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30 May 2023
Bullfight at San Marcos Fair, Aguascalientes, Mexico by Tomas Castelazo via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:San_marcos_bullfight_01.jpg

The fourth trading week of May 2023 had started out to be a gloomy one for the S&P 500 (Index: SPX). Several Federal Reserve officials signaled early in the week they were considering continuing the Fed's ongoing series of rate hikes in June because of their concerns U.S. inflation has not sufficiently abated.

That potential was enough to send the index down nearly 1.9% from the previous week's close by Wednesday, 24 May 2023.

But the fear that dragged stock prices down reversed during the next two trading days, as a "Unprecedented. Cosmological. Unfathomable." earnings report and outlook from Nvidia (NASDAQ: NVDA) sparked a speculative fury benefiting information technology firms advancing on the potential of their new Artificial Intelligence (AI) systems.

That speculative fury drove the level of the S&P 500 some 2.2% higher from where it bottomed, enough to boost the index by 0.3% from the previous week's close to 4205.45, its highest level to date in 2023. And that was *despite* Friday, 26 May 2023's confirmation U.S. inflation is running hotter than expected, all but guaranteeing the Fed will hike the Federal Funds Rate in June 2023.

That volatile action is shown in the latest update to the alternative futures chart, where we find the index' trajectory is still well within the redzone forecast range.

Alternative Futures - S&P 500 - 2023Q2 - Standard Model (m=+1.5 from 9 March 2023) - Snapshot on 26 May 2023

More stuff happened during the week that was, which we've captured in the week's market-moving headlines. Once again, we've all but omitted headlines related to the debt ceiling debate in the U.S., which still isn't moving the needle for stock prices in any meaningful way.

Monday, 22 May 2023
Tuesday, 23 May 2023
Wednesday, 24 May 2023
Thursday, 25 May 2023
Friday, 26 May 2023

Following personal consumption expenditure data that revealed higher than expected inflation, the CME Group's FedWatch Tool now projects the Federal Reserve will hike the Federal Funds Rate by a quarter point when its Open Market Committee meets on 14 June 2023. That would bring the Federal Funds Rate to a target range of 5.25-5.50%, which the tool anticipates will be the peak for the series of rate hikes that began in March 2022. However, the FedWatch Tool anticipates the Fed will then wait until its 1 November (2023-Q4) meeting to initiate a series of quarter point rate cuts at six-to-twelve-week intervals to address building recessionary conditions in the U.S. economy.

The Atlanta Fed's GDPNow tool estimate of the real GDP growth rate for 2023-Q2 plunged to +1.9% from the +2.9% growth rate it anticipated a week earlier.

Image credit: Bullfight at San Marcos Fair, Aguascalientes, Mexico by Tomas Castelazo via Wikimedia Commons. Creative Commons. Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0).

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26 May 2023
Primes vs Composites by David Eppstein via WikiMedia Commons - https://commons.wikimedia.org/wiki/File:Primes-vs-composites.svg

If you ever want to go down a very deep rabbit hole, and you're mathematically minded, searching out patterns in prime numbers is a great place to begin.

In fact, if you just want to start somewhere simple, try this. Set up a table with six columns. Starting in the first row of the table, with the first prime number, 2, number all the boxes of the table from left to right. Then, move down to the next row of the table and continue the numbering process. Add as many rows as you like.

When you've made a decent-sized table, stop adding rows and go back to visually distinguish the prime numbers among all the numbers you wrote. You should pretty quickly find your first patterns.

We did that exercise, using just the numbers from 2 to 211. Here's the table we generated, along with some of the patterns we were able to identify:

Patterns of Prime Numbers (Among numbers 2 through 211)

Except for the first row, which has four prime numbers (2, 3, 5, and 7), each subsequent row contains no more than two prime numbers in it. Each of those prime numbers appear in just two columns that we've identifed as Set D, which starts with 5 in the first row, and Set F, which starts with 7.

By setting up the list of numbers this way, we've effectively sieved the full set of integers to exclude multiples of 2 (Set A, Set C, and Set E) and multiples of 3 (Set B and Set E). We find that we can define all potential prime numbers larger than three as a multiple of six (Set E), where we either subtract one to obtain a potentially prime value in Set D or add one to obtain a potentially prime value in Set F.

We can then look at how frequently primes appear in these columns. When both the Set D and Set F values in the same row are prime, these are what mathematicians call twin primes. Whenever Set F in one row is prime and is followed by another prime in Set D in the next row, that's what mathematicians call couple primes. And whenever prime numbers appear next to each other in the same column, either in Set D or in Set F, mathematicians call "sexy" primes.

That last kind of prime is actually a bad mathematical pun. You'll notice that the minimum difference between any two sexy primes is six. In Greek, the word for six is εχι. If you're the kind of mathematician who slurs their words after consuming certain beverages, you might say that the Greek word for six issexi....

