Imagine this scenario. You are offered the opportunity to take a one-time lump sum payout or an annual payment for the rest of your life. Which option should you choose?

That's a scenario that may play out several times during your life. Sometimes it will be an employer who offers that deal with the company's retirement plan. If you're lucky, it may be a state lottery commission.

If you're like 70% of Americans who were offered that choice for their employer's pension plan in recent years, you will likely choose the lump sum cash offer. But is that the best choice? How can you find out?

If you want to boil it down to a single number without taking other considerations into account, you could base your decision on a figure called the pension income ratio. Simply take the amount of the annual payout you have been offered and divide it by the amount of the lump sum payout you've been offered as an alternative.

Let's do that math with an example in the following tool. If you're reading this article on a site that republishes our RSS news feed, you may need to click through to our site to access a working version of it.

Now, think about what kind of annual rate of return you could reliably get from investing the lump sum payout. If your result from the tool above is higher than that rate, you might be better off choosing the annual income payout over the lump sum.

Most financial planners will use a rate of return of 6.0% as the rule-of-thumb threshold for choosing which option is better, but a more conservative approach would be to use a lower figure.

For the default numbers in the tool, the result of 6.7% is higher than the 6.0% threshold, which would suggest the better option is to go with the annual income payments. Most financial planners would agree that rate of return would be difficult to average over a long period of time.

But what if the offer for the annual income payments was lower? What if it was $35,000 instead?

That figure would drop the pension income ratio down to 4.7%, where taking the lump sum would become more attractive.

There are other factors that can affect the decision of which choice is better (such as your age, health, etc.) but the idea here is to use the pension income ratio as a starting point for those additional considerations.

For more discussion, check out Michael Aloi's recent article on how a math formula drives one retiree’s choice and Wes Moss' article on the question of whether you should take a lump sum payout or a pension. And of course, our own 2015 article on whether you should take a pension buyout, which was a very topical question that year!

Image credit: Photo by Pepi Stojanovski on Unsplash

We called the failure of Neil Ferguson's Imperial College London (ICL) epidemiological model to reasonably project the severity of the coronavirus pandemic The Biggest Math Story of 2020. Now, armed with a year of actual outcomes to compare with its projections, analysts are able to quantify just how badly off the mark it was.

One year later we may now look back to see how Imperial College’s international projections performed, paying closer attention to the small number of countries that bucked his lockdown recommendations. The results are not pretty for Ferguson, and point to a clear pattern of modeling that systematically exaggerated the projected death tolls of Covid-19 in the absence of lockdowns and related NPIs.

The acronym NPI refers to Non-Pharmaceutical Intervention, which refers to things like the lockdown measures many governments enacted, including ordering businesses to close and residents to stay-at-home for sustained periods of time. It also covers practices such as wearing face masks or practicing social distancing for the purposes of trying to limit the spread of SARS-CoV-2 coronavirus infections.

Ferguson's ICL model was used to make several kinds of projections representing different scenarios at the pandemic's one-year mark.

These projections reflect an assumed replication rate (R0) of 2.4 – the most conservative scenario they considered, meaning Imperial’s upper range of projections anticipated substantially higher death tolls. The countries examined here – Sweden, Taiwan, Japan, and South Korea – are distinctive for either eschewing lockdowns and similar aggressive NPI restrictions entirely or for relying on them in a much more limited scope than Imperial College advised. The United States, where 43 of 50 states adopted lockdowns of some form, is also included for comparison.

At the time the ICL model's projections were generated, the assumed replication rate (R0) for estimating how aggressively the coronavirus might spread had been estimated to fall within a range between 2.2 and 2.7, although a CDC estimate was much higher than that.

Still, using the same assumption for all these countries provides an apple-to-apples means of comparing the projections of COVID-19 deaths for each. We've visualized that tabulated data in the following chart.

In this second chart, we've recalculated the projected and actual recorded COVID-19 deaths as a percentage of each country's estimated July 2020 population. This modification lets us account for the large differences between each country's population with the others.

The visualized results confirm Neil Ferguson's ICL epidemiological model deviated anywhere from multiples to multiple orders of magnitude from reality. That matters because the ICL model was used to justify restrictive measures that harmed many people's livelihoods and well-being. It will take years to recover from the resulting disruption.

Just over one year ago, the epidemiology modeling of Neil Ferguson and Imperial College played a preeminent role in shutting down most of the world. The exaggerated forecasts of this modeling team are now impossible to downplay or deny, and extend to almost every country on earth. Indeed, they may well constitute one of the greatest scientific failures in modern human history.

That potential is what earned the failure of Neil Ferguson's ICL pandemic model the title of The Biggest Math Story of 2020.

