Political Calculations
Unexpectedly Intriguing!
July 14, 2020

Trade data between the U.S. and China in May 2020 show early signs of economic recovery following the negative impact of government-mandated business closures to address the coronavirus pandemic earlier in 2020.

We can see that in the rebound of the combined value of trade in goods and services between the two countries, which continued to rise following April 2020's initial rebound that began after China reopened its economy. At $46.2 billion, the combined value of U.S.-China trade was within $2.1 billion of its May 2019 level, the narrowest gap between year-over-year figures since the outbreak of the coronavirus pandemic in China began at the end of 2019.

Combined Value of U.S. Exports to China and Imports from China, January 2008 - May 2020

Since the end of 2019, a $6.0 billion gap has opened up between the trailing twelve month average of the value of U.S.-China trade and a counterfactual based on a reasonable estimate of what that trade would look like following January 2020's 'Phase 1' trade deal between the two nations. More importantly, the downward trajectory of the trailing year average has begun to decelerate in May 2020, which is an indication a recovery from the global coronavirus trade recession is beginning to take hold.

May 2020 saw much of the U.S. economy beginning to incrementally open on a state-by-state basis, following the lifting of statewide lockdown restrictions that closed many businesses and ordered residents to stay-at-home to slow the spread within the U.S., but which continued to negatively weigh on its economy during the month. We can see that impact in the year-over-year growth rates of U.S. exports to China and U.S. imports from China, where the exchange rate-adjusted growth rate of exports was positive, but imports were negative, as might be expected.

Year Over Year Growth Rate of U.S.-China Trade, January 1986 - May 2020

The data for U.S. exports to China also answers the question we had last month regarding what extent the surge in U.S. exports to China in April 2020 might have been attributed to shipments that had been bottlenecked to that country while its economy was closed by its coronavirus epidemic earlier in 2020. Since the year over year growth rate of U.S. exports to China for May 2020 is 10.1% versus April 2020's 14.7%, the answer is "not all that much".

Looking forward, the delayed spread of coronavirus infections in parts of the U.S. that avoided the worst of the pandemic after it initially arrived presents the largest challenge for a rapid economic recovery. This delayed crest effect is not limited to the United States, as China is also experiencing a similar dynamic in confronting the continued spread of the SARS-CoV-2 coronavirus.

Previously on Political Calculations

Here are the previous episodes of our series exploring the impact of the coronavirus pandemic on trade between the U.S. and China, presented in reverse chronological order!


Board of Governors of the Federal Reserve System. China / U.S. Foreign Exchange Rate. G.5 Foreign Exchange Rates. Accessed 10 July 2020.

U.S. Census Bureau. Trade in Goods with China. Accessed 10 July 2020.

Labels: , ,

July 13, 2020

The S&P 500 (Index: SPX) inched up to its highest close since the second week of June 2020, but is still slightly over 201 points shy of the record high of 3,386.15 it recorded on 19 February 2020. On the other hand, it has risen 947.64 points since hitting bottom at 2,237.40 back on 23 March 2020.

But at 3,185.04, it's high enough that we're thinking that investors may have altered their their anticipation for what to expect from the Federal Reserve's monetary policy in the past week, where the alternative futures chart suggests they may now be leaning toward expecting more in the way of expansionary monetary policies.

Alternative Futures - S&P 500 - 2020Q2 - Standard Model (m=1.5 from 24 June 2020) - Snapshot on 10 Jul 2020

We see that change in the approximate value of the dividend futures-based model's amplification factor, m, which looks like it moved from a value of 1.5 toward a value of 1.0 in the last week. We think that change coincides with comments made by Fed officials on that day pledging more support for a recovery from the coronavirus recession.

Where we don't see any change is in the CME Group's FedWatch tool, which shows a 100% probability of the Fed maintaining its Federal Funds Rate in the zero bound range of 0-0.25% well into 2021. That expectation has been unchanged over the last several weeks.

Meanwhile, the Fed's combination of liquidity injections and lending to U.S. corporations has mitigated a collapse in expected future dividends that would have devasted pension funds and greatly amplified the economic damage from the coronavirus recession had the Fed not intervened to support the stock market. The expected future for the S&P 500's quarterly dividends per share has risen to their highest levels of the past several months, though at this point, that means the S&P 500's are now expected to bottom in 2020-Q4 and stabilize during 2021.

