Ever since the call option was invented by Thales of Miletus about 26 centuries ago, savvy investors have used these and similar financial instruments to make money.

But even though options have been around for a very long time, it wasn't until the last 12 decades and mostly within the last 60 years, in which the math needed to determine what their price should be was finally developed.

In the following 31-minute video, Veritasium's Derek Muller explains the origins of options and the Nobel-prize winning development of the math behind what became the world's first trillion dollar equation. Which turned out to be closely related to the math physicists use to describe the diffusion of heat.

This being a video from the modern internet, there's a mattress commercial built into the middle of the video. If you jump to the 16:02 mark after it starts, it is something you can skip past, unless you're perhaps in the market for a mattress.

In any case, the story is fascinating, because it also involves the one of the most successful investment managers of all time, a mathematician who earned that title by betting against the widely believed efficient market hypothesis by uncovering not-so-random patterns within it and using options to realize gains to beat the market year after year.

The pace at which the concentration of carbon dioxide in the Earth's atmosphere is increasing picked up in May 2025, fully reversing the downward trend that began after December 2024.

The latter half of 2024 had seen record high levels of CO₂ accumulation in the Earth's air thanks largely to efforts by Chinese firms to produce and export as many goods as they could ahead of new tariffs and trade restrictions that were expected to be imposed on China-produced goods. Industrial production slumped in China following its efforts to front-run (or front-load) their exports before these anti-free trade measures were implemented. Since China is by far and away the world's biggest producer of carbon dioxide emissions, changes in its economic output directly affect the rate at which the concentration of CO₂ changes.

From January 2025 through March 2025, the rate of CO₂ accumulation fell, before stalling in April. The data for May 2025 however shows it rose, which suggests a new effort to stimulate China's economy began in early April. This timing coincides with President Trump's "Liberation Day" tariff announcement, which saw the U.S.' highest tariff rates applied to goods produced in China, which then escalated even higher as China imposed retaliatory tariffs on U.S.-produced goods and the U.S. responded in kind.

The following chart, which tracks the trailing twelve month average of the year-over-year change in the rate at which the concentration of carbon dioxide measured at the remote Mauna Loa Observatory has changed from January 2000 through May 2025, shows the reversal:

The January-March 2025 downturn also coincides with a quarter of negative real economic growth in the U.S., which was highly influenced by the frontrunning (or front-loading) of exports to the United States following their production in China in 2024.

On the stimulus side of the story, there are several developments that indicate unusual interventions by China's government is behind the increase in CO₂. First, China's government has approved new coal-fired power plants:

China approved 11.29 gigawatts (GW) of new coal power capacity in the first quarter of 2025, Greenpeace’s review of official documents showed. This pace of coal-fired electricity approvals already exceeds the 10 GW China approved in the first half of 2024.

Second, China's coal-fired power plant managers have been directed to buy more coal, even though China's economy has slowed and its demand wouldn't support it unless part of a larger stimulus effort:

China is pressing its coal-fired power plants to stockpile more of the fuel and import less in an effort to shore up domestic prices, sources with knowledge of the matter said, but traders are sceptical the measures will help to stop the slide.

The coal industry in China faces rising stockpiles of the fuel after a massive expansion of output following shortages and blackouts in 2021 is churning out more coal than even the world's largest thermal power fleet can consume.

To support miners whose profits are under pressure, the state planner has asked power plants to prioritise domestic coal and increase thermal coal stockpiles by 10%, setting an overall target of 215 million metric tons by June 10, the sources said.

Third, China announced earlier it will build additional coal-fired power generation capacity to compensate for gaps in the reliability of power produced by renewable energy sources. The announcement will see China continue producing coal-fired power plants through 2027 and represents a significant stimulus initiative.

On that final count, the world had a wake-up call from the collapse of Spain and Portugual's electricity grid on 28 April 2025, which was caused by unstable solar energy production and ensured by the absence of more reliable conventional fossil-fuel or nuclear-based power generation. China's government is backing increased coal-fired electricity production as a solution to this problem in the near term.

