The dividend outlook of the S&P 500 (Index: SPX) once again delivered a mixed outlook for investors in August 2026.

Expected dividends for the index dipped in the current quarter of 2026-Q3, but the amount of cash dividends expected to be paid out in the upcoming future quarters of 2026-Q4 and 2027-Q1 increased. The more distant future quarters of 2027-Q2 and 2027-Q3 however both declined with respect to the July 2026 snapshot of the S&P 500's dividend outlook.

All these changes however are modest, with the magnitude of the changes for each quarter coming in at less than one percent. Here is the summary of how the expected future for the S&P 500's dividends changed between 14 July and 14 August 2026:

• 2026-Q3: Decrease of $0.11 to $21.02 per share
• 2026-Q4: Increase of $0.10 to $21.55 per share
• 2027-Q1: Increase of $0.06 to $22.81 per share
• 2027-Q2: Decrease of $0.15 to $21.60 per share
• 2027-Q3: Decrease of $0.11 to $21.81 per share

The following chart illustrates the expectations for the S&P 500's quarterly dividends per share as of 14 August 2026 and how they compare with the preceding quarters going back to 2024-Q3.

More About Dividend Futures

Dividend futures represent the quantified expectations investors have for the future income they will realize from owning shares of stocks, which in turn, affects how investors set current day stock prices. How changes in the outlook for dividends at specific points of time in the future contribute to changes in current day stock prices as represented by the value of the S&P 500 index is described by this math.

Dividend futures for the index indicate the market capitalization-weighted amount of dividends per share for all these dividend-paying stocks that are expected to be paid out over the period covered by each quarter's dividend futures contracts. These contracts 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. For example, as determined by dividend futures contracts, the now "current" quarter of 2026-Q3 began on Saturday, 20 June 2026 and will officially end on Friday, 18 September 2026. Since the expectations for this quarter's dividend payouts can change all the way up to that final date, it counts as a future quarter all the way up through that future point in time.

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.

The S&P 500 (Index: SPX) reached a new record high close of 7,798.99 on Thursday, 13 August 2026 before falling back on Friday to end the trading week at 7,785.76.

Two developments helped to spur the index to its new heights. First, investors received good inflation news on Wednesday, 12 August 2026 when the Consumer Price Index came in lower than expected. The second came on Thursday, when the Producer Price Index was likewise reported to be lower than expected.

Because of these benign consumer and producer price inflation reports, the CME Group's FedWatch Tool no longer anticipates the Fed will act to hike the Federal Funds Rate from its current target range of 3.50-3.75% in September 2026, but will instead delay a quarter point rate hike to take place sometime in the fourth quarter of 2026. In its latest snapshot, the FedWatch Tool sees a falling 53% chance the Fed will act to hike this core interest rate to a target range of 3.75-4.00% on 28 October (2026-Q4) but gives a more solid 93% chance this rate will be in effect on 9 December (2026-Q4).

With the next rate hike likely delayed and fewer rate hikes on the table as a result of the better than expected inflation reports, the resulting lower interest rates kept investors focused on the first quarter of 2027 as they set current day stock prices. The latest update of the alternative futures chart shows the level of stock prices is right where they dividend futures-based model forecasts it would be provided investors are focused on 2027-Q1.

While those were the biggest headlines, other things happened that contributed to the random onset of new information investors absorbed and reacted to during the week that was. Here is our summary of the week's market moving headlines:

Monday, 10 August 2026

• Signs and portents for the U.S. economy:
• July US container imports hit fourth-highest on record, Descartes says
• Oil climbs 5% as Iran, US both demand compensation and Hormuz hopes fade
• Oil in U.S. Strategic Petroleum Reserve falls below 300 million barrels, lowest since 1983
• Lower inflation, global ambitions developing in China:
• China July factory-gate inflation eases to 3-month low, CPI slows
• China's central bank vows to expand yuan's international use in five-year plan
• China bypasses shipping chokepoints with ‘Ice Silk Road’ through Arctic
• Bigger trouble developing in Japan as BOJ minions plan next rate hikes:
• BOJ's rate-hike path runs into Takaichi's bond market problems
• BOJ's debate on faster hikes bolsters September rate move odds
• Bigger trouble developing in Eurozone:
• German trade deficit with China grows as Beijing relies less on European industry
• Wall Street concluded moderately lower as hopes for Hormuz reopening fade
• Wall Street ends down as expectations of Hormuz deal fade
• Market breadth strengthens: Equal-weight S&P 500 pulls ahead of market-weight index
• Meta to open source its most powerful AI model as it takes swipe at OpenAI, Anthropic
• Microsoft plans to unveil next-generation AI chip in September, The Information reports