Past and Projected Quarterly Dividends Futures for the S&P 500, 2019-Q4 through 2021-Q4, Snapshot on  10 July 2020

Here's the roundup of the week's major market-moving news headlines.

Monday, 6 July 2020
Tuesday, 7 July 2020
Wednesday, 8 July 2020
Thursday, 9 July 2020
Friday, 10 July 2020

Over at The Big Picture, Barry Ritholtz divides the markets and economics news of the week into short, succinct lists of positives and negatives.

On a final note, we're thinking we need to take a broader view of the impact of the Fed's monetary policies in continuing to pay attention to the changing value of the amplification factor in the dividend futures-based model. We had been thinking that when it turned negative as the Fed flooded the market with liquidity during the last several months, it was an indication investors were expecting negative interest rates.

To be sure, they were, but the Fed doesn't need to set its Federal Funds Rate to be negative to achieve that effect. During the so-called "Great Recession", the Federal Reserve used its quantitative easing policies to achieve the effect of negative rates (as measured by Jing Cynthia Wu and Fan Dora Xia's shadow federal funds rate), without actually setting negative rates.

The difference between then and now is the Fed has implemented considerably more robust interventions which have transformed the amplification factor from being effectively constant to now be a variable, which means we will have to pay a lot more attention to what the Fed's minions are saying and doing.

Not that we weren't before given their role in setting the future time horizon of investors via their policies of foward guidance, but now their influence goes far beyond that, which the headlines of the past week make clear.

It is an exciting time. We are in new territory. What can possibly go wrong in the Fed's new world?

Labels: ,

July 10, 2020

Mathematician John Conway passed away of COVID-19 earlier this year. Among his many legacies was a particularly difficult-to-classify knot with 11 crossings that, in the five decades after he had identified it, had defied full mathematical classification for whether or not it was a slice knot.

Before we go any further, let's take a crash course in knot theory to understand why that posed a problem for mathematicians, starting with the gentlest entry into the subject we can find in the form of the following one-and-a-half minute video introduction:

Now that you've gotten your feet wet, let's expand on that introduction with the following 10-minute video description of the tools mathematicians have developed to study knots:

In maths, knots aren't just models of tangled bits of rope and string, but can often represent complex geometries, such as the edges of much more complex surfaces. In real life, those representations have application in molecular analysis, where knot theory has provided insights into understanding the properties of complex molecules, such as DNA.

That's where the concept of slice in knot theory comes into play. If you wrap a knot around a three or four-dimensional sphere and then cut through it to create a disc-shaped "slice" of the sphere while also creating a section cut of the knot in the process, if you can do that and produce simple loops without crossings like the "unknot" featured in the introductory videos, you have a slice knot, which puts it into a class of knots that share certain properties, like the simpler stevedore knot, which only involves six crossings. On the other hand, if you cannot avoid having a tangled crossing no matter how you might take a slice of the knot, then you do not have a slice knot, which puts it into a different family of knots with different properties.

In 2019, University of Texas grad student Lisa Piccarello cracked the classification problem, determining that Conway's 11-crossing knot was "not slice", which is a big deal because of how difficult it has been for mathematicians to arrive at that conclusion, and which has earned no fewer than two articles in Quanta magazine to cover the story. We can't do better in generally describing how she was able to successfully resolve the question than those two articles, which describe how she approached the problem in part by exploring it in four dimensional space.

That's not easy, so to better understand that part of how she determined Conway's knot was not slice, let's start with her own description of why a mathematician would go into the fourth dimension from the University of Texas' press release announcing her achievement:

If an ant living on the earth would like to leave an island without touching the water, it is going to have a hard time. Because on the 2-D surface of the Earth, the water completely surrounds the island. But, if the ant builds a bridge (which rises up, into a third dimension, above the water), then suddenly it has an option to leave the island. We naturally think about 3-D space all of the time. Studying 4-D space is fun because, just as the ant can leave the island once it's allowed to go up, in four dimensions more things are possible.

