After a strong rebound in July, the combined value of goods traded between the U.S. and China dipped in August 2025. The release of trade data for this month was delayed until 19 November 2025 because of the record 43-day shutdown of nonessential U.S. government functions that ended last week.
Exports from the U.S. to China totaled $8.272 billion, which were down 11% from July's level and down nearly 37% year-over-year. Imported goods shipped from China to the U.S. totaled $25.133 billion, which were down nearly 5% month-over-month and about 31% since August 2024.
The combined value of trade between the U.S. and China for August 2025 is $33.1 billion, a 6.5% decrease from July's showing.
The trailing twelve month average of the combined total of goods exchanged between the U.S. and China continued falling in August. It now falls 15.3% below a counterfactual projection of how the value of trade between the two nations would have grown in the absence of the global tariff war. The following chart presents the monthly data for the combined value of goods exchanged between the U.S. and China. It also presents the trailing twelve month average, which smooths out much of the year-to-year seasonal variation in the trade data in the period from January 2017 through August 2025.
On 1 November 2025, the U.S. and China struck a new truce in their tariff war that lowered tariffs considerably more than their 28 June deal, though we won't see its effect in the data until November 2025's data becomes available early in 2026. In the meantime, we anticipate we'll continue tracking an overall downward trend in trade between the U.S. and China until the trade between the two countries following the deal starts to gain traction.
References
U.S. Census Bureau. U.S. International Trade in Goods and Services (FT900). U.S. Trade in Goods with China, Not Seasonally Adjusted, Nominal Figures, Total Census Basis. [Online database]. Accessed 19 November 2025.
Image credit: Empty Storage Container photo by Moj Box on Unsplash.
Labels: trade
The S&P 500's dividend outlook for the final quarter of 2025 brightened in the month since our last snapshot of their outlook.
On 15 October 2025, the CME Group's S&P 500 Quarterly Dividend Index' Futures quotes indicated investors could expect to collect $19.90 per share during the period covered by 2025-Q4 dividend futures contracts. On Friday, 14 November 2025, that rose to $19.94 per share, an increase of 0.2% from the previous month's outlook.
Our October 2025 snapshot also presented the projections for the S&P 500's dividends per share through the second quarter of 2026. Here is how the dividends expected in the future quarters of 2026-Q1 and 2026-Q2 changed in the past month:
- 2026-Q1: Decrease of $0.01, dipping to $20.89 per share
- 2026-Q2: Increase of $0.02, rising to $19.73 per share
For this dividend snapshot, we're extending the outlook for the S&P 500's expected dividends per share through the fourth quarter of 2026. The following chart presents the S&P 500's quarterly dividends per share as provided by dividend futures contracts from 2024-Q1 through 2026-Q4.
A note of caution on the dividend projection for 2026-Q4. Because it covers expectations that are currently more than four quarters into the future, it's best understood as an initial projection based on very thin trading at this point of time. The projection for this quarter can be expected to change once it falls within the typical year-ahead period that defines the typical time horizon for investors and the investment activity for its related dividend futures contract picks up.
More About Dividend Futures Data
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.
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. As determined by dividend futures contracts, the now "current" quarter of 2025-Q4 began on Saturday, 20 September 2025 and will end on Friday, 19 December 2025. From the perspective of dividend futures, the next quarter of 2026-Q1 will begin on Saturday, 22 December 2025.
Because dividend futures are tied to options contracts that run on this schedule, that makes these figures different from the quarterly dividends per share figures that are 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.
Labels: dividends, forecasting, SP 500
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.
For Fall 2025, our snapshot was taken on 12 November 2025, 91 days after the Summer 2025 snapshot. The outlook for earnings improved since last quarter's snapshot, continuing a positive trend since Spring 2025.
The current projection for the S&P 500's earnings per share through the end of 2025 is $244.51, which would represent a 16.3% year-over-year gain over December 2024's finalized earnings of $210.17.