References

National Oceanographic and Atmospheric Administration. Earth System Research Laboratory. Mauna Loa Observatory CO2 Data. [Online Data]. Updated 5 June 2025.

Image credit: Shuozhou coal power plant in Shuozhou, Shanxi, China by Kleinolive on Wikimedia Commons. Creative Commons CC by-SA 3.0 Attribution 3.0 Unported Deed.

As expected, there was a dramatic deviation in the level of trade between the U.S. and China in April 2025.

The combined value of goods exchanged between the two nations plunged 17.8% from their level in March 2025, from $40.8 billion to $33.6 billion. Year-over-year, the decline is even larger, at 22.2%.

April 2025's plunge in trade is also large enough to affect the trajectory of the trailing twelve month average of the combined value of goods traded between the U.S. and China. We find the trailing twelve month average of trade between the two nations is $47.7 billion. That figure compares with our counterfactual projection for this month based on the trajectory of trade between the two nations from March 2024 through March 2025 is $48.9 billion. April 2025's deviation is $1.2 billion.

The following chart presents the monthly figures for the combined value of goods exchanged between the U.S. and China with the trailing twelve month average and counterfactual projection of the trailing twelve month average through April 2025.

We anticipate the deviation between our counterfactual and the actual trajectory of trade between the U.S. and China will continue growing when May 2025's trade data becomes available next month.

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 5 June 2025.

Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a container ship from the U.S. and another container ship from China that are both half empty and heading in opposite directions". We modified the image with a second prompt: "Only show one container on the U.S. ship and show two containers on the China ship. Also make the picture more colorful", which didn't work as well as intended, but the image produced does get across a sense of the relative difference in cargo volume transported in each direction between the two nations.

After five months of relatively little change, the number of U.S. teens counted as having jobs declined in May 2025.

This change lags behind the negative GDP reported for the U.S. in the first quarter of 2025. The seasonally-adjusted number of employed teens fell by 142,000 (-2.5%) from 5,732,000 to 5,590,000 April 2025.

The decline was experienced by both younger teens (Age 16-17) and older teens (Age 18-19), with younger teens experiencing a bigger decline. The total number of younger teens declined by 3.1% to a seasonally-adjusted 1,939,000, while the number of older teens fell by 2.0% to 3,646,000.

These declines are occurring before the summer teen hiring season gets underway. Job outplacement firm Challenger, Gray & Christmas anticipates fewer teens will find jobs in the upcoming summer:

Outplacement and executive coaching firm Challenger, Gray & Christmas, Inc. predicts teens will gain 1 million jobs in May, June, and July 2025, down from the 1.3 million jobs the firm predicted last year and the 1.1 million teen jobs employers actually added. This would be the lowest number of summer jobs added for teens since 2010, when teens accepted 960,000 new positions in the summer months.

The firm cites socio-political concerns that they anticipate will result in reduced tourism and potentially higher prices from tariffs, which they believe will prompt employers to reduce their summer hiring. They do not cite any factors for why the employment prospects of younger teens would be more negatively affected by these factors than older teens.

The following pair of charts presents seasonally adjusted U.S. teen employment and the teen employed-to-population ratio from January 2021 through May 2025.

The figures and percentages presented in these charts have each been subjected to their own seasonal adjustment, so the number of employed Americans Age 16-17 and employed Americans Age 18-19 won't necessarily add up to the indicated number of working Americans Age 16-19. If you want numbers that do add up, you'll want to access the non-seasonally adjusted data available at the BLS' data site.

References

U.S. Bureau of Labor Statistics. Labor Force Statistics (Current Population Survey - CPS). [Online Database]. Accessed: 6 June 2025.

Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a high school student who is having trouble finding a job". We tweaked the image so the Help Wanted sign indicates 'MUST BE 18 OR OLDER'.

The S&P 500 (Index: SPX) finally broke through the 6,000 in the past week, with the index achieving its new record high close of 6,000.36 on Friday, 6 June 2025!