Unfortunately, not every value in the Set D and Set F columns are prime numbers. Some are composite numbers, which is to say they are found by multiplying prime numbers together, and even they have a pattern. If you multiply two primes from Set D together, you'll find their product in the Set F column. That's also true if you multiply two primes from Set F together.

But if you multiply a prime from Set D with a prime from Set F, you'll only find the resulting composite product in the Set D column.

These are far from the only patterns going on with the distribution of prime numbers. Back in 1963, Stanislaw Ulam found that when he wrote numbers out in a spiral order on a square grid, the prime numbers would appear in diagonal patterns.

The Coding Train's Daniel Shiffman explains how to generate Ulam's Spiral and develops code to generate it in the following 24 minute video:

The Ulam (or Prime) Spiral forms when numbers are written in order in a spiral pattern on square grid paper, but since we already know that the distribution of primes is linked to multiples of six, what would we find if we repeated that exercise using a hexagonal grid?

The following image illustrates some new patterns that emerge in a hexagonal spiral. Just for fun, we've indicated the prime numbers with boldface font and have colored the hexagons that correspond to Set D and Set F in our original table and have used red lines to connect the twin primes:

Hexgrid number spiral with primes highlighted and twin primes connected

Using a hexagonal grid like this, additional relationships can be identified to map out where prime numbers may occur. In practice, that means we can break the Set D and Set F values into subsets that can be independently explored. In 2011, Dmitri Tishchenko mapped 90,000 numbers onto a hexagon grid like this, which gives some tantalizing hints at the underlying structure of primes. He had left the task of visualizing the Set D (6n-1) and Set F (6n+1) on the grid for a future project, which is what inspired us to create our hexgrid chart.

Then again, if you really want to things to the next level, you could write out the numbers using polar coordinates on an Archimedian spiral. The patterns that arise when you do that leads to a whole different story for another long holiday weekend.


José William Porras Ferreira. The Pattern of Prime Numbers. Applied Mathematics, Vol. 8, No. 2. DOI: 10.4236/am.2017.82015. [PDF Document]. February 2017.

Image credit: Primes vs Composites by David Eppstein via Wikimedia Commons. Creative Commons CC0 1.0 Universal (CC0 1.0) Public Domain Dedication.

Notes: We've released the Basic Patterns of Primes image, which is freely available via Wikimedia Commons under Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license.

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25 May 2023
Cash, Wealth, Money Assets concept by kalhh via Pixabay - https://pixabay.com/illustrations/cash-money-wealth-assets-1169650/

Not long ago, we looked at how inflation and interest rates changed the mortgage payment for the median new home sold in the United States in the two years between March 2021 and March 2023. As part of that exercise, we tracked down what the median down payment is for homes purchased in the U.S., which was given as 13 percent of the sale price of all homes sold in 2022. For the median new home sold in March 2023, that would be $58,474.

That raised a question. Who has that kind of cash laying around?

To answer the question, we tapped the Federal Reserve's 2019 Survey of Consumer Finances, which reports the median amount of assets held in bank transaction accounts, which includes savings, checking, and money market accounts among others by age group. It also tells us the median amount of financial assets of any type held by age group. The following chart shows that data:

Median Bank Account Balance and Holdings of Financial Assets of Any Type by Age*, 2019

What we find from this median data is that it's unlikely any family at or below the 50th percentile is ponying up the down payment for the median new home sold in the U.S.

Instead, it's much more likely the family buying median new home is closer to the average when it comes to having the financial assets needed to purchase the median new home sold in the U.S. The next chart shows the mean amount of assets held in bank transaction accounts and in any financial assets by age group.

Average Bank Account Balance and Holdings of Financial Assets of Any Type by Age*, 2019

These charts represent data that was collected during 2019. The Federal Reserve will release the data it collected during 2022 later this year, sometime in September 2023.

Analyst's Notes

Financial assets of any type start with bank transaction accounts and adds relatively liquid assets in the total, including as certificates of deposit, savings bonds, bonds, stocks, money in pooled investment funds, retirement accounts, the cash value of life insurance, and other similarly liquid assets.

According to the 2019 Survey of Consumer Finances, the median family income in 2019's survey was $58,600, while the average family income was $106,500. Both the SCF's estimates are less than the U.S. Census Bureau's estimates for total money income received by families in 2019, which were $86,011 and $116,735 respectively.


Board of Governors of the Federal Reserve System. 2019 Survey of Consumer Finances. Table 6. Family holdings of financial assets, by selected characteristics of families and type of asset. [Excel Spreadsheet]. September 2020.

Image credit: Image by kalhh from Pixabay.

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24 May 2023
New Home Under Construction - Source: WikiMedia Commons - https://commons.wikimedia.org/wiki/File:Wood-framed_house.jpg

The U.S. new home market expanded in April 2023. The market capitalization of new homes sold in the U.S. built rose during the month, with a surge in the number of new homes sold offsetting a decline in their prices.

