Political Calculations
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September 20, 2019
Fractional Approximations of Pi with Errors

Pi is an irrational number, which is to say that it is a real number than cannot be precisely written as the ratio of two integers in a simple fraction.

That's not to say that you cannot reasonably approximate the value of pi with such a fraction however - it's just a question of how much error you're willing to live with by doing so. If the results of your math would be okay if you only approximated pi to just two decimal places, which in decimal form is 3.14, you could substitute the rational fraction 22/7. If you needed up to six decimal places of rounded-up precision, 3.141593, you could use the relatively much easier-to-remember fraction 355/113 instead.

But how well can any irrational number like pi, e, phi, or 2 be approximated with a simple fraction with an integer numerator and denominator?

That has been an open question since 1941, when Richard Duffin and Albert Schaeffer conjectured that for whatever level of error you're willing to live with in your rational approximation of an irrational number, you can either find a nearly infinite number of possible fractions or almost none. Here's how Quanta Magazine's Kevin Hartnett described the conjecture:

The Duffin-Schaeffer conjecture is an attempt to provide the most general possible framework for thinking about rational approximation. In 1941 the mathematicians R.J. Duffin and A.C. Schaeffer imagined the following scenario. First, choose an infinitely long list of denominators. This could be anything you want: all odd numbers, all numbers that are multiples of 10, or the infinite list of prime numbers.

Second, for each of the numbers in your list, choose how closely you’d like to approximate an irrational number. Intuition tells you that if you give yourself very generous error allowances, you’re more likely to be able to pull off the approximation. If you give yourself less leeway, it will be harder....

Now, given the parameters you’ve set up — the numbers in your sequence and the defined error terms — you want to know: Can I find infinitely many fractions that approximate all irrational numbers?

The conjecture provides a mathematical function to evaluate this question. Your parameters go in as inputs. Its outcome could go one of two ways. Duffin and Schaeffer conjectured that those two outcomes correspond exactly to whether your sequence can approximate virtually all irrational numbers with the demanded precision, or virtually none. (It’s “virtually” all or none because for any set of denominators, there will always be a negligible number of outlier irrational numbers that can or can’t be well approximated.)

In what may be the biggest math story of 2019, the Duffin-Schaeffer conjecture may have been proven this past summer. Dimitris Koukoulopoulos and James Maynard posted a preprint of their paper confirming that choosing smaller 'acceptable' error ranges makes it harder to approximate irrational numbers with simple fractions, which would be a remarkable advance in the field of number theory.

Scientific American's Leila Sloman describes their approach:

Maynard and Koukoulopoulos knew that previous work in the field had reduced the problem to one about the prime factors of the denominators—the prime numbers that, when multiplied together, yield the denominator. Maynard suggested thinking about the problem as shading in numbers: “Imagine, on the number line, coloring in all the numbers close to fractions with denominator 100.” The Duffin-Schaeffer conjecture says if the errors are large enough and one does this for every possible denominator, almost every number will be colored in infinitely many times.

For any particular denominator, only part of the number line will be colored in. If mathematicians could show that for each denominator, sufficiently different areas were colored, they would ensure almost every number was colored. If they could also prove those sections were overlapping, they could conclude that happened many times. One way of capturing this idea of different-but-overlapping areas is to prove the regions colored by different denominators had nothing to do with one another—they were independent.

But this is not actually true, especially if two denominators share many prime factors. For example, the possible denominators 10 and 100 share factors 2 and 5—and the numbers that can be approximated by fractions of the form n/10 exhibit frustrating overlaps with those that can be approximated by fractions n/100.

Maynard and Koukoulopoulos solved this conundrum by reframing the problem in terms of networks that mathematicians call graphs—a bunch of dots, with some connected by lines (called edges). The dots in their graphs represented possible denominators that the researchers wanted to use for the approximating fraction, and two dots were connected by an edge if they had many prime factors in common. The graphs had a lot of edges precisely in cases where the allowed denominators had unwanted dependencies.