How does that actually work? Amanda Hager describes how to unknot knots using the fourth dimension in the following 4:22 minute video, in which she starts off by putting you in flatland as one of Piccarello's ants:

But as for what going four-dimensional can do for you in untangling knots, you can get a better sense from Zsuzsanna Dancso's discussion of her work in studying the related concept of braids in higher dimensions in the following 14:26 minute Numberphile video, where the part of her work that is directly analogous to slicing knots is about 8 minutes in:

That concludes this very short crash course introduction to both knot theory and four-dimensional geometry. If you're intrigued enough to learn more, or know someone who would be, we'll conclude by pointing you to Matt Parker's Things To Make And Do In the Fourth Dimension, which is a fun way to start digging deeper into the 4D world.


July 9, 2020

We thought it might be fun to take a quick look into the expected future for the S&P 500's quarterly dividends per share. The following chart shows what we saw when we looked into the CME Group's crystal ball for the S&P 500's dividend futures.

The Future for the S&P 500's Quarterly Dividends Per Share from 2020-Q3 through 2021-Q4

We've only become able to see through to the end of 2021 during the last two weeks. One important thing to know about these forecasts is that they correspond to dividends expected to be paid out by S&P 500 firms during the periods covered by futures contracts, which run from the end of the third Friday of the month preceding the indicated calendar quarter, through the third Friday of the month ending the indicated calendar quarter.

That makes them different from the quarterly dividends per share for the S&P 500 reported by Standard and Poor after the end of each quarter, which corresponds directly with the dividends that were paid out during the three months that make up a calendar quarter.


CME Group. S&P 500 Quarterly Dividend Index Futures Quotes. [Online Database]. Accessed 8 July 2020.

CME Group. S&P 500 Annual Dividend Index Futures Quotes. [Online Database]. Accessed 8 July 2020.

Standard and Poor. S&P 500 Index Earnings. [Excel Spreadsheet]. Quarterly dividends for S&P 500 updated on first business day following end of calendar quarter.

Labels: , ,

July 8, 2020

The fourth month of the coronavirus pandemic in the U.S. has carried a lot of bad news with it, but some good news as well. The bad news is that several states are experiencing a delayed first wave of infections, after exiting their lockdowns in May, which was followed by widespread political protests in early June that contributed to the surge in new infections.

But that's not all the bad news. A few states that had already experienced first wave coronavirus infections are showing signs of experiencing a second wave, indicating their residents failed to achieve the kind of herd immunity that appears to now be present in the locations that have been the most hard hit.

The good news however is that there are far fewer deaths occurring with the delayed first wave and new second wave than did in the states that were hardest hit in the first wave. Let's visualize the time series trends for individual states in the COVID Tracking Project's data to see what we mean.

Here is an interactive chart showing the rolling 7-day average of newly confirmed COVID-19 cases per 100,000 residents by state from 17 March 2020 through 7 July 2020. Hover your device's cursor over a point or line on the chart to highlight it (alternatively, if you want to see the day-by-day reported data for a single state, or a particular group of states, the COVID Time Series application is a good resource to bookmark):

Through 7 July 2020, Arizona continues to lead the nation in the number of new cases per 100,000 residents, exceeding the rate achieved by New York did in early April 2020, though that's partly because coronavirus testing back in March and April 2020 was very limited in comparison, failing to capture the full extent of the spread of the SARS-CoV-2 coronavirus in New York at the time.

Florida and South Carolina have risen to take the second and third positions respectively, as both states, like Arizona, are experiencing a delayed first wave of COVID-19 infections.

Three states appear to have begun to experience a second wave of coronavirus infections. Louisiana, Delaware, and Washington each had an early wave in March, which went on to subside, but now are each experiencing rising levels of infection.

If there is good news, it is that the rate of deaths attributed to COVID-19 in states experience both a delayed first wave and in the three states now experiencing a second wave is far lower than what was seen in previous epicenters for COVID-19 in the U.S. Here is an interactive chart showing the rolling 7-day average daily reported COVID-19 deaths per 100,000 residents by state from 17 March 2020 through 7 July 2020:

The chart shows anomalies for three states. The large spike for New Jersey in June 2020 is the result of delayed reporting of deaths that occurred over several months. Meanwhile, the rolling 7-day average deaths for both North Dakota and Colorado turned negative when both states corrected their cumulative COVID-19 death totals during May, as both had previously reported higher figures before these negative adjustments.

