to your HTML Add class="sortable" to any table you'd like to make sortable Click on the headers to sort Thanks to many, many people for contributions and suggestions. Licenced as X11: http://www.kryogenix.org/code/browser/licence.html This basically means: do what you want with it. */ var stIsIE = /*@cc_on!@*/false; sorttable = { init: function() { // quit if this function has already been called if (arguments.callee.done) return; // flag this function so we don't do the same thing twice arguments.callee.done = true; // kill the timer if (_timer) clearInterval(_timer); if (!document.createElement || !document.getElementsByTagName) return; sorttable.DATE_RE = /^(\d\d?)[\/\.-](\d\d?)[\/\.-]((\d\d)?\d\d)$/; forEach(document.getElementsByTagName('table'), function(table) { if (table.className.search(/\bsortable\b/) != -1) { sorttable.makeSortable(table); } }); }, makeSortable: function(table) { if (table.getElementsByTagName('thead').length == 0) { // table doesn't have a tHead. Since it should have, create one and // put the first table row in it. the = document.createElement('thead'); the.appendChild(table.rows[0]); table.insertBefore(the,table.firstChild); } // Safari doesn't support table.tHead, sigh if (table.tHead == null) table.tHead = table.getElementsByTagName('thead')[0]; if (table.tHead.rows.length != 1) return; // can't cope with two header rows // Sorttable v1 put rows with a class of "sortbottom" at the bottom (as // "total" rows, for example). This is B&R, since what you're supposed // to do is put them in a tfoot. So, if there are sortbottom rows, // for backwards compatibility, move them to tfoot (creating it if needed). sortbottomrows = []; for (var i=0; i
The U.S. stock market has been around since the founding of the nation. In the beginning, it wasn't very diversified, but that's changed dramatically over time. In January 2019, Visual Capitalist visualized how much its compensation has changed over the preceding 22 decades. Here's their chart:
Today, if we were to catch the chart up through the end of 2024, it would show a new surge for the Information Tech and Communication sectors of the market, similar to the inflation phase of Dot Com Bubble from 1998 to 2000. As the chart shows, that bubble went on to deflate from 2000 through 2003. At the end of 2024, the new surge in these sectors led by the so-called Magnificent 7 stocks was still growing it its share of the capitalization of the entire U.S. stock market.
Labels: data visualization, stock market
If you've ever had to clean out small debris from a yard or sidewalk, chances are you've thought about getting a leaf blower to do the job. Compared to using a rake and/or broom to do the job, leaf blowers can be amazing labor saving devices.
But, because of the way they're designed, they're also bulky items that can be a hassle to store when you're not using them. Wouldn't it be nice to have a compact device that do the job of a leaf blower without taking up all that space?
There's a Kickstarter project whose producer, Magpie Tech, is aiming to put "a storm in your hand" with their AirCannon air blower. Here's their 3-minute Kickstarter video pitch:
The AirCannon caught our attention because although it launched with a modest funding goal of just $3,000, it has already blown past it (pun intended) with pledges exceeding several hundred thousand dollars. That means the project has succeeded and will be produced after its funding drive ends on 3 March 2025.
While the video emphasizes the power of Magpie Tech's air blower, its real selling point is its size. It's much smaller than a typical leaf blower or, for that matter, the kind of shop vacuum that might otherwise be used for some of the applications demonstrated in the video. That in turn makes it possible to be used in more places to do more things than these other tools.
We think that additional potential, combined with the ability to store it away in a much smaller box than the alternatives, explains the runaway support for the Kickstarter project.
Magpie Tech deserves a lot of credit for its design. It takes genuine outside of the box thinking to find a way to put more into a smaller box. And like the proverbial better mousetrap, the world is beating a path to their door.
Labels: technology
New home sales were better than expected in December 2024. Here are Reuters' main takeaways from the month's new home sales report from the U.S. Census Bureau:
The U.S. Census Bureau's sales data is preliminary and will be revised three more times during the next three months. Still, that preliminary look along with the revisions to previous months allows us to get a good sense of how the entire U.S. new home market fared through the end of 2024. The three following charts present the trends for 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 the preliminary data for December 2024.
Our initial estimate of the time-shifted trailing twelve month average of the total value of new homes sold during December 2024 is $26.96 billion, which falls below November 2024's revised market cap estimate of $27.39 billion. The new home market cap remains more than 10% below its December 2020 level. The last four years have been lackluster ones for new home builders.