Using graphs allowed the two mathematicians to visualize the problem in a new way. “One of the biggest insights you need is to forget all the unimportant parts of the problem and to just home in on the one or two factors that make [it] very special,” says Maynard. Using graphs, he says, “not only lets you prove the result, but it’s really telling you something structural about what’s going on in the problem.” Maynard and Koukoulopoulos deduced that graphs with many edges corresponded to a particular, highly structured mathematical situation that they could analyze separately.

The graphs they develop to map the greatest common divisors for the rational approximations of irrational numbers are bipartite graphs. The following video provides a short introduction:

The Koukoulopoulos-Maynard proof of the Duffin-Schaeffer conjecture is now in the process of being validated. If determined to be valid, the proof may have an immediate impact on the related field of p-Adic approximation, which would have applications in quantum mechanics and field theory, as well as resolving other conjectures in number theory that rely on the Duffin-Schaeffer conjecture being true.

Image Credit: Stack Overflow


September 19, 2019

As expected, the Federal Reserve acted to cut short interest rates in the United States on 18 September 2019, reducing its target range for the Federal Funds Rate from 2.00%-2.25% down to 1.75%-2.00%.

That cut comes as the odds of a national recession starting in the U.S. sometime during the next twelve months, as might be determined at a later date by the National Bureau of Economic Research, has continued to drift higher even as the Fed has begun cutting interest rates, with just over a 11% probability according to the methodology laid out by the Federal Reserve Board's Jonathan Wright in a 2006 paper. This quarter point reduction was the second quarter point cut following the cut announced on 31 July 2019 at the conclusion of the Federal Open Market Committee's previous meeting.

Stock prices quickly dropped by nearly one percent from the previous day's closing value shortly after the announcement, as investors were looking for signs the Fed would start implementing quantitative easing in addition to the rate cut. That disappointment didn't last long, because Fed Chair Jerome Powell's comments during the following press conference hinted the Fed would be likely to start new rounds of quantitative easing in the near future when he said that "it is certainly possible that we'll need to resume the organic growth of the balance sheet sooner than we thought."

That prospect sent bank stocks up sharply and led the S&P 500 (Index: SPX) to close slightly higher for the day. The question now is whether quantitative easing will become a virtually permanent feature of the Fed's open market operations.

Updating the Recession Probability Track, we find that the rate at which the probability of recession is rising using Wright's methods is indeed beginning to slow, with just over a one-in-nine chance of a recession beginning in the U.S. before October 2020.

U.S. Recession Probability Track Starting 2 January 2014, Ending 18 September 2019

The Recession Probability Track is based on Jonathan Wright's recession forecasting method using the level of the effective Federal Funds Rate and the spread between the yields of the 10-Year and 3-Month Constant Maturity U.S. Treasuries. If you would like to run your own recession probability scenarios, as we recently did after factoring in all the quantitative tightening the Fed achieved prior to its policy reversal in July 2019, please take advantage of our recession odds reckoning tool.

It's really easy. Plug in the most recent data available, or the data that would apply for a future scenario that you would like to consider, and compare the result you get in our tool with what we've shown in the most recent chart we've presented above.

If you would like to catch up on any of the analysis we've previously presented, here are all the links going back to when we restarted this series back in June 2017.

Previously on Political Calculations


September 18, 2019

African swine fever (ASF) is devastating China's domestic hog herd. Starting with an estimated population of 460 million hogs, China has lost at least 100 million hogs, about 21% of the country's total herd, to the infectious and incurable disease, and is expected to see further losses of at least another 10% in the next year. Rabobank projects the losses could reach 50% of the county's overall pig herd before the disease has run its course.

As you might imagine, the growing shortage of domestically produced pork in China has affected prices for the meat, which we're featuring in the following chart, comparing China's prices with U.S. hog prices per hundredweight over the past year.

