Political Calculations
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22 September 2021

The arrival of the coronavirus pandemic in the United States in March 2020 and, perhaps more significantly, the lockdown measures that state and local governments imposed on Americans as their response had a major impact on how Americans spent money in 2020.

That much is evident from the results of the 2020 Consumer Expenditure Survey, which saw the average annual expenditures of American "consumer units" drop by 2.7% from their 2019 level. "Consumer units" is the affectionate nickname given by the BLS' data jocks to what are predominantly made up of U.S. households. Our first chart featuring data from the 2020 CEX survey shows that measure for each year from 1984 through 2020.

Average Annual Expenditures per Household Consumer Unit, 1984-2020

That's the big picture, but the Consumer Expenditure Survey breaks down the average annual expenditures of U.S. household consumer units into major categories of spending. Our second chart show the amount of spending from 1984 through 2020 for housing; transportation; life insurance, pension savings and Social Security; health expenditures and medical expenses; entertainment; charitable contributions; apparel and other products; and finally education, to rank them from largest to smallest.

Major Categories of Average Annual Expenditures per U.S. Household Consumer Unit, 1984-2020

The major categories of spending that rose in 2020 include housing; life insurance, pension savings and Social Security; and finally charitable contributions. Every other category fell, with the largest declines in expenditures for transportation; food; and apparel and other products.

This outcome confirms the extended negative impact of the various lockdown measures imposed by state and local governments. What's important to recognize here is that they continued in much of the country well beyond the two month-long recession that arrived when large population states first mandated their residents stay at home and shuttered businesses in March 2020 during the first wave of coronavirus infections in the U.S.

Our next chart presents the share of each of the major categories of household spending as a percentage of total annual average expenditures.

Percent Share of Major Categories of Average Annual Expenditures per U.S. Household Consumer Unit, 1984-2020

The most significant item here is housing, which jumped to represent 35% of the average American consumer unit household's spending, an all-time high for the data series.

Our final chart stacks all these major categories of household spending together to assemble the full picture of how the spending of American consumer unit households has changed each year from 1984 through 2020.

Major Categories of Consumer Spending as Share of Average Annual Total Expenditures, 1984-2020

This last chart is one of our favorites, in part because the colors convey which major categories of spending have generally risen over time (the purple-shaded components) or fallen over time (the green-shaded components).

We'll be exploring the wealth of data contained within the 2020 Consumer Expenditure Survey more over the next several weeks.


U.S. Bureau of Labor Statistics. Consumer Expenditure Survey. Multiyear Tables. [PDF Documents: 1984-1991, 1992-1999, 2000-2005, 2006-2012, 2013-2020]. Accessed 9 September 2021. 

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21 September 2021

We now have quarterly dividend futures data for the S&P 500 (Index: SPX) through the end of 2022. Here's what the future looked like as of the close of trading on 20 September 2021:

Past and Projected Quarterly Dividends Per Share Futures for S&P 500, 2020-Q4 Through 2022-Q4, Snapshot on 20 September 2021

The past and projected data shown in this chart is from the CME Group's S&P 500 quarterly dividend index futures. The past data reflects the values reported by CME Group on the date the associated dividend futures contract expired, while the projected data reflects the values reported on 20 September 2021. Until the futures contracts for their indicated quarter expire, projected dividends will fluctuate with changing expectations of the future for the index' dividends per share.

Readers should note these projections indicate the amount of dividends per share to be paid out over the period covered by each quarters 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 "current" quarter of 2021-Q4 began on Saturday, 18 September 2021 and will end on Friday, 17 December 2021.

That makes these figures different from the quarterly dividends per share figures reported by Standard and Poor, who 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.

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20 September 2021

The S&P 500 (Index: SPX) had what Reuters called a 'rollercoaster' week, but when all was said and done, stock prices still fell within the expected range.

Or rather, the range that would be expected if investors were mainly focusing on 2022-Q1 in setting current day stock prices. Or on 2021-Q4, since there's not much difference between the expectations for this quarter and 2022-Q1 at this point of time.