We'll take our next look at how affordable the new homes sold in December 2024 were in the near future.
U.S. Census Bureau. New Residential Sales Historical Data. Houses Sold. [Excel Spreadsheet]. Accessed 27 January 2025.
U.S. Census Bureau. New Residential Sales Historical Data. Median and Average Sale Price of Houses Sold. [Excel Spreadsheet]. Accessed 27 January 2025.
Image Credit: Construction framer working on new home by Josh Olalde on Unsplash.
Labels: real estate
The odds a U.S. recession will someday be determined to have begun between January 2025 and January 2026 has dropped to a little higher than a one-in-four chance.
This assessment is based on the yield curve-based recession forecasting model developed by Jonathan Wright in 2006. Going by this model, the odds of a U.S. recession being found to have started within the next year is a little over 27%.
The main factor lowering the probability of a recession beginning in the last several months is the Federal Reserve's interest rate rates during 2024. The Fed's reductions to the Federal Funds Rate have released some of the building recessionary pressure from the Fed having boosted short term interest rates in 2022 and 2023 to combat the Biden-Harris administration's inflation.
With the Federal Funds Rate being reduced, the yields of short-term U.S. Treasuries have followed, further reducing the recession start probability. The following chart tracking the probability of recession since 30 April 1983, the period from July 2024 through mid-September 2025 represents the most likely period in which the NBER will say the U.S. economy peaked before beginning a period of contraction.
This chart shows the recession probability 'pushed out' to the end of the period for which the recession forecast applies, which gives a "glass half empty" view of the recession probability data.
We've also updated the Recession Probability Track, which provides additional information about the factors that influence Wright's recession forecasting model.
We will continue following the Federal Reserve's Open Market Committee's meeting schedule in providing updates for the Recession Probability Track until the U.S. Treasury yield curve is no longer inverted and the future recession odds retreat below a 20% threshold.
At this writing, the first criteria has been met. The U.S. Treasury yield curve is no longer inverted, as the yield of the 10-year Treasury is now higher than the yield of the 3-month Treasury.
It will take longer for the second criteria to be met. We now anticipate the decline of the recession probability will slow and stall out above the 20% threshold in the weeks ahead in the absence of any additional interest rate cuts by the Fed in the next several months. That will change as we approach the second half of 2025, as the Fed is expected to cut the Federal Funds Rate by a quarter point when it meets in late June.
The recession probability we've presented is based on the Federal Reserve Board's yield curve-based recession forecasting model, which factors in the one-quarter average spread between the 10-year and 3-month constant maturity U.S. Treasuries and the corresponding one-quarter average level of the Federal Funds Rate. If you'd like to do that math using the latest data available to anticipate where the Recession Probability Track is heading, we have provided a tool to make it easy to do.
For the latest updates of the U.S. Recession Probability Track, follow this link!
We started this new recession watch series on 18 October 2022, coinciding with the inversion of the 10-Year and 3-Month constant maturity U.S. Treasuries. Here are all the posts-to-date on that topic in reverse chronological order, including this one....
Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a banker having their palm read by a fortune teller with the Federal Reserve in the background".
Labels: recession forecast
The S&P 500 (Index: SPX) touched a new record high during the Martin Luthor King Jr. holiday-shortened trading week.
It hit that high on Thursday, 23 January 2025 as it closed at 6,118.71, before reteating to end the week at 6,101.24. The index was up 1.74% over its previous week's close.
The driving factor behind that change is increasing expectations of a second rate cut later in 2025. The CME Group's FedWatch Tool gives a greater than 75% probability the Fed will act to cut interest rates by a quarter point on 18 June (2025-Q2), but more significantly, it now indicates a greater than 50% probability of another quarter point rate cut on 10 December (2025-Q4).
The latest update of the alternative futures chart the trajectory of the S&P 500 is now consistent with investors focusing their forward-looking attention on that distant future quarter.
Unlike most holiday-shortened weeks, the trading week ending Friday, 24 January 2025 was packed with market-moving headlines.
The Atlanta Fed's GDPNow tool's final projection of real GDP growth rate for the now-past quarter of 2024-Q4 is unchanged from the previous week's +3.0% annualized growth estimate. With the BEA's upcoming first estimate of GDP in 2024-Q4 release on 30 January 2024, the GDPNow tool's next forecast will be for real GDP in the first quarter of 2025.