U.S. and China Hog Prices, September 2018 - September 2019

Our sources for the data are below, where we recognize we may not have a proper apples-to-apples comparison between the two countries' hog prices. The U.S. hog prices are for "national base 51-52% lean" barrows and gilts, while the Chinese prices are simply given in yuan per kilogram, which we converted to U.S. dollars per 100 pounds. There may be a conversion factor that needs to be incorporated to make them truly equivalent, where our estimates for the Chinese prices would be off by a consistent scale factor.

As such, the more important factor to consider is the trend in China's prices, which have spiked upward in recent months after having largely paralleled U.S. prices through May 2019. It also appears that Chinese prices may lead U.S. prices, which we'll continue monitoring in upcoming months to see if the spike in Chinese pork prices comes to be reflected in U.S. prices. With China exempting U.S. hogs from their trade war tariffs during the past week to help alleviate the shortages the country is facing, the resulting increase in quantity demanded for U.S.-produced pork should put upward pressure on U.S. prices in the near term, assuming no other changes in the supply and demand for U.S.-produced pork.

In theory, anyway. We'll see what happens in practice.


U.S. Department of Agriculture. Livestock Prices (Hog Prices). [Excel spreadsheet]. Accessed 17 September 2019.

Pig333. Pig Prices in China (CNY/kg). [Online Database]. Accessed 17 September 2019.

Federal Reserve. China/U.S. Foreign Exchange Rate. [Online Database]. Accessed 17 September 2019.

Metric Conversions. Weight Conversion. [Online Application]. Accessed 17 September 2019.

Previously on Political Calculations


September 17, 2019

Nationally, the total valuation of aggregate existing home sales have continued to dip in June 2019 from April 2019's level. All but the U.S. Census Bureau's Northeast region has seen dips from recent peaks.

Preliminary and revised state level existing home sales data through June 2019 is now available from Zillow's databases, which now includes data from New Hampshire in the period July 2017 to the present. The following chart illustrates the trends we see for the 44 states for which Zillow provides seasonally-adjusted sale prices and volumes for existing homes in 44 states and the District of Columbia.

Estimated Aggregate Transaction Values for Existing Home Sales, 44 States and District of Columbia*, January 2016 to June 2019

The following charts break the national aggregate existing home sales totals down by U.S. Census Bureau major region from January 2016 through June 2019. The first two charts below show the trends for the West and the Northeast, which have respectively been the weakest and strongest regions in the nation over the last several months. [Please click on the individual charts to see larger versions.]

Estimated Aggregate Transaction Values for Existing Home Sales, U.S. Census West Region, January 2016 to Juney 2019
Estimated Aggregate Transaction Values for Existing Home Sales, U.S. Census Northeast Region, January 2016 to June 2019

Meanwhile, the U.S. South and Midwest regions have seen relatively flat levels of aggregate existing home sales since early 2018, although recently revised data indicates that aggregate sales in the Midwest reached a peak in April 2019. In the months since, preliminary data indicates that both regions have seen a softening in existing home sales.

Estimated Aggregate Transaction Values for Existing Home Sales, U.S. Census South Region, January 2016 to June 2019
Estimated Aggregate Transaction Values for Existing Home Sales, U.S. Census Midwest Region, January 2016 to June 2019

Of all these regions, the West has shown the most weakness, with California's market accounting for the lion's share of that weakness since March 2018.

Estimated Aggregate Transaction Values for Existing Home Sales, U.S. Census Bureau South Region, Individual States, January 2016 to June 2019

Aside from California, which is the 800-pound gorilla of state-level real estate markets, Washington, Colorado, Utah, and Oregon have also seen declines in recent months, with other states' markets appearing relatively flat. Only Arizona stands out with a rising volume of existing home sales in the last several months.


September 16, 2019

After all the fireworks of volatility over the last several weeks, the second week of trading in September 2019 saw precious little for the S&P 500 (Index: SPX), which closed up for the entire week by less than 1% from the previous week's close.

All the action during the week was fully consistent with investors being closely focused on 2020-Q1 in setting current day stock prices, as suggested by our alternate futures spaghetti chart.