Alternative Futures - S&P 500 - 2021Q3 - Standard Model (m=-2.5 from 16 June 2021) - Snapshot on 17 Sep 2021

As for the market's rollercoaster week, Friday, 17 September 2021 was a quadruple witching day, with a slew of options and futures contracts expiring. That includes the dividend futures contract for 2021-Q3, which as far as the alternative futures chart is concerned, is over.

If you read the marking moving headlines of the week below carefully, you can see why 2021-Q4 or 2022-Q1 are points of interest for investors looking forward in the story considering the timing of when the Fed will start tapering off its pandemic stimulus bond buying program, which it identifies as likely to happen in either November (2021-Q4) or in December (2022-Q1), where the quarters are defined by dividend futures contract expiration dates.

Monday, 13 September 2021
Tuesday, 14 September 2021
Wednesday, 15 September 2021
Thursday, 16 September 2021
Friday, 17 September 2021

With expectations for the future of U.S. interest rates often influencing investors, one resource for checking out recent trends you might find useful is the Daily Treasury Yield Curve Rates database from the U.S. Treasury.

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17 September 2021

In a sign the strange new world of innovation is becoming stranger, U.S. District Judge Leonie Brinkema ruled on 2 September 2021 that an artificial intelligence machines cannot be inventors under the U.S. Patent Act. That ruling contradicts rulings made in favor of AI systems being eligible to be granted patents in Australia and in South Africa and may influence patent applications and appeals currently under consideration in a number of other nations.

The case involves two patent applications filed on 29 July 2019 for a "neural flame" (ASN 16/524,350) and a "fractal beverage container" (ASN 16/524,532) filed by Stephen Thaler, whose DABUS artificial intelligence system is listed as the inventor, with Thaler as the AI system's owner listed as the assignee. In the plaintiff's argument advanced in the court case protesting the U.S. Patent and Trademark Office's earlier rejection of patent awards, Thaler would be the owner of any patent awarded for inventions generated by the artificial intelligence.

But as the judge ruled, because the AI system does not qualify as a person under the U.S. Patent Act, no U.S. patent will be awarded. Consequently, the U.S. patent office's rejection of the two DABUS' patent applications was upheld.

Rather than delve further into the legal considerations, the Inventions in Everything team was curious to see what kind of patentable innovations the DABUS AI system came up with. Here's the basic abstract describing the neural flame, whose purpose is to attract human attention:

The present invention discloses devices and methods for attracting enhanced attention. Devices include: an input signal of a lacunar pulse train having characteristics of a pulse frequency of approximately four Hertz and a pulse-train fractal dimension of approximately one-half; and at least one controllable light source configured to be pulsatingly operated by the input signal; wherein a neural flame emitted from at least one controllable light source as a result of the lacunar pulse train is adapted to serve as a uniquely-identifiable signal beacon over potentially-competing attention sources by selectively triggering human or artificial anomaly-detection filters, thereby attracting enhanced attention.

Here's the abstract for DABUS' fractal container invention:

A container for use, for example, for beverages, has a wall with and external surface and an internal wall of substantially uniform thickness. The wall has a fractal profile which provides a series of fractal elements on the interior and exterior surfaces, forming pits and bulges in the profile of the wall and in which a pit as seen from one of the exterior or interior surfaces forms a bulge on the other of the exterior or interior surfaces. The profile enables multiple containers to be coupled together by inter-engagement of pits and bulges on corresponding ones of the containers. The profile also improves grip, as well as heat transfer into and out of the container.

Because it's more visually interesting than DABUS' neural flame invention, here's an illustration of the AI system's fractal container:

U.S. Patent Application Serial Number 16/524,352 Figure 6

Fans of fractal geometry will recognize the profile of the Koch Snowflake. The novel application that would be potentially patentworthy is its application for use as a beverage container, where the combination of an infinite perimeter with a finite cross-sectional area would in fact make it useful for transferring heat through its sides either to or from the beverage or fluid contained within. Here's an video overview of the Koch Snowflake from the Khan Academy:

The invention would have use in applications where its desirable to rapidly transfer heat either into or out of the sides of the container, such as in cooking, where fluted ramekins are often used for that purpose.