Tuesday, 11 August 2026

• Signs and portents for the U.S. economy:
• US court rules Meta, other tech firms must face thousands of lawsuits over social media addiction
• US existing home sales fall further; small business sentiment at 11-month high
• Oil prices settle up as Iran says Strait of Hormuz to stay shut
• U.S. oil tops $84 as Hormuz deal hopes dwindle and deadlock deepens
• US auto loans hit record high in second quarter, New York Fed says
• US officials work to close supply chain gaps as foreign investment grows
• Fed minions say inflation is their biggest problem:
• Inflation is the biggest problem, Fed's Goolsbee says
• Atlanta Fed's Venable: Inflation too high, with prospect of easing dependent on events in Middle East
• Bigger trouble, stimulus developing in China:
• China's car sales extend slide as shift accelerates to overseas markets
• Surge in China's coal imports may start to taper off
• Bigger trouble developing in Japan:
• Yen sinks as effect of US-Japan intervention fades
• Wall Street ended lower as eyes remain on the Middle East and upcoming inflation data
• Wall Street ends down as US-Iran peace optimism fades

Wednesday, 12 August 2026

• Signs and portents for the U.S. economy:
• US annual inflation cooled to 3.4% in July
• Headline CPI rises 3.4% in July, slowing from June's pace
• Rate-Hike Odds Tumble As US Consumer Price Inflation Prints Slowest Since Pre-War
• Oil prices edge up as investors weigh US-Iran talks deadlock against lower demand
• OPEC further lowers 2026 global oil demand growth forecast
• Mortgage rates finally stop rising, causing demand to trickle back
• Before the CPI inflation report: Fed minions say poor Americans are struggling to make ends meet, want to hike their interest rates:
• Boston Fed's Collins open to interest rate increase in September, FT says
• Poorer Americans are struggling to make ‘ends meet’, top Fed official says
• Investors worry leaner Fed guidance may come at a price
• After the CPI inflation report:
• Fed expected to leave rates unchanged next month after soft inflation data
• Bigger trouble, stimulus developing in China:
• China's central bank pledges timely new policy rollout
• Wall Street finished up in the green after the latest inflation report
• S&P 500 ends higher as CoreWeave results fuel AI optimism
• CoreWeave, Super Micro surge on signs of sustained AI buildout
• 23 dividend safety stocks beating the S&P 500 this year

Thursday, 13 August 2026

• Signs and portents for the U.S. economy:
• US producer prices unchanged in July, further dimming rate hike odds
• Oil settles down 2% on weak demand outlook, hefty US crude build
• One Fed minion notices inflation data doesn't support rate hikes, other Fed minion is slow on the uptake, while third is flapping in the wind:
• Fed's Goolsbee says latest inflation data is better
• Fed should raise rates to restrain growth and inflation, Hammack says
• Fed's Barkin: Still an "open question" if rate hike will be needed to meet inflation target
• BOJ minions excited to get inflation data to support their plans to keep hiking Japan's interest rates:
• Japan's wholesale inflation stays hot, bolstering odds of September BOJ hike
• Rate hike bets leave yen's post-intervention gains at BOJ's mercy
• Japan may see more yen intervention, faster BOJ rate hikes, ex-top FX diplomat says
• Wall Street ended on top as the S&P 500 notched a new record high
• S&P 500 notches record-high close as rate-hike worries ease
• S&P 500 hits 27th record high of 2026 — History says more likely ahead

Friday, 14 August 2026

• Signs and portents for the U.S. economy:
• US retail sales post first decline in nine months in July
• Oil set for weekly gains after US threatens indefinite blockade of Iran
• Fed rate hike odds sink further as retail sales, consumer sentiment fall
• US retail sales post first decline in nine months in July
• Fed minions expected to sit on hands rather than hike rates in September 2026:
• Cooler inflation data may force Warsh's divided Fed to hold the line on rates
• Bigger trouble developing in and out of China:
• China July bank loans post record contraction as credit demand falters
• Chinese car sales are booming almost everywhere - just not at home
• BOJ minions getting super excited to hike Japan's interest rates again:
• BOJ eyeing September rate hike, faster pace of tightening, sources say
• Central bank minions around globe betting big on gold:
• Central banks spearhead renewed gold rush
• Wall Street ended lower a day after the S&P 500 notched a record high
• S&P 500 ends lower as investors weigh data, Middle East tensions
• S&P 500 posts weekly gain as strength spreads beyond technology

The Atlanta Fed's GDPNow tool anticipates real GDP growth for the U.S. economy of +4.3% in 2026-Q3, down from the +5.8% annualized growth it forecast a week earlier.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull and bear who give each other a high-five after news breaks that inflation came in lower than expected while Federal Reserve officials are sad they won't be able to hike U.S. interest rates when they wanted".

Knots hold a special place in the hearts of sailors and mathematicians.

That's almost self-explanatory for sailors, who have been tying knots as an essential part of their craft for centuries. They even used them to tell how fast they're going over open water.

Mathematicians' fascination with knots is harder to explain, but comes down to their love of counting. The more complicated the knot, the more the knots strands cross each other, the better. And what better way to make a knot more complicated than by taking two knots, cutting each and then joining their open ends together to make an even bigger, more complicated knot?