Alternative Futures - S&P 500 - 2019Q3 - Standard Model - Snapshot on 13 Sep 2019

The reason for that was an outbreak of relatively good news, which has reduced the odds of future Fed rate cuts in upcoming months. As of the close of trading on Friday, 13 September 2019, the CME Group's FedWatch Tool is projecting quarter point rate cuts at the conclusion of the Fed's upcoming meetings this week, and again in December 2019. But whether there will be another in 2020-Q1 has become an open question, which is why investors would continue to be focusing on that particular distant future quarter:

CME Group FedWatch Tool Probabilities of Federal Funds Rate Changing at Future FOMC Meeting Dates, Snapshot on 13 September 2019

We said there was an outbreak of good news, and we meant it! Here are the headlines that caught our attention during the less-than-volatile week that was:

Monday, 9 September 2019
Tuesday, 10 September 2019
Wednesday, 11 September 2019
Thursday, 12 September 2019
Friday, 13 September 2019

Elsewhere, Barry Ritholtz listed six positives and six negatives he found in the week's economics and market-related news over at the Big Picture.

Given overseas events, we're afraid the upcoming week will be quite different.

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September 13, 2019

The U.S. Census Bureau has reported its income distribution data for the United States in 2018. The following animated chart shows what the cumulative distribution of income in the U.S. looks like for individuals, families, and households, looping through each on five second intervals.

Animation: Cumulative Distribution of Total Money Income for U.S. Individuals, Families, and Households in 2018

Want to find out how you rank among U.S. men, women, individuals, families and households? We have updated our What Is Your Income Percentile Ranking? tool to include the 2018 income distribution data just so you can!

Looking just at the distribution of household income over time, Mark Perry shows a pretty remarkable finding for the middle class contained within the Census Bureau's historic income distribution data since 1967:

Carpe Diem: Yes, the Middle Class Is Shrinking... Because Americans Are Moving Up

If you look at the right hand side of the chart, it's not just middle income earning households that are moving up into higher income echelons - after adjusting for inflation, the lowest income earning households are too!


September 12, 2019

There was big news in the world of maths last week, when Andrew Booker announced that he had solved a long-standing puzzle in maths on Reddit in a post titled Life, the Universe, and Everything, which simply linked to an equation showing the values of three numbers that, when cubed and added together, produce the number 42 as the result.

What makes this seemingly simple problem and solution such big news is that it completes a 65-year old challenge in maths to determine whether every integer from 1 to 100 can be found as the result of such a sum of cubes. Until last week, every other number within this range has either had three integer values found that can produce them or has been determined that no such combination of integers exist to produce them.

All except for the number 42, which has now yielded to a joint effort between the University of Bristol's Andrew Booker and MIT's Andrew Sullivan.

The discovery is also a demonstration of the role that social media has in propagating news of an event. The same discussion thread also contains the initial inquiry that led to Numberphile's news-breaking video describing the achievement being produced and posted the next day:

The discussion thread also contains some of the first independent checking to confirm the result, which was remarkably easy for this particular problem.

The hard part was finding the three values that would work together to produce the result, the story for which the University of Bristol told via a press release. Picking up the story following Booker's development of an improved method for solving the problem, which had led to the discovery of a sum of three cubes for the number 33 after several weeks of effort using a supercomputer earlier in 2019:

However, solving 42 was another level of complexity. Professor Booker turned to MIT maths professor Andrew Sutherland, a world record breaker with massively parallel computations, and - as if by further cosmic coincidence – secured the services of a planetary computing platform reminiscent of “Deep Thought”, the giant machine which gives the answer 42 in Hitchhiker’s Guide to the Galaxy.

Professors Booker and Sutherland’s solution for 42 would be found by using Charity Engine; a ‘worldwide computer’ that harnesses idle, unused computing power from over 500,000 home PCs to create a crowd-sourced, super-green platform made entirely from otherwise wasted capacity.

