On Monday, 30 March 2026, the S&P 500 bottomed at 6,343.72. Stock prices had been battered in the month after the Iran War geopolitical conflict started, falling 535.16 points (7.8%) from the close of trading on Friday, 27 February 2026, the day before it began.

Then came word the conflict was likely to get worse. Oil prices surged. The possibility the U.S. economy might contract began to be seriously considered. All signs seemingly pointed to a bigger downward move for stock prices.

But then, something else happened. Stock prices began to rise as investors considered what those possibilities would mean. And what they saw was a Federal Reserve that had been considering hiking interest rates take them off the table instead.

Stock prices continued their new rally after a two-week cease fire was announced in the geopolitical conflict a little over a week later. Then 2026's second quarter earnings season got underway and investors were treated to some of the best earnings reports they had seen in years, combined with improved business outlooks for many companies standing to benefit from the buildout of Artificial Intelligence (AI) system infrastructure.

In the weeks since, that pattern has continued. The Iran war cease fire has been extended several times. In the stock market, companies kept reporting much better than expected earnings and business outlooks. Stock prices have taken off like they were strapped to a Spacex rocket, to name one firm whose imminent Initial Public Offering (IPO) is exciting the investing world. Through the close of trading on Friday, 29 May 2026, stock prices have increased by 16.3% above where they bottomed on 30 March 2026.

A month ago, when we looked at the value of the S&P 500 with respect to its underlying dividends per share, we weren't surprised to see the index was on track to make a full recovery from its geopolitical swoon. But now that it has, the rise of stock prices hasn't slowed down very much, which makes it different from previous recoveries in recent years. Instead, they are almost within a single standard deviation of crossing a critical level that would represent a breakdown of the relative order in the stock market that has been in place since 31 December 2023. The following chart presents the phenomenal rise of stock prices from 30 March 2026 through 29 May 2026 in the context of that relative period of order.

From where it closed on Friday, 29 March 2026, the S&P 500 would need to rise a little over 300 more points, or almost 4.0%, before the end of the quarter to break through the upper red dashed line that would potentially represent a break down of order in the stock market. We say potentially because just crossing the line isn't enough to qualify as a break down in order. Stock prices would have to be sustained above that upper threshold for long enough to rule out the possibility that it's just a simple statistical outlier. Much like how we determined the current period of order did not break down after stock prices broke below the lower limit back in April 2025.

But that's not all there is to need to be concerned about. This rally might qualify as a stock market bubble according to our working definition:

An economic bubble exists whenever the price of an asset that may be freely exchanged in a well-established market first soars then plummets over a sustained period of time at rates that are decoupled from the rate of growth of the income that might be realized from owning or holding the asset.

For stock prices, the income that might be realized from either owning or holding stocks are dividends. As shown in our chart, the rocketship ride of the S&P 500 in the last eight weeks is very close to qualifying as the inflation phase of a bubble.

What could possibly go wrong?

Aside from the now-classic example of the Dot Com Bubble, we've seen something like this pattern in historic data at least two other times. Once was before the Black Monday Crash of 1987. The other occurrence dates back to 1929, which defines an event we refer to as the Ultimate Sell Signal.

Which is not to say that stock prices are destined to immediately crash if they cross that upper threshold. The Dot Com Bubble inflated for years before it entered its deflation phase. What we can say is that if stock prices rise above that upper threshold and stay elevated above it, the stock market will have entered into a chaotic phase. Investors will need to adapt accordingly.

Previously on Political Calculations

• How Big is the AI Bubble and Is It Really a Bubble?
• The Definition of a Bubble
• The Ultimate Sell Signal
• What Caused the Dot Com Bubble to Begin and What Caused It to End?
• The Black Monday Stock Market Crash Explained
• Not Necessarily Wrong But Useful

Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull and bear riding on the outside of a rocket that is accelerating after launch".

Over the final trading week of May 2026, the S&P 500 (Index: SPX) rose 1.4% over its previous week's close to reach 7,580.06, a new record high for the index.

According to news headlines, it did so because of hopes of realizing a Middle East peace deal that might reopen the Hormuz Strait to oil shipping and because of strong earnings among technology companies whose products have become in high demand to build out the infrastructure to support Artificial Intelligence (AI) systems.