From the Inventions in Everything Archives

When IIE the IIE team has previously looked at beverage containing-related inventions, the goal of the inventor has often been to prevent or to minimize the amount of heating or cooling taking place across the walls of a beverage container. Here's where the IIE team has previously paid attention to the heat transfer properties of beverage-containing innovations:

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16 September 2021

The U.S. Census Bureau released its annual estimate for median household income in the U.S. for the 2020 calendar year on 14 September 2021. It reported median household income for the 2020 calendar year was $67,521.

If you compare that number with the official estimate of median household income of $68,703 reported for the 2019 calendar year, that is a 1.8% decline. But there was a big problem with the 2019 estimate. The Census Bureau was collecting the data that would be used to determine that figure in March 2020, when the coronavirus pandemic reached the U.S. and the lockdowns imposed by state and local governments to "flatten the curve" disrupted the Census Bureau's ability to collect data. It particularly affected the rate of responses for its Current Population Survey's Annual Social and Economic Supplement from lower income households, where many households in this demographic group did not respond.

Census Bureau analysts have estimated that had they been able to collect a more complete data sample, they would have estimated median household income to be $66,790 for the 2019 calendar year, which we first reported in October 2020. And that brings us to the most remarkable aspect of the median household estimate for 2020. If not for the disruptive effect of the pandemic lockdowns, median household income would have risen by 1.1% from the adjusted estimate for 2019 to 2020's official estimate.

The following chart shows the Census Bureau's estimates of median household income from 2018 through 2020, illustrating how different 2019's estimate would be when accounting for the pandemic's disruption.

How the Pandemic Affected the Census Bureau Estimates of Median Household Income (2018-2020)

Only the Census Bureau's official estimate for 2019 was significantly impacted by the coronavirus pandemic. It wasn't a factor at all in March 2019 when data was collected for the 2018 calendar year, and it wasn't a significant factor in March 2021 when data was collected for 2020. The data sources supporting our exclusive analysis are presented below.


U.S. Census Bureau: Jessica Semega, Melissa Kollar, John Creamer, and Abinash Mohanty. Report Number P60-266. Income and Poverty in the United States: 2018. [PDF Document]. 15 September 2020.

U.S. Census Bureau: Jessica Semega, Melissa Kollar, Emily A. Shrider, and John Creamer. Report Number P60-270. Income and Poverty in the United States: 2019. [PDF Document]. 15 September 2020.

U.S. Census Bureau: Jonathan Rothbaum and Adam Bee. Coronavirus Infects Surveys, Too: Survey Nonresponse Bias and the Coronavirus Pandemic. [PDF Document]. 3 May 2021.

U.S. Census Bureau: Emily A. Shrider, Melissa Kollar, Frances Chen, and Jessica Semega. Report Number P60-273. Income and Poverty in the United States: 2020. [PDF Document]. 14 September 2021.

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15 September 2021

In July and August 2021, the active variants of the SARS-CoV-2 coronavirus spread through China, Japan and several nations in southeast Asia, disrupting global supply chains. How much has that disruption affected the world's economy?

We can estimate that impact by tracking the pace at which carbon dioxide is added to the Earth's atmosphere. The trailing year average of that rate has fallen sharply since June 2021, as shown in the latest update to the chart tracking its history since January 1960.

Trailing Twelve Month Average of Year-Over-Year Change in Parts per Million of Atmospheric Carbon Dioxide, January 1960 - August 2021

Since December 2019, a net reduction of 0.57 parts per million of atmospheric carbon dioxide has been recorded in the trailing twelve month average of the year over year rate of change in atmospheric carbon dioxide levels measured at the remote Mauna Loa Observatory. Of that, a net reduction of 0.10 parts per million occurred since June 2021. We can convert both these changes into an estimate of the lost GDP for the global economy using the following tool. If you're accessing this article on a site that republishes our RSS news feed, please click through to our site to access a working version of the tool.