The answer, which took over a million hours of calculating to prove, is as follows:

  • X = -80538738812075974
  • Y = 80435758145817515
  • Z = 12602123297335631

And with these almost infinitely improbable numbers, the famous Solutions of the Diophantine Equation (1954) may finally be laid to rest for every value of k from one to 100 - even 42.

If you want to check the results for yourself, copy and paste the following expression into the Online Big Number Calculator:

(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3

The odds of Douglas Adams identifying 42 as an answer demanding a question and anticipating what kind of computer would be needed to find the question to correspond to it in Hitchhiker’s Guide to the Galaxy will likely take an Infinite Improbability Drive to resolve.

Previously on Political Calculations

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September 11, 2019

We can now put together the picture for the S&P 500's future quarterly dividends per share through the end of 2020!

Past and Projected S&P 500 Quarterly Dividends Per Share Futures, 2018-Q1 Through 2020-Q4

The "past" quarterly dividend futures is the last value we recorded for the CME Group's quarterly dividends per share futures before their related contracts expired on the third Friday of the month ending the indicated quarters. The "projected" quarterly dividend futures are what the CME Group's site reports for the S&P 500 as of the close of trading on 10 September 2019.

If you click through to the CME Group's site however, you'll find that they haven't yet started covering 2020-Q4. We had to infer that value by pulling the CME Group's annual dividend futures for the S&P 500, then subtracting the available quarterly futures for 2020-Q1, 2020-Q2, and 2020-Q3 from it. What remains is a reasonable initial estimate for 2020-Q4's expected dividends per share for the index!

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September 10, 2019

In July 2019, the gap between the pre-trade war trend and the trailing twelve month average of the value of goods exchanged between the U.S. and China expanded to $10.4 billion. The cumulative gap since the first tariffs were imposed in March 2018 has now grown to $62.8 billion.

That cumulative gap is measured with respect to a counterfactual trend, which represents what the total value of direct trade between the U.S. and China could reasonably have reached in the absence of the two nations' tariff war.

There is another way to assess the direct economic losses that have accumulated in the value of trade between the two countries as a result of the tariff war. We can compare the current downturn in the actual recorded trailing twelve month average of the value of goods and services exchanged between the U.S. and China with previous downturns, as indicated by the heavy black line on the above chart.

Going back to the Great Recession, the trailing twelve month average of trade between the U.S. and China peaked at $34.3 billion in October 2008, which then proceeded to drop to a low of $30.0 billion in October 2009 before beginning to recover. That $4.3 billion drop in value represents a decline of 12.5%, or one-eighth the combined value of goods and services traded between the U.S. and China.

Ten years later, the trailing twelve month average in the value of direct trade between the U.S. and China peaked at $55.7 billion in October 2018 and has since experienced a $4.9 billion drop in value through July 2019, exceeding the nominal loss of direct trade recorded during the Great Recession, the worst economic downturn since the Great Depression of the 1930s.

In percentage terms, the loss in trade coinciding with the U.S.-China tariff war represents 8.7% of the peak in the trailing twelve month average value of goods exchanged between the two countries. To match the Great Recession's overall percentage trade volume losses, the trailing twelve month average of trade between the U.S. and China will have to fall by another $2.1 billion, to $48.7 billion.

Assuming nothing changes in the U.S-China trade war to affect its current rate of decline, that level could be reached in or by November 2019.


September 9, 2019

2019 is proving to be an active year for fans of Lévy flight events in the stock market! The S&P 500 (Index: SPX) completed its fifth Lévy flight of the year on Friday, 6 September 2019, as investors completed shifting the time horizon of their future-linked attention from 2019-Q4 outward to 2020-Q1.