But we can't help noticing that these are variations of the same headlines that have accompanied the rise of the S&P 500 over much of the last two months. Can the prospect of a negotiated end to the Iran war geopolitical event still be powering stock prices higher? At what point are the expectations associated with a Middle East peace deal fully priced into the market? Especially when the proverbial can for actually reaching a deal to satisfactorily end the conflict keeps getting kicked down the road?

The real story is the outlook for both earnings and dividends has improved substantially throughout the past two months as the conflict's cease fire has held. These positive changes are the main drivers behind the rise in stock prices and they have benefited stock prices in two ways:

• They reversed the negative momentum that had sent stock prices substantially lower from the end of February through the end of March 2026.
• As affected firms have progressively reported the associated improvement in their outlooks, stock prices have continued rising, even though no deal has yet been reached.

That's a state of affairs that could change quickly and negatively if the cease fire breaks down, but short of the announcement of a deal that definitively ends the conflict, there's little room left for stock prices to rise more on these headlines with 2026-Q2's earnings season mostly having come and gone.

Meanwhile, the progress of AI technologies and the massive investments being made to advance them continues to be *the* market moving story of the year. There's a strong argument to be made the development is a modern day analog of the 19th century's boom in railroads. The booming earnings of companies whose products have become essential to the rapid, widespread adoption of AI technologies have been key in powering stock prices higher.

Speaking of which, the latest update of the alternative futures chart shows we have come to the end of the redzone forecast range we added in late February. The S&P 500's trajectory has shifted in the last few days away from the trajectory associated with investors focusing mainly on 2026-Q2 in setting stock prices to the more distant future quarter of 2026-Q4.

Although this is a relatively small change, the shift in how far forward in time investors are focusing their attention represents a Lévy flight event.

That timing is interesting because it coincides with a growing expectation of when the Fed might act to next change U.S. interest rates. The CME Group's FedWatch Tool pushed back the expected timing of a quarter point increase in the Federal Funds Rate to 9 December (2026-Q4), six weeks later than it had projected on Friday, 22 May 2026. Beyond that hike, the FedWatch tool no longer anticipates the Fed will hold the Federal Funds Rate at a target rate of 3.75-4.00% through all of 2027.

But there's a bigger question that now needs to be asked. Since the S&P 500 bottomed on 30 March 2026, has the index risen too far too fast? We'll take that question on in the very near future.

Meanwhile, how long investor expectations might hold depends upon the random onset of new information. Here are the market moving headlines that affected investor outlooks for stock prices in the Memorial Day holiday-shortened trading week.

Tuesday, 26 May 2026

• Signs and portents for the U.S. economy:
• US single-family home prices edge up in March, FHFA says
• Oil prices bounce around over Memorial Day holiday weekend with geopolitics:
• Oil tumbles nearly 7% as US and Iran seen moving closer to deal
• Brent crude jumps 4%, as US strikes in Iran set back hopes for Hormuz re-opening
• Oil and LNG tankers exit Hormuz, heading for Pakistan and China
• Bigger trouble, stimulus developing in China:
• China's weak steel output, strong iron ore imports show structural shift
• Explainer: China's latest coal mine closures, in context
• BOJ minions excited to see inflation data to support plan to hike Japan's interest rates:
• BOJ's new trend gauge shows inflation exceeding target
• ECB minions getting ready to ditch their perfect monetary policy for the Eurozone, say private credit is no big deal:
• ECB to revise inflation, growth forecasts, its chief economist says
• ECB should raise rates in June, even if Iran peace deal is struck, Schnabel says
• ECB will not hesitate to act to bring down inflation, Villeroy says
• Euro zone may face pockets of stress from private credit, not systemic risk: ECB
• S&P 500, Nasdaq hit record closing highs on AI optimism, Micron joins $1 trillion club
• Wall Street ended mostly higher on hopes of U.S.-Iran conflict resolution
• Micron joins $1 trillion club as AI race powers memory chip boom