Looking at the most current data, Arizona now leads the nation for deaths per 100,000 residents attributed to COVID-19, although considering its number of cases per 100,000 residents, the state so far appears to be better managing its surge of coronavirus cases than did other states that experienced similar rates of viral infection, such as New York.

That apparent better performance can be seen by comparing Arizona's current populaton adjusted data for deaths with the state of New York's data from when it reported a similar rate of incidence of cases back on 25 April 2020.

Back then, New York had accumulated some 1,450.3 cases per 100,000 residents, which is directly comparable to Arizona's cumulative 1,443.9 cases per 100,000 residents as of 7 July 2020. But with that level of reported cases, New York's rate of COVID-19 deaths was 3.2 times higher than what Arizona is experiencing today, with 85.3 deaths per 100,000 residents versus Arizona's 26.5 deaths per 100,000 residents.

One key difference that helps explain a large portion of Arizona's significantly lower COVID-19 death rate to date is that Arizona's top state officials haven't panicked and tried to open up hospital bed space by transferring coronavirus-infected patients to the state's nursing homes, as occurred in New York and other states that stupidly copied its policies.

The skyline charts for each state show the dynamics of how things have changed in the four months from 10 March 2020 through 7 July 2020. Each tower chart within the presentation shows the relative number of confirmed cases, hospitalizations, recoveries (or discharges), and deaths for the 56 individual U.S. states or territories, all indexed to the same 2% of the state or territories population, making it easy to see which have been most affected and where coronavirus are now either spreading the fastest or the slowest.

Progression of COVID-19 in the United States by State or Territory, 10 March 2020 through 7 July 2020

New York continues to lead the country in having experienced the most coronavirus cases, with just over 2% of its population having been confirmed with the infection. The spread of infections is slowing however, as the sides of its tower chart are becoming more vertical. The following chart group shows New York's full tower chart (including negative tests), its daily test positivity rate, and its rolling 7-day average of newly confirmed coronavirus cases and deaths.

Progression of COVID-19 in New York, Daily Test Positivity Rate, 7-Day Total Newly Confirmed Cases and Deaths per Day, 10 March 2020 through 7 July 2020

Here's the same chart group for Arizona, covering the same period of time for comparison.

Progression of COVID-19 in Arizona, Daily Test Positivity Rate, 7-Day Total Newly Confirmed Cases and Deaths per Day, 10 March 2020 through 7 July 2020

We've been covering Arizona's situation since we determined it became the new epicenter for coronavirus cases in the U.S. several weeks ago. We'll continue to do so in upcoming weeks.

Finally, we'll close on a potentially hopeful note. The U.S. Centers for Disease Control and Prevention reported on 27 June 2020 that "mortality attributed to COVID-19 decreased compared to last week and is currently at the epidemic threshold", which is to say that if COVID-19 deaths continue to fall in the U.S., the nation will no longer be considered to be undergoing a national epidemic. While the CDC cautions that late reporting of deaths may prevent it from changing classification in the near future, that the U.S. is nearing this threshold is a positive development.

Previously on Political Calculations

While this is the last planned article for this particular series, here are all of the articles featuring the data visualization we've developed to track the spread and severity of the coronavirus epidemic at the state level, which we've listed in reverse chronological order, starting with this very article!


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:

ironman at politicalcalculations.com

Thanks in advance!

Recent Posts

Stock Charts and News

Most Popular Posts
Quick Index

Site Data

This site is primarily powered by:

This page is powered by Blogger. Isn't yours?

CSS Validation

Valid CSS!

RSS Site Feed

AddThis Feed Button


The tools on this site are built using JavaScript. If you would like to learn more, one of the best free resources on the web is available at W3Schools.com.

Other Cool Resources

Blog Roll

Market Links

Useful Election Data
Charities We Support
Shopping Guides
Recommended Reading
Recently Shopped

Seeking Alpha Certified

Legal Disclaimer

Materials on this website are published by Political Calculations to provide visitors with free information and insights regarding the incentives created by the laws and policies described. However, this website is not designed for the purpose of providing legal, medical or financial advice to individuals. Visitors should not rely upon information on this website as a substitute for personal legal, medical or financial advice. While we make every effort to provide accurate website information, laws can change and inaccuracies happen despite our best efforts. If you have an individual problem, you should seek advice from a licensed professional in your state, i.e., by a competent authority with specialized knowledge who can apply it to the particular circumstances of your case.