Alternative Futures - S&P 500 - 2019Q3 - Standard Model - Snapshot on 7 Sep 2019

We think that investors have shifted their forward-looking focus to 2020-Q1 because that is when the CME Group's FedWatch Tool sees some degree of uncertainty regarding the prospects of a third quarter point rate cut taking place within the upcoming months that are visible within their current time horizon:

CME Group FedWatch Tool Probabilities of Federal Funds Rate Changing at Future FOMC Meeting Dates, Snapshot on 06 September 2019

Here are the dates we've identified for the timing of the S&P 500's Lévy flight for the year-to-date, along with what our observations of what dividend futures-based model indicates investors were shifting their forward-looking focus from one future quarter to another:

  • 07-Jan-2019 to 14-Jan-2019: Inward shift from 2019-Q3 to 2019-Q1, stock prices rise from 2,549.69 to 2,582.61
  • 17-May-2019 to 31-May-2019: Inward shift from 2020-Q1 to 2019-Q4, stock prices fall from 2,859.53 to 2,842.98
  • 05-Jun-2019 to 10-Jun-2019: Outward shift 2019-Q4 to 2020-Q1, stock prices rise from 2,826.03 to 2,886.98
  • 31-Jul-2019 to 05-Aug-2019: Inward shift from 2020-Q1 to 2019-Q4, stock prices fall from 2,980.38 to 2,844.74
  • 28-Aug-2019 to 06-Sep-2019: Outward shift from 2019-Q4 to 2020-Q1, stock prices rise from 2,887.94 to 2,978.71

Technically, there was a sixth Lévy flight that occurred near the end of 2019-Q1, as the clock for that quarter ran out and investors shifted their focus toward 2020-Q1. Unlike the other Lévy flight events listed above however, there was very little difference in the expected change in the year-over-year growth rate of dividends projected in 2019-Q1 and in 2020-Q1, which is why stock prices didn't significantly alter their trajectory as they did during all these other, more noticeably volatile events.

Meanwhile, the random onset of new information is what often prompts investors to shift their forward-looking attention from one of point time to another. Here are the headlines we noted in the first week of September 2019 for their market-moving potential.

Tuesday, 3 September 2019
Wednesday, 4 September 2019
Thursday, 5 September 2019
Friday, 6 September 2019

Barry Ritholtz succinctly summarizes seven positives and seven negatives he found in the week's economics and market-related news over at the Big Picture.

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September 6, 2019

It's the technology that protects your credit card information from being discovered whenever you buy anything online. Whenever you send or receive an encrypted e-mail, it's the technology that keeps it from being intercepted and read by hackers with access to the internet nodes the electronic message might pass through between sender and receiver. But it may not be as secure as you might hope it would be.

Public key cryptography using asymmetric encryption is the basis of much of today's computer-based encryption. Most of today's public key cryptography is based on a coding descendent of the RSA algorithm, which was developed by MIT's Ron Rivest, Adi Shamir and Leonard Adleman back in 1977, which uses prime numbers and the difficulty in factoring very large composite numbers back into their component primes to encrypt and decrypt secure messages. The following 14-minute video from F5 DevCentral's John Wagnon explains the basics of how the algorithm works and talks through an example of it in work:

In March 2019, Robert Grant and Talal Ghannam released a preprint paper in which they claim that because the distribution of prime numbers is not entirely random, with identifable patterns that appear within them, it may be possible to develop a decryption algorithm that can efficiently crack an RSA-encoded message, without having to go through the brute force of running a multitude of trial divisions and consuming mammoth amounts of processing time in doing so to break the encryption.

Or not. In July 2019, mathematician Mark Carney identified several errors with the math in Grant and Ghannam's paper and demonstrated more computationally efficient methods of identifying prime numbers. Moreover, Carney notes that the efficiencies that might be gained by Grant and Ghannam's approach doesn't appear to scale upward with ever increasing prime numbers, which means that the Grant-Ghannam proposed RSA-breaking method has limited potential.

Ars Technica tells much of this story and the reactions that Grant's presentation at a recent "Black Hat" cryptography convention generated.