Image credit: Stable Diffusion Dreamstudio Beta. Prompt: "An editorial cartoon of a blindfolded Federal Reserve official who is throwing darts at calendars. One dart is sticking out of the calendar that says 'DEC-2025'."
The world's largest known prime number has 41,024,320 digits.
That's so big it doesn't make sense to even attempt to write it down. Fortunately, it's a Mersenne prime, which means it can be written more simply with an equation with the following form:
M(p) = 2p - 1
Where p, the exponent in the formula, is also a prime number. For the new world's largest prime number, p = 136,279,841. Here's Matt Parker announcing the discovery of the new Mersenne prime on 21 October 2024 in a 10-minute video and presenting all of its 41,024,320 digits:
To get a sense of how big this number is, we created the following chart showing the exponents of each of the known Mersenne primes as of 23 January 2025 on the vertical axis plotted against their rank from lowest to highest on the horizontal axis. The newest Mersenne prime, M(136,279,841) is shown in red.
Two things immediately stand out on the cart. First, it's a true hockey stick chart, thanks to the exponential increase in the Mersenne prime exponents. Second, there is an exceptionally large gap between the previous record-holder for largest known prime number M(82,589,933) at Rank 51 and the newest Mersenne prime M(136,279,841) that is currently at Rank 52.
We can de-hockey stick the chart in one of two ways. We can either convert the vertical axis to be in logarithmic scale or we can express the exponents as their natural logs. In the second chart, we've taken the second route in part because it makes the numbers easier to handle.
When we present the Mersenne prime exponents this way, they appear to follow a straight line pattern, which is interesting. In our third chart, we did some basic linear regression analysis to tease out the overall relationship between the size of the Mersenne prime exponents and their rank, which is really telling us about how far apart the exponents are from each other.
The dashed line represents the overall trend for the increasing size of the known Mersenne prime exponents, which seems to fit the data fairly well. But when we look back at the second chart, we can't help but see what looks like a change in the space between exponents that kicks in after they get past Rank 40. Specifically, once we're looking at Mersenne prime exponents above Rank 40, there is less space between them than what our initial linear regression suggests there should be.
We wondered if there might be a second pattern in these figures, so we generated two new linear regressions. One based on the ten Mersenne prime exponents from Rank 42 through 51 (omitting the newest one since our first chart suggests it may be an outlier) and another based on the Mersenne prime exponents from Rank 1 through 42. The fourth chart presents our results:
This fourth chart strongly suggests there may be something to our observations. Mersenne prime exponents above M(25,964,951) at Rank 42 appear to have branched off from the overall trend we see for Mersenne prime exponents from Rank 1 through 42 and may possibly have branched off earlier with M(20,996,011) at Rank 40. But as we're about to show, that may not the only branch because that pattern appears to repeat. In the fifth chart, we've added several parallel branches that pass in close proximity to many of the lower ranked Mersenne prime exponents.
If this pattern reliably repeats, it would provide a means by which we could reasonably predict where to find the "next" Mersenne prime exponents on a given branch. For example, if the newest, largest Mersenne prime M(136,279,841) is on such a branch, the next larger Mersenne prime exponent might be found lurking among potential prime exponents somewhere between it and a possible upper end of 155,645,033, with a exponent of 142,143,581 falling in the middle of a likely range in which it might be found.
Going back to our observation that there appears to be an exceptionally large gap between the Mersenne primes corresponding to M(82,589,933) at Rank 51 and the newest Mersenne prime M(136,279,841) currently at Rank 52, the branching pattern we've identified suggests there may be as many as two additional Mersenne prime in between them. The first could potentially fall between the potential prime exponents of 87,747,713 and 103,582,291 and the second could fall between the potential prime exponents of 100,504,603 and 118,641,197. The final chart shows where these 'next' Mersenne prime numbers might be if they fall on the same branch defined by the spacing between Mersenne prime exponents from Rank 42 through Rank 51. Note that the current Rank 52 Mersenne prime M(136,279,841) would move out to Rank 54 in this scenario.
Then again, the large gap in the value of the Mersenne Prime exponents may be a sign that the Mersenne prime exponents have reached the end of a branch and will have more distance between them. At least, until a new branch might become evident.