There is, of course, nothing special about the number 6,000 as it affects the value of the index, which analysts first started predicting would become inevitable back in September 2024.

Back then, the prospect of the S&P 500 reaching 6,000 was closely linked to the expectation the Fed would continue cutting interest rates well into 2025, which didn't materialize as expected. The Fed's minions started off like they would, cutting rates by a half-percent on 18 September 2024 and by a quarter percent on 7 November 2024 and again on 18 December 2024.

But they haven't since, keeping the Federal Funds rate at their target range of 4.25-4.50%. Not that they haven't played with the idea of more cuts before ultimately pushing back and choosing to delay their next action. Right now, the CME Group's FedWatch Tool 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 by quarter point rate cuts at twelve-week intervals, with the cuts expected on 10 December (2025-Q4) and 18 March (2026-Q1).

With rate cuts thus delayed, the S&P 500 has absorbed the news of market moving events that have changed the market regime, with the result being the index has pushed its way through the 6,000 level without the additional rate cuts analysts thought it would take to get there. The latest update of the alternative futures chart shows the all-time high level of stock prices is consistent with investors focusing on the fourth quarter of 2025 as they set current day stock prices.

This shift in investor time horizon coincides with the increasing realization the Fed was going to hold rates steady through the summer, which has taken place over the last several weeks. The shift also completes the Lévy flight event we described developing in the previous edition of the S&P 500 chaos series.

The completion of the Lévy flight also rules out the potential of another market regime change like the others that have taken place during 2025-Q2, at least through Friday, 6 June 2025.

As for what will drive the market next, that's up to the random onset of new information. Here are the market-moving headlines investors weighed during the week that was:

Monday, 2 June 2025

• Signs and portents for the U.S. economy:
• Trump says he plans to double steel, aluminum tariffs to 50%
• US aluminium, steel prices jump, shares drop on Trump's new tariffs
• Oil leaps 4% after OPEC+ keeps output increase unchanged
• Fed minions say they'll get around to cutting rates later in the year, say tariffs may cause temporary inflation:
• Fed's Waller still open to cutting interest rates later this year
• Fed’s Goolsbee: Tariffs will drive inflation, but effects may be temporary
• Federal Reserve’s Goolsbee sees path to lower interest rates despite recent turbulence
• Eurozone minions incented to think about making tariff deal with US:
• Trump tariffs deals major blow to European steelmakers, Salzgitter CEO warns
• EU says it will make strong case for US tariff cuts this week
• Euro zone factory downturn eased in May, PMI shows
• Nasdaq, S&P, Dow ended higher despite U.S.-China trade tensions

Tuesday, 3 June 2025

• Signs and portents for the U.S. economy:
• US auto sales rate plunges in May after pre-tariff rush fades
• US factory orders slump in April
• Trump to sign order doubling metals tariffs, White House says
• Oil climbs 2% to 2-week high on geopolitical tensions
• Fed minions keep saying they won't rush to cut U.S. interest rates, claim tariffs are boosting inflation:
• Fed officials beat the policy patience drum as tariff uncertainty persists
• Fed's Goolsbee says tariffs could boost inflation quickly, take longer to slow economy
• Fed's Bostic says current uncertainty calls for patience on rate policy
• Bigger trouble developing in China:
• China's factory activity cools in May as US tariffs hit
• China car dealers urge automakers to stop dumping inventory on them
• BOJ minions say US tariffs no big deal, ready to raise Japan's interest rates if economic growth picks up:
• BOJ chief voices confidence economy can withstand US tariff hit
• BOJ's Ueda signals readiness to raise rates if growth re-accelerates
• ECB minions getting excited for more Eurozone interest rate cuts:
• Euro zone inflation eases below ECB target, supporting rate cut bets
• Wall Street takes home gains, Nasdaq adds nearly 1% while S&P approaches 6,000
• Magnificent Seven power ahead as earnings outpace rest of S&P 500 by nearly 3-to-1
• Wall Street stocks end higher on Nvidia, trade talks hopes