References

Magness, Phillip W. The Failure of Imperial College Modeling Is Far Worse than We Knew. American Institute for Economic Research. [Online Article]. 22 April 2021.

U.S. Central Intelligence Agency. Population Estimates (July 2020). The World Factbook. [Online Data]. Accessed: 6 January 2021.

In August 2005, the market capitalization of the new home market peaked at $31.05 billion, going by the trailing twelve month average for this figure.

In January 2021, fueled by a surge in demand by Americans fleeing coronavirus pandemic lockdown restrictions and amplified by sustained breakdowns of public order in large cities in the U.S., the market cap of the new home market reached $30.32 billion, just 2.4% shy of the housing market's previous nominal peak.

Since January 2021 however, the trailing twelve month average market cap for new homes in the U.S. has fallen somewhat, dropping to $29.91 billion in the initial estimate for March 2021, as the supply of new homes sold has increased while the average price of new homes sold in the U.S. has dipped from a six-year high in January 2021.

Adjusted for inflation, the market cap for new homes now would have to be over a third higher to come close the August 2005 peak in terms of constant March 2021 U.S. dollars.

References

U.S. Census Bureau. New Residential Sales Historical Data. Houses Sold. [Excel Spreadsheet]. Accessed 24 April 2021. 

U.S. Census Bureau. New Residential Sales Historical Data. Median and Average Sale Price of Houses Sold. [Excel Spreadsheet]. Accessed 24 April 2021. 

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 Application]. Accessed 13 April 2021. 

Three of the four high quality COVID-19 datasets we track for Arizona indicate a new adverse change in trends for the coronavirus pandemic in the state. Arizona's data for positive test results by date of sample collection, new hospital admissions, and ICU bed usage are confirming an increase in the incidence of COVID in the state. The fourth dataset for COVID-19 deaths by recorded date of death certificate does not as yet, but would not be expected to as yet because this data has the greatest lag from a change in the rate of incidence to the confirmation of a change in trend.

We've generated the following animated chart to cycle through each of the charts for these four datasets.

Considering the respective lags that apply for each dataset, the likely timing of a significant change in the rate of incidence for SARS-CoV-2 coronavirus infections in the state between 26 March 2021 and 30 March 2021. This period coincides with contemporary news accounts of the Biden administration moving migrants from overloaded Border Patrol migrant facilities in Arizona counties bordering Mexico to facilities and small towns in Maricopa and Pinal Counties.

We think this activity is showing up in Arizona's COVID-19 statistics because these migrants have been exposed to Mexico's higher incidence of COVID-19 infections. While those cases peaked in late January 2021, several weeks after they peaked and began falling in Arizona, the relative difference in infection rates between Arizona's population and the entering migrants is enough to affect the trends for Arizona's COVID-19 data.

On 26 March 2021, Senator Mark Kelly (D-AZ) stated the Biden administration did not have an effective plan for the border. It took another month for President Biden to acknowledge the migration crisis at the U.S. border with Mexico as a crisis.

President Biden, talking to reporters after finishing golf today, concedes border issues are a “crisis,” saying refugee cap was linked to the “crisis that ended up on the border with young people.”

“We couldn’t do two things at once. And now we are going to increase the number.” pic.twitter.com/dwvrRM792k

— TV News HQ (@TVNewsHQ) April 18, 2021

On 21 April 2021, Arizona Governor Doug Ducey declared a state of emergency and sent Arizona National Guard troops to Arizona's border counties.

Coincidentally, that was the last date we updated our series on the COVID-19 pandemic in Arizona, where our analysis of the trends just before that point of time appeared very early in the morning....

Previously on Political Calculations

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

• Improving COVID Trends Bottom and Flatline in Arizona
• Surge of Migrants, Lifting of Business Capacity Limits Change Arizona COVID Trends
• COVID-19 in Retreat in Arizona With Vaccines Gaining Traction
• The Ebb and Flow of COVID-19 in Arizona's ICUs
• Arizona's Plunging COVID-19 Caseloads and the Vaccines
• Arizona Enters Downward Trend for COVID-19 After Second Peak
• Arizona Passes Second COVID-19 Peak
• A Tale of Two States and the Coronavirus
• COVID-19 Questions, Answers, and Lessons Learned from Arizona
• The Deadly Intersection of Anti-Police Protests and COVID-19
• 2020 Campaign Events Drive Surge in Arizona COVID Cases
• Arizona Arrives at Critical Junction for Coronavirus Cases
• Arizona To Soon Reach A Critical Junction For COVID-19
• Getting More Than Care from Arizona's COVID ICU Beds
• Arizona's Decentralized Approach to Beating COVID
• Going Back to School with COVID-19
• Arizona Turns Second Corner Toward Crushing Coronavirus
• Arizona's Coronavirus Crest in Rear View Mirror
• The Coronavirus Turns a Corner in Arizona
• A Delayed First Wave Crests in the U.S. and a Second COVID-19 Wave Arrives
• The Coronavirus in Arizona
• A Closer Look at COVID-19 Deaths in Arizona
• The New Epicenter of COVID-19 in the U.S.
• How Long Does a Serious COVID Infection Typically Last?
• How Deadly is the COVID-19 Coronavirus?
• Governor Cuomo and the Coronavirus Models
• How Do False Test Outcomes Affect Estimates of the True Incidence of Coronavirus Infections?
• How Fast Could China's Coronavirus Spread?