It's quite possible the scenarios we described for locating the next Mersenne primes are reasonable. At this writing, there are still thousands of potential Mersenne prime exponent candidates within the target ranges we've identified whose status has not yet been determined. The only thing we reasonably know for certain is that there will be another Mersenne prime identified someday that's larger than M(136,279,841).
In terms of potential, should the existence of these branching patterns pan out and be useful, they would make it possible for future Mersenne primes to be discovered in clusters, with several found within a relatively short period after each new Mersenne prime is confirmed. With luck, it won't take another six years to locate the next Mersenne prime.
When Joseph Robinette Biden Jr. was sworn into office as the President of the United States on 20 January 2021, the U.S. national debt stood at $27.75 trillion. Four years later, as President Biden departs from office, the U.S. national debt was sitting at $36.21 trillion. The national debt increased by $8.46 trillion, or 30.5%, in those four years.
Because the concept of trillions of dollars of debt is difficult to comprehend in human terms, it's easier to understand the impact of President Biden's national debt legacy by dividing the national debt equally among all the households in the United States.
When we do that math, 2021's national debt total of $27.75 trillion becomes $216,050, which represents the national debt burden per household before any of President Biden's spending initiatives were implemented.
After four years of President Biden's spending initiatives, we find the household burden of 2025's national debt total of $36.21 trillion is $273,844. The burden of the national debt per household has increased by $57,724, or 27%, during President Biden's tenure.
The following chart reveals the level of the household burden of the national debt at each of President Biden's anniversaries in the White House. In it, we've also shown how much of the nation's debt is owed to its creditors by major category.
Remarkably, even though former President Biden came into office during a time of national emergency with the coronavirus pandemic and the severe economic disruption of state and local government-mandated lockdowns, most of the increase in the national debt during his tenure occurred during the final two years of his administration, after the pandemic had ended.
Altogether, while President, the $57,724 increase in the national debt burden per household is nearly enough for the government to give every household in the U.S. a Certified Pre-Owned 2024 Lexus RX 350 Premium Plus with low mileage. Because the U.S. government borrowed that money, you would have to add that debt to all your other household debt. Including your mortgage or rent, your credit card bills, every other vehicle loan you might have, and more.
By comparison, the increase in the national debt per household since Joe Biden became President was only enough to buy a brand new 2024 Toyota RAV4 Hybrid. Even used, the 2024 Lexus RX 350 Premium Plus is definitely a luxury upgrade.
Do you feel like you got that kind of luxury upgrade from four years of Joe Biden's debt-fueled spending? Did the U.S. government give you the equivalent of a shiny, almost-new red Lexus RX-350? If the government didn't buy you the equivalent of a Lexus for your household, at least you can enjoy paying it off over time, either through your taxes or through Joe Biden's incredibly persistent inflation.
U.S. Census Bureau. Historical Households Tables. Table HH-1. Households by Type: 1940 to Present. [Excel Spreadsheet]. Accessed 22 January 2025.
U.S. Treasury Department. Debt to the Penny. [Online Database]. 17 January 2025. Accessed 22 January 2025. Note: As 20 January 2025 fell on the Martin Luther King Jr. holiday, when the U.S. Treasury Department's debt window was closed with no changes to the national debt taking place, the national debt recorded for Friday, 17 Janaury 2025 is the appropriate reference for the end of President Biden's fourth year in office.
U.S. Treasury Department. Major Foreign Holders of Treasury Securities. [Online Data]. Accessed 22 January 2025.
U.S. Treasury Department. Monthly Treasury Statement of Receipts and Outlays of the United States Government for Fiscal Year 2025 Through December 31, 2024. [PDF Document]. 14 January 2025.
Labels: national debt, personal finance
A month has passed since our previous look at the expected future quarterly dividends of the S&P 500 (Index: SPX) in 2025.
Since that date in mid-December 2024, investors expectations of how many rate cuts there will be during 2025 have see-sawed between zero and two, which goes a long way to explaining why the value of the S&P 500 has traded in a range that's gone as low as 5,827.04 on 10 January 2025 and as high as 6,049.24 as investors expectations of how many interest rate cuts there will be during 2025 have changed. The low figure corresponds to "fewer" rate cuts, with just one in the second quarter of the year, the high figure corresponds to the expectation of "more" rate cuts, with the odds now building for a second rate cut in the fourth quarter of 2025. The high figure also happens to be the closing value of the S&P 500 on Tuesday, 21 January 2025.