The following chart, covering how earnings expectations have changed from the end of 2021 through 12 November 2025:
Looking further forward through the end of 2026, Standard & Poor projects the S&P 500's earnings will be $281.78 per share. If this projection holds, it would represent a little over a 15% year-over-year increase over the current earnings projection for 2025.
But will it hold? There's a lot of time between now and the end of December 2026 and if there's one thing the chart makes clear, it's very unlikely the earnings recorded then will match what they were projected to be four quarters earlier!
Reference
Silverblatt, Howard. Standard & Poor. S&P 500 Earnings and Estimates. [Excel Spreadsheet]. 12 November 2025. Accessed 15 November 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.
Labels: earnings, forecasting, SP 500
The S&P 500 (Index: SPX) saw very little change week over week. The index closed the trading week ending on 14 November 2025 at 6,734.11, up less than 0.1% from its previous week's close.
There was more action than that during the week. The index rose early in the week by 1.75% as AI-related firms jumped only to give nearly all of its gain back by the end of the week. The main culprits behind that disappointing development were a number of Federal Reserve officials who signaled on Thursday, 13 November 2025 they are unlikely to cut the Federal Funds Rate again next month. That impacted the direction of stock prices because it prompted investors to revisit their expectations for the mega-caps funding their AI-technology infrastructure plans using debt, several of which represent some of the biggest firms within the S&P 500.
The CME Group's FedWatch Tool absorbed that new information and changed to indicate just a 44% probability of one more quarter point cut to the Federal Funds Rate in 2025. In 2026, the FedWatch tool anticipates better than 50% probabilities for quarter point rate cuts on 28 January (2026-Q1), 17 June (2026-Q1), and 16 September (2026-Q3). The potential timing of all these projected rate cuts remains very fluid with substantial changes in expectations from week to week.
Meanwhile, the latest update of the alternative futures chart shows investors focused most their forward-looking attention on the current quarter of 2025-Q4 in the latter part of the week, which is consistent with the now open question of whether or not the Fed will cut rates in December 2025.
Here are the week's market-moving headlines:
- Monday, 10 November 2025
-
- Signs and portents for the U.S. economy:
- At China's largest import expo, US exhibitors hopeful worst of trade war is over
- US container imports fall in October amid tariff driven caution
- China suspends port fees on US-linked ships for a year
- US Senate advances bill to end federal shutdown
- Democrats Concede Shutdown Fight Without Health Care Win in Hand
- US fourth-quarter GDP could be negative if shutdown drags on, White House economic adviser says
- US surpasses 10,000 flight delays Sunday in worst day of shutdown
- Oil settles higher as tight fuel markets offset crude supply concerns
- Fed minions thinking about how to set US interest rates:
- Bigger trouble, stimulus developing in China:
- China's car sales unexpectedly contract in October after eight-month expansion
- China's internet firms cautiously revive lending as Beijing pushes consumer loans
- Bigger stimulus developing in Japan as BOJ minions told by top politicians to hold off December rate hike, even though BOJ minions really want one:
- Japan's stimulus plan to urge BOJ focus on boosting growth, draft outline shows
- BOJ should avoid December rate hike, says Takaichi's economic adviser
- BOJ saw growing case for near-term rate hike, October meeting summary shows
- ECB minions say Eurozone interest rates are right where they want them, Eurozone banks subsidizing "greener" companies with lower interest rates:
- ECB's rates at right level barring deviations, ECB VP says
- Euro zone banks tilting loan pricing towards greener firms, ECB blog says
- Wall Street rallies as investors await the end of the U.S. government shutdown
- Tuesday, 11 November 2025
-
- Signs and portents for the U.S. economy:
- SoftBank unloads entire stake in Nvidia for $5.8B
- Trump calls 50-year mortgages no 'big deal' as right-wing conservatives balk
- US Senate passes bill to end government shutdown, sends to House
- Oil up as investors balance sanctions risks, oversupply worries
- Bigger trouble, stimulus developing in China:
- Chinese goods dumping started before tariffs, ECB study finds
- China to provide new investment opportunities to US companies
- China's central bank to maintain accommodative policy as challenges persist
- Japan's new boss wants "wage-driven" inflation:
- Wall Street closed mixed as the government shutdown resolution appears close
- Wednesday, 12 November 2025
-
- Signs and portents for the U.S. economy:
- US lost jobs through late October, new private-sector data shows
- China's soybean glut could defeat US export hopes after trade thaw
- Oil prices fall, markets look to US government reopening
- After the bell....