Perhaps a more interesting development to come out of the controversy is Grant's proposal for an RSA algorithm replacement, one that wouldn't use prime factors at all, which his company, Crown Sterling, is developing. Unfortunately, there isn't much information available about that new algorithm, called Time AI, at this time:

Crown Sterling claims that its Time AI cryptographic system will fix the breakable-ness of RSA cryptography by using an entirely different method of generating keys, one that doesn't rely on factoring large prime numbers. Time AI is intended to resist cracking even by advanced quantum computing technology—which has concerned cryptographers because of its potential to more rapidly perform algorithms capable of solving the difficult math problems that cryptography relies on.

Time AI, announced by Grant in a controversial sponsored presentation at Black Hat USA earlier this month, is not yet a product. In fact, Crown Sterling has not published any technical details of how Time AI works. (Grant said that the company is working on a "white paper," and it should be out by the end of the year.)

Here's how Grant and Crown Sterling's COO Joseph Hopkins described it to Ars Technica, where the algorithm would start with a snippet of an irrational number, then have an artificial intelligence system make it sing....

"It's a very unique algorithm," Grant said. "It's based on mathematical constant numbers—like pi for example—that have infinite tails that can be derived through equations, that are then connected to an AI. Basically, the AI is writing its own music. And each of the musical notes has a time signature associated with it. And then we oscillate them at a scale of time that's at 10 to the negative ninth power, which is in the nano scale of time. So it's a very rapid moving target of a dynamic encryption key."

"So what Robert just described to you," said Hopkins, "is sort of like our quantum key generator and it also has to do with its own particular crypto system. And in terms of post-quantum, we also believe that Time AI would also be quantum resistant."

That may not as be as crazy as it might at first sound. Today, Cloudflare utilizes a wall of lava lamps at its headquarters to help generate random numbers for maintaining Internet security on its servers. Check out the following video:

But would Crown Sterling's AI system be better than an established lava lamp-based computer security system? And regardless of whether it was or wasn't, how could you tell?

Previously on Political Calculations

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September 5, 2019

August 2019 was a mixed month for the U.S. stock market's dividend payers. Compared to July 2019, there were fewer announced dividend cuts, which is a positive for the market, but also fewer announced dividend rises, which is what makes for a mixed outcome for dividend investors.

Here is August 2019's dividend metadata for the U.S. stock market:

  • A total of 3,540 U.S. firms declared dividends in August 2019, an increase of 417 over the 3,123 recorded in July 2019. That figure is also 12 lower than what was recorded a year ago in August 2018.
  • 34 U.S. firms announced they would pay a special (or extra) dividend to their shareholders in August 2019, an increase of 9 over the number recorded in July 2019 and an increase of 3 over the number recorded a year ago in August 2018.
  • 125 U.S. firms announced they would boost cash dividend payments to shareholders in August 2019, a decrease of 14 from the 139 recorded in July 2019, and a decrease of 3 from the 128 dividend rises declared back in August 2018.
  • A total of 20 publicly traded companies cut their dividends in August 2019, a decline of 11 from the 31 recorded in July 2019 and also an increase of 5 over the 15 recorded in August 2018.
  • 4 U.S. firms omitted paying their dividends in August 2019, an increase of 2 over the number recorded in July 2019. That figure is also an increase of 2 over the total recorded in August 2018.

The following chart shows the monthly increases and decreases for dividends reported by Standard and Poor for each month from January 2004 through August 2019.

Number of Public U.S. Firms Increasing or Decreasing Their Dividends Each Month, January 2004 through August 2019

We've previously presented our ongoing sampling of real time dividend cut announcements for 2019-Q3 with data through 26 August 2019. There were no additions to that list during the remainder of the month.

Meanwhile, if you'd ever like to review our sources, here they are!


Standard and Poor. S&P Market Attributes Web File. [Excel Spreadsheet]. 3 September 2019.

Seeking Alpha Market Currents. Filtered for Dividends. [Online Database]. Accessed 30 August 2019.

Wall Street Journal. Dividend Declarations. [Online Database when searched on the Interent Archive]. Accessed 30 August 2019.


