weak Again: Egg Prices Fall By the Most Since 1984
• Tradeflation Stays Out of April CPI Report
• Boeing deliveries nearly double in April
• China lifts Boeing delivery ban as tariff war cools, Bloomberg News reports
• Fed minions working harder to find excuses to not cut U.S. interest rates:
• Fed to stay patient amid cooling trade war and inflation
• Trump calls on Fed to cut rates, saying prices of 'practically everything' are down
• April CPI: The Case For A Cut Gets Stronger
• BOJ minions will keep hiking Japan's interest rates:
• BOJ upbeat on wages despite US tariffs, sees scope to resume rate hikes
• ECB minions will keep stimulating Eurozone economy the way they've been doing stimulus, with more rate cuts:
• ECB to stand by past stimulus policies in strategy review
• ECB's Villeroy sees room for additional rate cut by summer
• S&P 500, Nasdaq end higher on soft inflation data, trade optimism
• Wall Street closes with YTD gains for the first time since February-end
• S&P 500 wipes out 2025 losses as stocks extend rally
• A look at the S&P 500's wild ride since 'Liberation Day'

Wednesday, 14 May 2025

• Signs and portents for the U.S. economy:
• Oil falls after US crude inventories rise
• US smartphone shipments rose 30% in March due to tariff concerns, report says
• US cattle producers have started rebuilding herds, or will soon, Tyson Foods CEO says
• Fed minions keep chanting mantra of tariffs causing inflation despite lack of evidence to date:
• Fed's Jefferson: Expect economy to slow, future inflation uncertain due to tariffs
• Trump tariffs have little impact on prices so far, defying grim forecasts
• Fed's Goolsbee: Data still noisy as Fed waits to understand tariff impacts
• Bigger growth developing in China:
• US slashes 'de minimis' tariff on small China parcels to as low as 30%
• Exporters ‘shocked and elated’ as China trade cranks back into gear
• BOJ minions get inflation data to support plan to hike Japan's interest rates:
• Japan's wholesale inflation hits 4%, keeps BOJ under pressure
• Wall Street manages to extend rally, moves further into the green for the year
• S&P 500 barely gains, investors focus on trade, wait for data

Thursday, 15 May 2025

• Signs and portents for the U.S. economy:
• Oil prices drop on US-Iran progress; global shares gain in choppy trade
• US producer prices unexpectedly fall in April
• Trump: India has offered US a trade deal with no tariffs
• Fed minions say US economy is doing well and that they need to think about what they're doing with monetary policy:
• Fed's Barr says economy on solid footing, trade dispute clouds outlook
• Fed's Powell: Strategy around both jobs and inflation needs to be reconsidered
• Bigger trouble developing for Eurozone:
• Euro zone growth downgraded but employment holding up
• Wall Street ends mixed, but the benchmark S&P 500 extends rally to four straight days
• Wall Street ends mixed; Cisco rallies while UnitedHealth tumbles
• UnitedHealth under criminal probe for possible Medicare fraud, WSJ reports
• Gold prices fall to over one-month low as trade optimism rises

Friday, 16 May 2025

• Signs and portents for the U.S. economy:
• Oil heads for weekly gain but remains under supply hike pressure
• Trump says U.S. will set tariff rates for most nations within weeks
• Trump says U.S. officials will send letters within weeks over trade
• Conservatives block Trump’s big tax breaks bill in a stunning setback
• Trump’s ‘beautiful’ bill spans 1,116 pages. Here’s what’s inside it
• Fed minions find out there are too many Fed minions:
• Federal Reserve to slash staff by 10% over several years
• Bigger trouble developing in China:
• China-US air freight tumbles on 'de minimis' tariff; airlines adjust routes
• Bigger trouble developing in Japan:
• Japan's economy shrinks more than expected as US tariff hit loom
• Japan's April core inflation likely sped up to fastest pace in two years: Reuters poll
• BOJ minions starting to think hiking interest rates might not be smart:
• Dovish BOJ policymaker urges pause in rate hikes on US tariff uncertainty
• Japan's fiscal woes put BOJ bond taper plans to test
• ECB minions maybe rethinking their enthusiasm for rate cuts and transparency:
• ECB may be nearing end of rate cuts but trade war is a risk, policymaker says
• ECB's Lane queries value of publishing economic scenarios
• Wall Street set for weekly gains on trade deal, weak data curbs enthusiasm
• S&P 500 gains 5% on the week, as U.S. stocks rally despite inflation data, record low sentiment

The CME Group's FedWatch Tool now projects the Fed will avoid cutting the Federal Funds Rate until the conclusion of its 17 September (2025-Q3) meeting, twelve weeks later than what it projected a week earlier. After that, the FedWatch Tool forecasts the Fed will reduce U.S. interest rates a quarter point at a time at twelve week intervals, coming after it meets on 10 December (2025-Q4) and 18 March (2026-Q1).

The Atlanta Fed's GDPNow tool boosted its projection of real GDP growth in the U.S. during the current quarter of 2025-Q2 from +1.1% to +2.3%. This estimate is near the upper end of the so-called "Blue Chip consensus" range, where the overall average expected real GDP growth rate for the quarter is about 0.8%.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull who is excited by trade and tariff deals".