Wednesday, 27 May 2026

• Signs and portents for the U.S. economy:
• US mortgage rate rises to nine-month high
• Oil prices drop as traders look for US-Iran talks progress
• Fed minions want to see lower demand, worry about inflation:
• Fed's Logan: world may need to cut use of oil and natural gas
• Fed's Kashkari calls for focus on inflation risk, mum on timing of next rate move
• Fed's Cook says she is prepared to raise rates if inflation doesn't ease
• Fed's Jefferson says monetary policy is 'well positioned' amid inflation risks
• Fed's Goolsbee says oil shock could exacerbate inflationary impulse of AI hype
• Bigger trouble, stimulus developing in China:
• Job ad for shepherds goes viral in China, exposing labour market strains
• China's new carbon metrics 'erased half' of emissions growth reported from 2020 to 2025, report says
• BOJ minions making less money because of their higher interest rates, worry energy shock may not be temporary, may need action to bailout Japan's currency again:
• BOJ's net income falls due to higher interest payments on reserves
• BOJ's Ueda warns temporary energy shock could become persistent
• Japan yen nears intervention zone; dollar steady as traders watch Iran
• Bigger trouble developing in Eurozone:
• Chinese brands gain as Europe car sales rise
• ECB tells banks to invest more to get a grip on AI security risk
• Wall Street indexes post closing record highs, AI rally pauses
• Wall Street ended slightly higher as eyes remained focused on U.S.-Iran negotiations

Thursday, 28 May 2026

• Signs and portents for the U.S. economy:
• US new home sales slump in April amid higher mortgage rates, prices
• US first-quarter GDP growth revised lower to 1.6% pace
• US PCE inflation firmer in April
• VIEW Inflation rises but isn't hotter than expected while GDP slips
• Oil prices fall as market awaits possible US-Iran ceasefire deal
• Fed minions say they have monetary policy right where they want it, don't think AK will reduce inflation:
• Fed's Williams reiterates rate policy is in right place given outlook
• Fed's Musalem says it's risky to bet that AI will ease inflation
• Fed's Williams: Productivity shifts hard to spot in real time
• Fed's Jefferson says he is focusing on inflation as US labour market 'very resilient'
• Bigger trouble, stimulus developing in China:
• China's auto industry is unlikely to return to 'golden era,' NIO CEO says
• BOJ minions getting Japan ready for their plan to hike interest rates:
• BOJ rate hike timing secondary to economy's readiness, ex-BOJ Deputy Governor Wakatabe says
• Japan banks battle to secure deposits as savers chase market highs
• ECB minions say Eurozone inflation will be persistent:
• ECB chief economist sees persistent impact on inflation from Iran war
• S&P 500 and Nasdaq hit record closing highs as US and Iran agree to extend ceasefire
• Wall Street closed in the green as speculation of a U.S.-Iran deal surfaced
• S&P 500 hits new record high while VIX falls to a 4-month low on U.S.-Iran news

Friday, 29 May 2026

• Signs and portents for the U.S. economy:
• US goods trade deficit narrows in April on strong exports
• Oil tumbles, stocks gain on US-Iran deal hopes
• Fed minions starting to eye rate hike as next move:
• More Fed policymakers eye possible rate hike as inflation risks rise
• Fed's Bowman backs 'easing bias' as core inflation runs 'a bit above 2%'
• Fed's Bowman says extended energy shock could drive shift in policy outlook
• Fed's Schmid warns against viewing oil shock as transitory
• BOJ minions busy with yen bailout, see inflation come in lower than they want to justify next rate hike:
• BOJ may heed calls to pause bond taper next year
• Japan spent $73 billion in yen-buying intervention, ministry data shows
• Core inflation in Tokyo stays below BOJ goal, factory output rebounds
• ECB minions getting excited for Eurozone interest rate hikes:
• ECB will act to head off persistent inflation, Panetta says
• German inflation eases in May, even as core inflation rises
• S&P 500 logs strong May gain as tech stocks lead rally
• Wall Street hits new closing highs on tech strength, Middle East deal hopes

The Atlanta Fed's GDPNow toolestimate of real GDP growth for the U.S. economy in the current quarter of 2026-Q2 decreased to +3.8%, falling back from the +4.3% it projected a week earlier.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a suit wearing Wall Street bull who is happy the S&P 500 has hit a new high and a bear who is reading a newspaper that says 'STOCKS UP ON MIDDLE EAST DEAL HOPES' and asks 'HOW MANY DAYS CAN STOCKS BE UP ON THE SAME HEADLINE?'"

There are quite a few famous unsolved problems in mathematics. Some are so famous they have million dollar bounties on them that will be paid out to the first mathematicians who definitively either prove or disprove them.