Change in Atmospheric Carbon Dioxide
Input Data Values
Change in Carbon Dioxide in Atmosphere [Parts per Million]
World Population [billions]

Change in Amount of Carbon Dioxide Emitted into Atmosphere
Calculated Results Values
Carbon Dioxide Emissions [billions of Metric Tonnes]
Estimated Net Change in World GDP [trillions]

Using the default value of a -0.10 parts per million to account for the change in the rate of growth of atmospheric carbon dioxide since June 2021, we find the equivalent net loss to global GDP attributable to the spread of COVID in southeast Asia and its disruptive effect on the world economy is 3.3 trillion.

Going back to the beginning of the coronavirus pandemic, the reduction of 0.57 part per million in the rate at which carbon dioxide is being added to the Earth's air corresponds to a net loss to global GDP of $18.9 trillion.

We'll conclude by recognizing that not all the decline in the pace at which CO₂ is being added to the Earth's air is related to the disruption to global supply chains from the spread of COVID in southeast Asia. The Chinese government's action to shutter energy-intensive aluminum production to meet environmental goals is also a contributing factor. Since China is the world's largest smelter of aluminum, halts to its production both reduces China's carbon dioxide emissions at the cost of shrinking its economic output.


National Oceanographic and Atmospheric Administration. Earth System Research Laboratory. Mauna Loa Observatory CO2 Data. [Text File]. Updated 7 September 2021. Accessed 7 September 2021.

Previously on Political Calculations

Here is our series quantifying the negative impact of the coronavirus pandemic on the Earth's economy, presented in reverse chronological order.

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14 September 2021

From time to time, our peers in Asia will alert us to developing stories on the state of economic affairs in their home region. On 30 August 2021, they really rang a bell suggesting they were highly concerned about the potential for a developing recession within the region.

Just over two weeks later, we can confirm their fears for the future have largely abated. But that doesn't address the developments that led them to have cause for concern. Here's a sampling of headlines that coincided with their heightened concerns:

All but the last story is significant in demonstrating the extent to which the coronavirus pandemic is still driving national economies. Among the nations of southeast Asia, which had largely escaped the negative impact of COVID in 2020, it's having an especially large impact. One with global dimensions:

That impact has been building since June 2021. We'll feature an estimate of how disruptive COVID has been to the global economy tomorrow, when we'll also explain why that last headline matters.

Screenshot: 6 September 2021 CNBC Interview with HSBC Joseph Incalcaterra

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13 September 2021

The S&P 500 (Index: SPX) closed at a record high of 4,536.25 on Thursday, 2 September 2021. The index has since lost steam and has fallen in each of the five trading days since. As stock prices have only dropped 1.7% from its recently recorded high, that still puts it within the latest redzone forecast range.

Alternative Futures - S&P 500 - 2021Q3 - Standard Model (m=-2.5 from 16 June 2021) - Snapshot on 10 Sep 2021

At this point, we think investors are still focusing on 2022-Q1 in setting current day stock prices, where the dip in stock prices is most likely attributable to typical levels of noise in the market. The best example of that involves the news story of an adverse court ruling affecting the biggest company in the S&P 500, Apple (NASDAQ: AAPL), which we've captured in this week's roundup of market moving news headlines.

Tuesday, 7 September 2021
Wednesday, 8 September 2021
Thursday, 9 September 2021
Friday, 10 September 2021

Here's a news source that can keep you posted on when various economic data will be released: the National Bureau of Economic Research's New Economic Indicates and Releases RSS news feed. The downside of the feed is that it doesn't link to those items after they come out, but at least you'll know when you need to look for them!

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10 September 2021

We're marking a unique achievement today, the development of which has eluded mathematicians, biologists, and fowl farmers for centuries: a universal formula for avian eggs!

Here's a diagram we created to mark the occassion, followed by the formula presented in a recently published paper by Valeriy G. Narushin, Michael N. Romanov, and Darren K. Griffin.