But expectations of when the Federal Reserve might change interest rates is not the only driver of stock prices. While those changing expectations affect how far forward in time investors set their focus as they set current day stock prices, expectations for the dividends that will be paid out in the future quarters of 2025 play just as important a role. The following animated chart confirms that outlook has brightened over the past month. 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.
How changes in the outlook for dividends at specific points of time in the future affects 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. So for example, as determined by dividend futures contracts, the now "current" quarter of 2025-Q1 began on Saturday, 21 December 2024 and will end on Friday, 21 March 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.
Labels: dividends, forecasting
The S&P 500 (Index: SPX) had its best trading week since the 2024 elections. The index closed up 2.9% to end the week at 5,996.66.
The index had its best day on Wednesday, 15 January 2025 thanks to a better-than-expected consumer price inflation report. Although headline inflation ran hot, thanks largely to food prices, which are showing the effects of a reduced supply of eggs because of bird flu. Less volatile components of the Consumer Price Index were muted however, which firmed the odds for at least one rate cut during 2025 and raised the potential for additional rate cuts.
After the tamer than expected inflation data, the CME Group's FedWatch Tool gives much stronger odds of the Fed acting to cut interest rates by a quarter point on 18 June (2025-Q2). Meanwhile, the probability of another rate cut later in the year also rose, but as yet remain below 50%, with December 2025 coming the closest to that threshold.
That's a significant development because the latest update of the alternative future chart shows investors shifting their forward-looking attention toward the distant future quarter of 2025-Q4.
Here's the full rundown of the trading week's market moving headlines:
The Atlanta Fed's GDPNow tool's projection of real GDP growth rate for the now-past quarter of 2024-Q4 rose to +3.0% from the previous week's +2.7% annualized growth estimate. The BEA's first estimate of GDP in 2024-Q4 will be released on 30 January 2024, when the GDPNow tool will shift to start nowcasting GDP for the current quarter of 2025-Q1.
Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull taking a box that says '2025 RATE CUTS' from a bear."
The climbing limo method of forecasting future GDP in the United States projects the nation's economic output in the fourth quarter of 2024 will be approximately $29.6 trillion.
If that number sounds familiar, it's nearly identical to the climbing limo's forecast for 2024-Q3, in which we indicated that quarter's nominal GDP would "be within a few percentage points" of that figure. With the third estimate of GDP now available, we can confirm that forecast was less than one percent off the mark. At $29,374.9 billion, nominal GDP came in below the climbing limo's forecast by 0.8%.
This time around, we think that with the climbing limo forecast nearly unchanged from the previous quarter, the actual nominal GDP figure to be reported by the Bureau of Economic Analysis has a good chance of coming in higher that the climbing limo forecast, similar to what happened in 2024-Q1.
You can judge that likelihood for yourself in the following chart, which tracks the climbing limo method's forecast against the recorded nominal GDP over the past 10 quarters for which GDP data has been finalized outside of annual revisions.
This chart adds the climbing limo's forecast for GDP in 2025-Q2, which at nearly $30.54 trillion, represents a 1.3% increase over the forecast for 2025-Q1.
The climbing limo method is a very simple forecasting technique that projects the level of GDP some three quarters into the future using the nominal GDP figures from five quarters and three quarters before that point in time. As such, its forecast represents the momentum of the U.S. economy recorded between the two data points it uses. Deviations between the actual trajectory of GDP and the forecast tells how the momentum of the U.S. economy has changed, which provides useful information even when the differences between forecast and actual values are large.
For example, the biggest deviations it sees typically happen at turning points for the U.S. economy, when it either enters or exits periods of recession. Since 2022-Q3, the forecasts confirm the growth momentum of the U.S. economy has slowed, though it remains on an upward trajectory.
U.S. Bureau of Economic Analysis. National Income and Product Accounts. Table 1.1.5. Gross Domestic Product. [Online Database]. Accessed 19 December 2024.
Political Calculations. Forecasting GDP Using the Climbing Limo. [Online Tool]. 10 May 2005.
Image Credit: Microsoft Copilot Designer. Prompt: "A limousine driving up a bumpy, dirt road with the license plate labeled 'GDP'".
Labels: gdp forecast
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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Closing values for previous trading day.
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