And then there are other important conjectures out there that, in addition to academic recognition, might pay smaller rewards to the people who crack them. But which if they are cracked, can be even more valuable if they can successfully be put to use.

One of those smaller conjectures is the Talagrand Convexity Conjecture. Proposed by French mathematician Michael Talagrand in 1995, Talagrand famously offered a $2,000 prize to anyone who solved it. Here is Jules Aknin's simplified description of the conjecture:

Talagrand’s convexity conjecture is a statement about high‑dimensional geometry: even in enormous, messy clouds of points, simple convex shapes are guaranteed to appear. In other words, no matter how chaotic the configuration looks, there is unavoidable structure hiding inside it.

If such structures are truly unavoidable, they can open the door to practical applications, including in financial markets. Aknin describes how they might contribute to finding order within chaos:

At a deeper level, results like this sit exactly at the intersection of geometry and probability. They don’t just create “pretty shapes” in higher dimensions, they show how structure emerges inside high‑dimensional random systems, which is the same conceptual problem we face when building models for complex datasets. In fact, as the original article notes, this kind of unification between geometric and probabilistic thinking could eventually influence how machines process high‑dimensional data and how we design algorithms that operate in those spaces.

[...]

On the surface, a high‑dimensional cloud of points in geometry and the Australian equity market do not look related. But in practice, we deal with a very similar object every day: hundreds of stocks, multiple time horizons, momentum profiles, risk factors, macro shocks and behavioural flows all interacting at once.

From a distance, that system may appear as pure noise. Talagrand’s result reinforces an idea that systematic managers have believed for a long time: structure is not optional, it is inevitable; the real question is whether you have the tools and discipline to find it.

Even though it doesn't carry the million-dollar prize of mathematics most famous unsolved problems, the stakes for those who can successfully build on the proven conjecture are still very high. That work is quite possibly worth a lot more than Talagrand's two-thousand dollar prize for the proof itself.

A team of three mathematicians stand to collect Talagrand's $2,000. Merrick Hua, Antoine Song, and Stefan Tudose posted a preprint paper of their proof on 11 May 2026, in which they converted the problem from one involving geometry to one involving probability and combinatorics. Like many math stories this year, AI is involved, but unlike those other stories, it's only a bit player.

The new proof was worked out by Dongming Hua and Antoine Song from the California Institute of Technology, and Stefan Tudose from Princeton University, who joined the other authors after hearing about their work. Together, the mathematicians reformulated Talagrand's geometric conjecture to a problem of probability theory and random vectors. In their paper published on the arXiv preprint server, they proved an equivalent conjecture for probability, showing that any 1-subgaussian random vector in n dimensions can be expressed as the sum of three standard Gaussian random vectors.

This result solves Talagrand's convexity problem, proving that for any large enough set in Gaussian space, a convex set of significant measures can be found inside a triple sum of the original set. The solution also confirms a combinatorial analog of the problem, which is important for discrete mathematics.

Initially, Song and Hua say they attempted to work out a solution with the help of ChatGPT. However, while the LLM helped to answer some of their questions and move them closer to a solution, it was Tudose who provided the final proof. Ultimately, the team did not use the work done with ChatGPT. In their paper, the team writes that Tudose's proof was "more general and conceptual."

It's a remarkable achievement. It is also a harbinger of the kind of role AI will find as just another tool used by people.

Image credit: Texture of an iced leaf image by Daniela deGol on Wikimedia Commons. Creative Commons CC By 4.0 Attribution 4.0 International Deed.

The U.S. new home market has largely recovered from the disruption of January 2026's blizzards. Unfortunately, rising mortgage rates combined with an uptick in the average sale price of new homes to reduce the quantity of sales. This combination of factors resulted in the total valuation of new homes sold in April 2026 to decline below the levels recorded a month earlier.

Political Calculations' initial estimate of the total value of new home sales in the United States during April 2026 is $28.30 billion. This value is slightly higher than the initial estimate of $28.24 billion for March 2026, but has declined from a revised value of $28.43 billion for the month.

The number of new home sales continues to hold relatively steady. The initial estimate of the annualized trailing twelve month average of the total number of new home sales for April 2026 is 665,000. This value falls below the range of 671,000 and 684,000 that had held since January 2024.

The initial estimate of the trailing twelve month average of a new home sold in April 2026 is $521,300. New home prices have generally rising since bottoming at $502,525 in September 2024. The average remains below the peak of $529,692 recorded for June 2022 at the height of the high inflation unleashed by the Biden administration.