September 4, 2019

July 2019 saw median household income in the United States reach new record highs in both real and inflation-adjusted terms, with the typical American household earning $65,084 according to Sentier Research's latest monthly report. That's a 0.4% increase over the $64,430 estimate the demographic analytics firm announced for June 2019.

The following chart shows the nominal (red) and inflation-adjusted (blue) trends for median household income in the United States from January 2000 through July 2019, with July 2019's estimate marking the top of both scales. The inflation-adjusted figures are presented in terms of constant July 2019 U.S. dollars.

Median Household Income in the 21st Century: Nominal and Real Estimates, January 2000 to July 2019

Year over year, median household income for July 2019 rose by 4.2%, or by 2.4% after adjusting for inflation.

Median Household Income in the 21st Century: Year Over Year Growth Rate, January 2001 to July 2019

The monthly data reported by Sentier Research is showing signs of a rebound after having hit a speedbump earlier in 2019.

Analyst's Notes

Our alternate methodology for estimating median household income from data reported by the U.S. Bureau of Economic Analysis would put the figure at $65,020 for July 2019, which is within 0.1% of Sentier Research's estimate for the month.

In generating inflation-adjusted portion of the Median Household Income in the 21st Century chart and the corresponding year-over-year growth rate chart above, we've used the Consumer Price Index for All Urban Consumers (CPI-U) to adjust the nominal median household income estimates for inflation, so that they are expressed in terms of the U.S. dollars for the month for which we're reporting the newest income data.


Sentier Research. Household Income Trends: January 2000 through July 2019.  [Excel Spreadsheet with Nominal Median Household Incomes for January 2000 through January 2013 courtesy of Doug Short]. [PDF Document]. Accessed 30 August 2019. [Note: We've converted all data to be in terms of current (nominal) U.S. dollars.] 

U.S. Department of Labor Bureau of Labor Statistics. Consumer Price Index, All Urban Consumers - (CPI-U), U.S. City Average, All Items, 1982-84=100. [Online Database (via Federal Reserve Economic Data)]. Last Updated: 13 August 2019. Accessed: 13 August 2019.


September 3, 2019

Perhaps the biggest event to affect expectations for the S&P 500 (Index: SPX) during the final week of August 2019 was also the least noticed.

Unless you paid attention to the CME Group's quarterly dividend futures for the index, you would have missed that the amount of cash dividends expected to be paid out by S&P 500 firms during 2020-Q1 increased from $14.50 per share to $14.95 per share between Wednesday, 28 August 2019 and Friday, 30 August 2019.

Meanwhile, there was no change in the expectations for dividends in other future quarters, but the change in the amount of dividends expected to be paid out from 21 December 2019 and 20 March 2020 may explain much of why investors would appear to have shifted their focus to that particular future quarter, as indicated by the trajectory of the S&P 500 with respect to our dividend futures-based model's projections.

Alternative Futures - S&P 500 - 2019Q3 - Standard Model - Snapshot on 30 Aug 2019

At the same time, the CME Group's FedWatch Tool became a little more myopic in the last week, dropping its early projections for 2020-Q2, making 2020-Q1 the most distant future quarter to which investors paying attention to likely changes in the Federal Reserve's interest rate policies are seeing in their crystal balls.

CME Group FedWatch Tool Probabilities of Federal Funds Rate Changing at Future FOMC Meeting Dates, Snapshot on 30 August 2019

Meanwhile, we think that last week's news headlines don't provide much of an explanation for why stock prices rose during the week that was, but you can judge that impression for yourself:

Monday, 26 August 2019
Tuesday, 27 August 2019
Wednesday, 28 August 2019
Thursday, 29 August 2019
Friday, 30 August 2019

At the Big Picture, Barry Ritholtz identifies seven positives and seven negatives he found in the week's economics and market-related news.

Over the Labor Day holiday weekend, the U.S. and China imposed new tariffs on each other's nations' goods, which will factor into this upcoming week's stock market action. If you were hoping for less noise in in the markets following a lazy long weekend, you'll likely be disappointed.

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