The Dimensioned Egg, based on photo by Jasmin Egger via Unsplash - https://unsplash.com/photos/PcGNb3QJjXI
Narushin (2021) et al. Universal Formula for Egg Shape

The press release issued by the University of Kent explains what's now possible because of the development of a universal formula for bird eggs:

This new formula is an important breakthrough with multiple applications including:

  1. Competent scientific description of a biological object. Now that an egg can be described via mathematical formula, work in fields of biological systematics, optimization of technological parameters, egg incubation and selection of poultry will be greatly simplified;
  2. Accurate and simple determination of the physical characteristics of a biological object. The external properties of an egg are vital for researchers and engineers who develop technologies for incubating, processing, storing and sorting eggs. There is a need for a simple identification process using egg volume, surface area, radius of curvature and other indicators for describing the contours of the egg, which this formula provides;
  3. Future biology-inspired engineering. The egg is a natural biological system studied to design engineering systems and state-of-the-art technologies. The egg-shaped geometric figure is adopted in architecture, such as London City Hall’s roof and the Gherkin, and construction as it can withstand maximum loads with a minimum consumption of materials, to which this formula can now be easily applied.

The "Gherkin" is the nickname of a visually distinctive building at 30 St. Mary Axe in London. The next time any architects want to make a building that looks like an egg, they'll finally have the math to make it happen!


Valeriy G. Narushin et al, Egg and math: introducing a universal formula for egg shape, Annals of the New York Academy of Sciences (2021). DOI: 10.1111/nyas.14680. Ungated Preprint: BioRxiv (PDF Document).

Image Credit: Photo by Jasmin Egger on Unsplash, to which we added the dimensional annotations.

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09 September 2021

Arizona's third COVID wave has peaked and begun to recede.

Since our last update three weeks ago, the number of cases and new hospital admissions in the state has reached their peaks and begun to fall. Meanwhile, the state's data for deaths is still too incomplete over the last few weeks to confirm the pattern seen for cases and hospitalizations, but can be expected to follow.

In the following chart, we've aligned the rolling seven-day averages for the number of COVID cases, new hospital admissions, and deaths to the approximate date of exposure for the Arizonans affected by the spread of the various strains of the SARS-CoV-2 coronavirus. The chart is presented in linear scale, where you can see the third wave of infections begin to accelerate at the end of June 2021, which coincides with the mass exposure event of the Phoenix Suns advancing to the finals in the NBA playoffs. [Note the vertical scale of the chart is presented in logarithmic scale.]

Arizona's Experience During the Coronavirus Pandemic, 15 March 2020 - 6 September 2021, Logarithmic Scale

The data indicates the incidence of initial exposure to the active variants of SARS-CoV-2 coronavirus in Arizona's third COVID wave peaked in the period between 11 August 2021 and 15 August 2021.

The data also confirms that COVID-19 has become less risky for Arizonans, with the number of new hospital admissions and deaths falling below the trendlines (shown as the dashed yellow lines for the third wave) that would be expected from the number of cases based on the patterns observed during the state's experience of its first two coronavirus waves in 2020. That change corresponds to the state's high rate of vaccination for its most vulnerable elderly population, where COVID tends to be less serious for those in younger demographic groups, whose rate of vaccination has been lower.

There is a point of concern in that the state's ICU Bed Usage for COVID patients is still in a rising trend. We've put togther the following animation to cycle through charts illustrating Arizona's data for COVID cases, new hospital admissions, deaths, and ICU Bed Usage, showing each frame for five seconds. The vertical scale on each of these charts is presented in linear scale.

Animation: Arizona's Experience During the Coronavirus Pandemic, COVID Cases, New Hospital Admissions, Deaths, and ICU Bed Usage, 15 March 2020 - 6 September 2021, Linear Scale

The data confirms Arizona's third COVID wave peaked and began to recede at levels far lower than occurred during the state's first two waves.

Arizona is interesting because other than news reports communicating the rising number of hospitalizations and ICU bed usage at the time the incidence of cases and hospital admissions peaked, we have not been able to identify any state-level interventions that might explain the timing of its third peak.

Previously on Political Calculations

Here is our previous coverage of Arizona's experience with the coronavirus pandemic, presented in reverse chronological order.