They even defined a special rule about the practice to calculate how much more complicated the resulting knot would be. They conjectured that if they took the unknotting number for each knot, which is to say the number of steps it would take to tranform the knot into a simple loop (imaginatively called the "unknot"), and added them together, the result would be the unknotting number of the combined, more complicated knot.

This additivity conjecture worked with just about every combination of knots they could throw at it. Until two mathematicians discovered an example where that rule didn't work. Instead of leading to a more complicated knot, they found a knot that became easier to unknot after being joined. It didn't add up as previous generations of mathematicians had believed it should, and because it didn't, they proved the conjecture about the additivity of unknotting numbers is untrue for all cases.

In the following video, Trefor Bazett guides viewers through basic knot theory in an easy to understand presentation before getting to the remarkable disproof of the additivity conjecture in knot theory by Mark Brittenham and Susan Hermiller, which only took them ten years to work out:

Brittenham and Hermiller's paper is here. Bazett has a second video featuring an extended interview with Brittenham and Hermiller.

The knot they found that broke the rule is the (2,7) Torus Knot, an example of which is the featured illustration for this article. It's also known as the 7₁ knot in a different mathematical knot nomenclature system, but we're not going to get into that topic because why complicate knots any more than needed?

Image credit: Blue 7₁ Knot or (2,7) Torus Knot by Jim.belk on Wikimedia Commons. Public Domain.

Measuring economic activity using astronomical and other scientific tools is a relatively recent development that has come into its own during the 21st century.

One of the neater tools are telescopes and cameras mounted on Earth-orbiting satellites that take pictures of the night-darkened surfaces of the world. NASA's Black Marble project uses those images to tracks how the nighttime lights spread across entire regions change in brightness over time, with fully processed imagery now covering the years from 2014 through 2022.

We haven't gotten too far into the data behind the images yet, but what we see in how nighttime lights have changed the years between 2014 and 2022 appears to correspond with how carbon dioxide emissions have changed in those regions. Nighttime lights in Asia, and especially in China and India have become significantly brighter during a period in which those nation's emissions of carbon dioxide have risen. By contrast, regions that have seen falling levels of CO₂ emissions such as the eastern portion of the U.S. and western Europe have seen the brightness of their nighttime lights grow dimmer.

That introduction brings us to the latest measurements of the concentration of carbon dioxide in the Earth's atmosphere, which is measured at the remote Mauna Loa Observatory. The latest data indicates the pace at which carbon dioxide is being emitted into the Earth's atmosphere is continuing to decline, which indicates the world's economic activity is falling.

The following chart reveals how the trailing twelve month average of the year-over-year change in the rate at which the concentration of carbon dioxide in the Earth's air is changing has changed from January 2000 through July 2026.

The rate at which CO₂ is increasing in the atmosphere is nearing levels where it has bottomed during periods of global recessions, or rather, significant regional recessions, in the 21st century.

References

National Oceanographic and Atmospheric Administration. Earth System Research Laboratory. Mauna Loa Observatory CO2 Data. [Online Data]. Updated 5 August 2026.

Image credit: Eastern Hemisphere Map: Total Radiance Change from 2014 through 2022, NASA Earth Observatory images by Michala Garrison, using data from Li, T., et al. (2026). Public Domain.

As expected, the value of goods exchanged between the U.S. and China increased in June 2026.

The U.S. Census Bureau reports a combined total of $34.7 billion worth of goods were processed through U.S. ports during the month. Both outgoing exports to China and incoming imports from China increased month-over-month. Exports rose 5% from $9.117 billion to $9.571 billion and imports grew 7% from $23.508 billion to $25.150 billion between May and June 2026.

Year-over-year, the combined value of goods traded between the U.S. and China has increased by 22%. Digging into that number, we find some really lopsided results. The increase of U.S. exports to China accounts for just 2% of the year-over-year increase, while China's exports make up the remaining 98%.

Reports indicate technology goods such as semiconductors, computing hardware, and AI technology components led the increase in China's exports to the U.S. in June 2026. In addition, U.S. firms importing lower-value goods for the upcoming Christmas shopping season had a strong incentive to pull their orders forward 1-2 months earlier than normal, seeking to beat the clock on new U.S. tariffs.

The following chart shows how the flow of trade between the U.S. and China has evolved from January 2017 through July 2026.

June 2026 saw the twelve month trailing average value of goods directly traded between the U.S. and China record its second increase after having registered declines in each month from February 2025 through April 2026. The cumulative total loss of direct trade between the U.S. and China with respect to a counterfactual projection of what that trade would have been without the tariff war between the two nations adds up to $187.4 billion through June 2026.

Image credit: Port of Seattle cranes on a sunny October day by Ron Clausen on Wikimedia Commons Creative Commons CC BY-SA 4.0 Attribution-ShareAlike 4.0 International.