Wednesday, 4 June 2025

• Signs and portents for the U.S. economy:
• US service sector unexpectedly contracts in May; inflation heats up
• US labor market easing in the face of tariff uncertainty
• Oil steady as OPEC+ hikes output while wildfires curb Canadian supply
• Trump again urges Powell to cut rates after soft private sector job growth
• Fed hawks and doves: what US central bankers are saying
• Potential trade deal with US developing in China:
• Trump and Xi agree to more talks as trade disputes brew
• Exclusive: China issues rare earth licenses to suppliers of top 3 US automakers, sources say
• BOJ minions say they're thinking about holding more bonds that what they previously planned:
• BOJ to consider slowing pace of bond tapering next year, sources say
• Eurozone minions trying to negotiate trade troubles on two fronts:
• EU, China tackle trade issues ahead of leaders' summit
• China's rare earth export curbs hit Europe's auto industry
• Global alarm as China's critical mineral export curbs take hold
• EU says US trade talks move in right direction, but metals tariffs not helping
• ECB minions getting excited to cut Eurozone interest rates again:
• ECB to cut rates again as the case builds for a summer pause
• Stocks end flat, Treasury yields slide as traders flock to bonds after weak data

Thursday, 5 June 2025

• Signs and portents for the U.S. economy:
• Trump, Musk in public spat over spending bill; Tesla stock gets hit in the aftermath
• Trump, China's Xi agree to visit each other over 'very good phone call'
• US trade deficit narrows sharply in April; imports post record drop
• Oil settles up as US, China teams to meet following Trump, Xi trade call
• Fed minions say they're paralyzed by inflation fear:
• Fed policymakers flag inflation concerns, a view that argues against rate cuts
• Fed's Harker says its time for caution on monetary policy amid uncertainty
• Fed's Schmid: uncomfortable with looking through tariff-driven price push
• Bigger trouble developing in China:
• The world's auto supply chain is in the hands of a few Chinese bureaucrats
• ECB minions thinking they might be near done cutting Eurozone interest rates:
• ECB cuts rates again but hints at pause
• For markets, end to ECB rate cuts just got closer
• ECB governors see July pause but Sept up in the air
• Stocks close lower as Tesla slides 14% amid Trump and Musk public spat

Friday, 6 June 2025

• Signs and portents for the U.S. economy:
• US payrolls growth slows in May, unemployment rate steady
• Jobs data in charts: Payroll growth slows in May; unemployment rate remains at 4.2%
• Crude climbs on US jobs report, China talks
• US oil/gas rig count falls for 6th week to 2021 lows, Baker Hughes says
• Fed should cut interest rate by a full point, Trump says
• Fed minions say they're thinking about rate cuts later in year, don't trust their data, and think they're too strict in overseeing US banks:
• Fed's Harker says rate cuts this year still possible, amid data quality worries
• Fed's Bowman lays out ambitious agenda to overhaul and ease bank oversight
• Bigger trouble developing in China:
• China's yuan slips to 2-year low versus peers after Trump-Xi call leaves issues unresolved
• China's exports likely slowed in May amid trade uncertainties - Reuters poll
• BOJ minions get green light to continue hiking Japan's interest rates:
• US Treasury says BOJ should continue to tighten policy
• ECB minions starting to worry about Eurozone inflation being too low:
• ECB policymakers debate risk of inflation going too low
• S&P 500 closes above 6,000 for the first time since February after strong May jobs data
• Microsoft marks new milestone as market cap hits $3.5T, holds slight edge over Nvidia
• Tesla shares gain after $152 billion selloff, but Trump-Musk truce uncertain

The Atlanta Fed's GDPNow tool projection of real GDP growth in the U.S. during the current quarter of 2025-Q2 increased to +3.8%, up from the +3.3% that it previously projected.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of Wall Street celebrating the S&P 500 reaching a value of 6,000."