- Fed minions say they're reluctant to cut rates as they're expected to in December 2025, taking actions to fend off liquidity problems:
- Fed's Bostic favors no change in rates while inflation remains greater risk
- Atlanta Fed’s Bostic: ‘I see little to suggest that price pressures will dissipate before mid- to late 2026’
- Bostic announces retirement amid Trump push for more influence over Fed
- US Supreme Court to hear Trump's bid to fire Fed's Lisa Cook on January 21
- Fed split deepens as Collins says she would hesitate to support another cut
- Fed to cut rates again in December on weakening job market, say most economists
- Fed may soon start buying bonds to manage market liquidity, Williams says
- Bigger trouble developing in China:
- China's Singles' Day shopping festival winds down with 'muted' sentiment
- US House report accuses China of minerals market interference
- Bigger stimulus developing in Japan:
- ECB minions thinking Eurozone inflation risk is low:
- Dow finishes at all-time high as government shutdown end nears; Nasdaq lags amid struggling tech trade
- Thursday, 13 November 2025
-
- Signs and portents for the U.S. economy:
- Oil prices steady after steep losses in previous session
- US corporate bankruptcies set to hit 15-year high amid credit jitters, S&P data shows
- Fed's December rate cut looks increasingly like a toss-up
- Bigger trouble developing in China:
- China's October new home prices fall at fastest pace in a year
- https://www.reuters.com/world/asia-pacific/chinas-october-new-bank-loans-fall-sharply-missing-forecast-2025-11-13/
- Bigger trouble developing in Japan with prices, BOJ minions want wage inflation:
- Japan's wholesale prices rise more than expected on sticky food inflation
- Bank of Japan aims for wage-driven inflation, aligns with government view
- U.S. stocks sink as post-shutdown optimism fades, rate cut odds fall
- Friday, 14 November 2025
-
- Signs and portents for the U.S. economy:
- Oil settles up more than 2% as Russian port suspends oil exports after Ukrainian attack
- Trump cuts tariffs on beef, coffee and other foods as inflation concerns mount
- More Fed minions signal reluctance to cut rates in December, another minion revealed to have ethics problem that led to their unexpected exit:
- As Fed hawks press their case, traders bet against December cut
- Former Fed Governor Kugler's exit came amid forbidden trading activity
- Bigger trouble, stimulus developing in China:
- China's economy jolted by weakest factory output, retail sales growth in over a year
- China vows to boost consumption, better balance demand and supply
- Wall Street ends mixed, Nasdaq survives from selloff amid valuation worries
The end of the federal government shutdown had very little impact on stock prices. That's an expected outcome because most political events that don't involve changes in tax rates tend to contribute little more than noise to markets. That doesn't mean it won't have an economic impact, because of its length and because it began to disrupt air transportation with air traffic controllers not showing up for work at major airports after a month of going unpaid.
We don't know yet how big that impact might be. The Atlanta Fed's GDPNow tool projection of real GDP growth in the U.S. during the recently ended 2025-Q3 was unchanged at +4.0%, as many economic data reports remain on hold with the government slowly resuming operations after the Senate Democrats' failed shutdown. The BEA's official estimates of GDP in 2025-Q3 remain on hold as well. And for that matter, 2025-Q4, which is when any actual economic contraction related to the shutdown occurred.
Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon showing Federal Reserve officials in suits carrying football goalposts labeled 'RATE CUT' away from a Wall Street bull wearing a football uniform and preparing to kick a field goal, who looks frustrated as the goalposts are being moved further away"
Imagine you're in charge of placing security cameras inside a gallery filled with valuable objects. Your boss is willing to pay to put in as many cameras at it will take to protect the gallery's contents, provided you meet two conditions:
- The cameras must collectively provide 100% visual coverage of the entire area of the gallery.
- You have to determine the minimum number of cameras that will be needed to do the job.
Believe it or not, this is a famous 50-year old geometry problem that's known as the art gallery problem. In the following 50-minute video, CC Academy describes how the problem can be solved using graph theory for any strangely shaped floorplan:
Kit Yates discusses why the recent heist of the French royal jewels from the Louvre Museum in Paris brings home the importance of this geometry problem:
At a hearing in front of the French Senate in the immediate aftermath of the robbery, Laurence des Cars, the director of the world famous museum, admitted that the museum had "failed to protect" the crown jewels. She admitted that the only camera covering the balcony the thieves used was facing the wrong way and a preliminary report revealed one in three rooms in the Denon wing where the thieves struck had no security cameras. More generally Des Cars acknowledged that cuts in surveillance and security staff had left the museum vulnerable and insisted that the Louvre's security system must be reinforced to "look everywhere".
Alarms at the museum apparently sounded as they should, according to the French culture ministry. Yet it is the third high profile theft from French museums in two months, which have left the ministry implementing new security plans across France.
As they should, if for no other reason than because their security scheme has been shown to have gaping holes that thieves an easily drive a Böcker Agilo truck-mounted moving lift through.
But more to the point, had those responsible for overseeing the Louvre's security solved their specific version of the art gallery problem, the thieves' plans might have been thwarted. Yates concisely explains how to quickly determine how many cameras you might need using only geometric principles:
The answer, it turns out, depends on the number of corners (or, as mathematicians call them, "vertices"), as there will be as many walls as there are corners in a room. Some simple division helps us work out how many cameras are needed.
By dividing the number of corners in a room by three, that will tell us how many cameras are needed to cover it, assuming they have a full 360 degree field of view....
This even works if the number of corners isn't neatly divisible by three. For a 20-sided gallery, for example, the answer works out at six and two thirds. In these cases you can take the whole number – so we'd never need more than six cameras in a 20-sided room.
Yates continues by getting into the graph theory that tells where those 360-degree view cameras can then be optimally placed.
In 1978 Steve Fisk, a mathematics professor at Bowdoin college in Maine, US, came up with a proof – considered one of the most elegant in all of mathematics – of this lower limit on the number of cameras needed.
His strategy was to divide the gallery up into triangles (check out the left image of the figure below). He then proved that you can pick just three colours – say red, yellow and blue – and assign a different colour to the corners of each triangle. This would mean that every triangle in your gallery has a different colour in its three corners (See the right image of the figure below for an example). This is known as "three-colouring" the corners.
Triangles are one of those "convex" polygons we mentioned earlier, so a camera positioned at any corner (or indeed anywhere in the triangle) can see every point in that shape. Every triangle has corners with each of the three colours. That means you can pick just one of the colours and place cameras at those positions. Those cameras will be able to see every part of every triangle, and hence every part of the gallery. But here's the best part.
The beauty of Fisk's proof is you can just choose the colour with the fewest dots, and you'll still cover the whole gallery. In the 15-sided shape above, by choosing the red dots, we can get away with only four cameras.
What are the chances that all of France's art gallery security problems are now homework assignments for the country's undergraduate math students taking courses in either geometry or graph theory?
Image credit: Art Gallery Problem sample with 4 cameras by Rocchini on Wikimedia Commons Creative Commons CC BY 3.0 Attribution 3.0 Unported Deed.
Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:
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