All these figures represent time-shifted, partial trailing twelve month averages for each data series, which will be subject to revision for the next ten months before being finalized. The following charts present the U.S. new home market capitalization, the number of new home sales, and their average sale prices as measured by their time-shifted, trailing twelve month averages from January 1976 through April 2026.

Declining trend for new home sales:

Rising trend for new home prices:

New home sales were reported to have surged in March as prices fell to a five-year low, but much of this boost in sales may represent a springback from the impact of blizzards in much of the U.S. in January 2026 that shrank sales far below expectations.

Bloomberg confirms the April 2026 sales slump for new homes was not expected:

Sales of new US homes declined in April by more than forecast as builder incentives failed to motivate potential buyers at the start of the spring selling season.

Purchases of new single-family homes decreased 6.2% from March to a 622,000 annualized pace, according to government data released Thursday. Economists expected a 660,000 rate, based on the median estimate in a Bloomberg survey.

It would seem the springback in sales from January 2026's blizzards was truly that and not the start of an upward trend.

References

U.S. Census Bureau. New Residential Sales Historical Data. Houses Sold. [Excel Spreadsheet]. Accessed 28 May 2026. 

U.S. Census Bureau. New Residential Sales Historical Data. Median and Average Sale Price of Houses Sold. [Excel Spreadsheet]. Accessed 28 May 2026. 

Image Credit: High angle shot of suburban neighborhood photo by David McBee on Pexels.

Six months and two earnings seasons have come and gone since Thanksgiving 2025 when we were introduced to the worst performing stocks of the S&P 500 (Index: INX). How many of those 10 stocks have seen their fortunes improve and how many are proving to be an even bigger investment turkey than they appeared on the day after last Thanksgiving?

Let's cut to the chase! Here are the relative winners as measured by the percentage of their stock price recorded value on 28 November 2025:

• Dow Inc. (NYSE: DOW) - 148.1%.
• Deckers Outdoor (NYSE: DECK) - 126.6%.
• Molina Healthcare (NYSE: MOH) - 118.9%.

The stock price of these S&P 500 component companies are all higher than they were on 28 November 2026 and are also beating the S&P 500's growth, which has risen to 109.8% of its day-after-Thanksgiving-Day-2025 level. What each of these companies have in common is improved business performance combined with an improved outlook for their earnings.

Meanwhile, all seven of the other Thanksgiving Leftover stocks have experienced continuing declines in their stock prices. Here they are, ranked from best-to-worst performing over the past six months:

• Chipotle Mexican Grill (NYSE: CMG) - 93.6%
• Fiserv (NASDAQ: FISV) - 90.5%
• Alexandria Real Estate Equities (NYSE: ARE) - 90.3%
• Factset Research Systems (NYSE: FDS) - 83.3%
• Lululemon Athletica (NASDAQ: LULU) - 69.1%
• Gartner (NYSE: IT) - 67.8%
• Trade Desk (NASDAQ: TTD) - 56.1%

The following spaghetti chart shows how each performed throughout the last six months:

Since our last update, Lululemon Athletica (NASDAQ: LULU) has taken the most negative turn for the worse. The athletic apparel company is struggling to sell its mostly foreign-made clothing line in the U.S. after hiking prices to cover the cost of new tariffs. But higher costs are not the "athleisure" clothing company's biggest problem. Its latest products have been on the wrong side of fashion trends as it faces increased competition.

If that weren't enough, the company's top management is involved in war of words with Chip Wilson, the company's founder, who criticized them for losing the company's "cool" factor.

TLDR: Poorly managed Lululemon has become costly and unfashionable with few indications that will change anytime soon, sending its stock price even lower.

Breaking away from the ongoing drama of a failing business, the next chart reveals how the performance of the Thanksgiving 2025 Leftover stocks compares as a group with the S&P 500 index, both as a market-cap weighted index and as an equal-weighted index.

By both grouping methods, the Thanksgiving Leftover stocks are substantially underperforming the S&P 500 index.

Compared to a month ago, the equal-weighted group is close to the same, but the market-cap weighted group is worse off. If you went double-or-nothing in betting whether the Thanksgiving Leftover stocks were going to be doing better or worse than they were a month ago, we'd have to give the edge to worse this month.