We've continued following Arizona's experience during the coronavirus pandemic because the state's Department of Health Services makes detailed, high quality time series data available, which makes it easy to apply the back calculation method to identify the timing and events that caused changes in the state's COVID-19 trends. This section links that that resource and many of the others we've found useful throughout the coronavirus pandemic.

Arizona Department of Health Services. COVID-19 Data Dashboard: Vaccine Administration. [Online Database]. Accessed 7 September 2021.

Stephen A. Lauer, Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng, Hannah R. Meredith, Andrew S. Azman, Nicholas G. Reich, Justin Lessler. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Annals of Internal Medicine, 5 May 2020. https://doi.org/10.7326/M20-0504.

U.S. Centers for Disease Control and Prevention. COVID-19 Pandemic Planning Scenarios. [PDF Document]. 10 September 2020.

More or Less: Behind the Stats. Ethnic minority deaths, climate change and lockdown. Interview with Kit Yates discussing back calculation. BBC Radio 4. [Podcast: 8:18 to 14:07]. 29 April 2020.

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08 September 2021

The growth of trade between the U.S. and China flashed warning signs in July 2021. While U.S. exports to China showed year-over-year growth, the growth rate in the value of goods imported to the U.S. from China turned slightly negative for the first time since August 2020, suggesting the onset of stalled growth conditions for the U.S. economy.

Year Over year Growth Rate of Exchange Rate Adjusted U.S.-China Trade in Goods and Services, January 1986 - July 2021

The change reversed the positive trend of growth that began in August 2020 with the post-Coronavirus Recession trade recovery between the two countries. That change shows up in the following chart showing the combined value of U.S. exports to China and imports from China.

Year Over year Growth Rate of Exchange Rate Adjusted U.S.-China Trade in Goods and Services, January 1986 - July 2021

Here, we see the gap between trailing twelve month average of trade between the two countries and the 'No Coronavirus Pandemic' counterfactual grow for the first time since August 2020. The gap between the trailing year average of trade between the two nations and a 'No Coronavirus Pandemic' counterfactual increased to $7.5 billion in June 2021. We estimate the cumulative loss of trade between the two countries has reached $139.1 billion.


Board of Governors of the Federal Reserve System. China / U.S. Foreign Exchange Rate. G.5 Foreign Exchange Rates. Accessed 2 September 2021.

U.S. Census Bureau. Trade in Goods with China. Accessed 2 September 2021.


07 September 2021

The S&P 500 (Index: SPX) is following its expected trajectory following the Federal Reserve's annual Jackson Hole event. Investors remain focused on the upcoming future quarter of 2021-Q4, which for as long as that holds, suggests a relatively flat, range-bound trajectory for the index.

At least, that's what we're already seeing in the alternative futures spaghetti forecast chart, where we've added a redzone forecast range to project the likely trajectory of the S&P 500 based on that assumption.

Alternative Futures - S&P 500 - 2021Q3 - Standard Model (m=-2.5 from 16 June 2021) - Snapshot on 3 Sep 2021

We've had to add the latest redzone forecast because of the dividend futures-based model's use of historic stock prices as the base reference points from which its future projections are made. Here, the past volatility of stock prices can skew the model's projections of the future, which we've found we can generally compensate for by bridging across the period we know will be impacted by the echoes of the index' historic volatility.

For the latest redzone forecast, we're bridging a period that continues into early December, making it the longest we've attempted since early early 2019.

Looking backward at the past week, we find little to motivate investors to shift their forward-looking focus to other points of time in the future as the market headed into the long Labor Day holiday weekend.

Monday, 30 August 2021
Tuesday, 31 August 2021
Wednesday, 1 September 2021
Thursday, 2 September 2021
Friday, 3 September 2021

Did you know the CME Group trades annual dividends futures contracts for the S&P 500? And that they cover 10 years out into the future? We normally follow the CME Group's quarterly dividend futures for the index, because the five future quarters it covers corresponds to the typical investment horizon for investors and directly influences current day stock prices. For us, the annual dividend futures data is useful for filling in gaps in future quarterly data, but you might find the data useful in other ways.

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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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