The initial estimate of 683,000 new homes sold during April 2023 represents the highest level of this seasonally-adjusted annual rate recorded since March 2022. That month marked the beginning of the Federal Reserve's series of interest rate hikes, which has coincided with an increase in mortgage rates that have negatively affected the affordability of new homes. The time-shifed trailing twelve month average of new homes sold rose to 638,000 on an annualized basis.

Meanwhile, the average sale price of new homes sold in the U.S. declined to $501,000, with the time-shifted trailing twelve month average dipping below $527,500.

Here is the latest update to our chart tracking market capitalization of new homes sold in the U.S., which shows the improving situation for U.S. new home builders:

Trailing Twelve Month Average New Home Sales Market Capitalization in the United States, January 1976 - April 2023

The chart reveals the time-shifted twelve month average of the U.S. new home market capitalization for April 2023 is $27.94 billion. This figure is an initial estimate, which will be subject to revision during each of the next three months.

The next two charts show the latest changes in the trends for new home sales and prices:

Sales of new homes increased:

Trailing Twelve Month Average of the Annualized Number of New Homes Sold in the U.S., January 1976 - April 2023

New home prices declined:

Trailing Twelve Month Average of the Mean Sale Price of New Homes Sold in the U.S., January 1976 - April 2023

Here's how Reuters reported the continued recovery for the U.S. new home market in April 2023:

Sales of new U.S. single-family homes jumped to a 13-month high in April, boosted by a persistent shortage of previously owned houses on the market and a sharp decline in prices from last year's lofty levels....

"The evidence continues to accumulate that the housing market may have largely adjusted to the higher level of mortgage rates but the decline in the median home price is consistent with the hypothesis that home builders may be tailoring the construction of new homes towards first-time buyers," said Conrad DeQuadros, senior economic advisor at Brean Capital in New York.

New home sales increased 4.1% to a seasonally adjusted annual rate of 683,000 units last month, the highest level since March 2022. March's sales pace was revised lower to 656,000 units from the previously reported 683,000.

Coming out of the first quarter, we were uncertain how strongly the positive momentum in the new home market might continue. The lack of supply of existing homes coming onto the market was a wild card factor we couldn't anticipate, but which is proving to be a positive. It's a welcome development in that the new home market directly boosts Gross Domestic Product. New residential investment, which includes new homes, typically accounts for about 3% to 5% of the nation's GDP.


U.S. Census Bureau. New Residential Sales Historical Data. Houses Sold. [Excel Spreadsheet]. Accessed 23 May 2023. 

U.S. Census Bureau. New Residential Sales Historical Data. Median and Average Sale Price of Houses Sold. [Excel Spreadsheet]. Accessed 23 May 2023. 

Image credit: WikiMedia Commons: Wood-framed House by Jaksmata. Creative Commons Attribution-Share Alike 3.0 Unported License.


23 May 2023

FIFO has become the most popular accounting method U.S. businesses use to determine both the cost of the goods they sell and the value of the goods they have in their inventories. With about 53% of firms in the S&P 500 (Index: SPX) using the accounting method, which plays a big role in determining how profitable they are on paper, it's high past time we took a closer look at how the First In, First Out (FIFO) accounting method works!

For a really good introduction, here's Excel spreadsheet guru Leila Gharani's eight-and-a-half minute video explaining how the First-In-First-Out (FIFO) accounting method is used to calculate the Cost of Goods Sold (COGS) for a business.

While her examples reflect how a modest amount of inflation can affect a business' cost of goods sold, how might a surge of inflation like what the U.S. has experienced during the past two years affect how profitable it appears to be on paper?

For the answer to that question, let's turn to Breaking Bad Accounting's shorter video from September 2020, which compares how the different the net earnings (or profit) results are for firms using the different accounting methods. Given what happened after inflation was unleashed in 2021, it's somewhat prophetic (although their example is more fun to talk about!):

Under FIFO accounting rules, reported profits soar in an inflationary environment because the calculated Cost of Goods Sold lags behind the rising cost of replenishing their inventories with higher cost goods.

About 16% of the firms making up the S&P 500 use the Last In, First Out (LIFO) accounting method. The remaining firms utilize variations of the Average Cost method. Firms that use the LIFO method see much lower profits than FIFO firms report, while Average Cost firms come out somewhere in between these extremes.

During periods of deflation, the opposite pattern develops. LIFO firms will report the highest profits, FIFO firms will report the lowest, and Average Cost firms come out in the middle again. If prices were stable however, all three methods would produce identical results.

The United States is somewhat unique in allowing firms to utilize any of these methods, and the LIFO method in particular, which is banned under International Financial Reporting Standards. Despite that prohibition, major accounting firms like Price Waterhouse Coopers have recommended private U.S. firms adopt the practice because of the high inflation environment established during the past two years.

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About Political Calculations

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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