References

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 25 April 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]. Updated 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.

In addition to rising prices, S&P 500 (Index: SPX) gained a new concern in the trading week ending on Friday, 23 April 2021 in the form of much higher capital gains tax rates.

Those prospects caused stock prices to fall sharply as the first details of the proposal were announced on Thursday, 22 April 2020. See if you can tell within 2-4 minutes of when the story broke and investors began absorbing that new information in a chart showing the index' trading value for the day:

If not for that news, the S&P 500 would almost certainly have closed the week at a new record high. As it was, the S&P 500 is trading within the lower end of the redzone forecast range on the alternative futures chart:

That's expected given the assumptions behind the redzone forecast range, which has just another couple of weeks to run.

Here's our summary of the market moving headlines for the week that was:

Monday, 19 April 2021

• Signs and portents for the U.S. economy:
• Exclusive: Fearing foreclosure crisis, U.S. watchdog cracks down on mortgage servicers
• Our factories are hungry' - U.S. farm machinery maker faces dearth of components
• Inflation fighting in emerging economies:
• The cycle turns: Emerging central banks hike rates in March
• ECB minions shocked to discover gambling going on in casino:
• ECB finds top euro zone banks underreport risk
• Wall Street slips off record highs, Tesla drops after fatal crash

Tuesday, 20 April 2021

• Fed minions starting to get nervous about rising inflation:
• Exclusive: Fed will limit any overshoot of inflation target, Powell says
• Positive recovery signs in Eurozone:
• Europe Inc eyes record first quarter earnings jump as economy recovers
• Wall Street closes lower as virus spike hits travel stocks

Wednesday, 21 April 2021

• Signs and portents for the U.S. economy:
• COVID-19 concerns keep oil in check; stocks rebound
• Analysis: The housing boom, central banks and the inflation conundrum
• Bigger inflation developing all over:
• Canada annual inflation rate in March accelerates to 2.2%
• Wall Street rebounds after two-day decline; Netflix slides
• Wall St. fears Netflix fatigue as subscriber growth slumps

Thursday, 22 April 2021

• Signs and portents for the U.S. economy:
• Vaccines put U.S. airlines on runway to recovery
• U.S. weekly jobless claims hit 13-month low; home sales tumble
• Republicans unveil $568 billion infrastructure package to counter Biden
• Factbox - Republicans vs. Biden: What's in their infrastructure plans?
• Biden to propose almost doubling capital gains tax rate for wealthy individuals - Bloomberg
• Bigger inflation developing all over:
• The housing boom, central banks and the inflation conundrum
• Positive recovery signs in UK:
• UK factories expect strongest rebound since 1973 after COVID-19
• British shoppers rush back to reopened clothes stores
• ECB minions do nothing different; BOJ minions find themselves trapped in a puzzle box:
• ECB keeps policy unchanged, sees scope for rebound
• Analysis-BOJ faces communication dilemma as weak inflation leaves Kuroda with complex policy
• Wall St falls on capital tax increase angst; dollar rises

Friday, 23 April 2021

• Daily signs and portents for the U.S. economy:
• Soaring lumber prices reverberate through U.S. housing market
• U.S. new home sales rebound exceeds expectations in March
• U.S. manufacturing, new homes sales underscore booming economy
• Bigger trouble developing in Japan from new COVID curbs:
• Japan factory output seen down again, retail sales up amid fragile recovery
• Mixed economic signals in Eurozone:
• German private sector in two-speed recovery due to coronavirus curbs - PMI
• Euro zone economic recovery accelerates in April as services bounce back -PMI
• ECB minions standing by as bigger inflation develops in Eurozone:
• From chips to drivers, euro zone firms warn supply is tight: ECB
• ECB survey sees slower growth, faster inflation this year
• Wall Street rallies on strong economic data; tech in focus

What were the positives and negatives in the past week's markets and economics news? Click through to find Barry Ritholtz' take, where the positives outweighed the negatives!

Some of the best magic tricks are the ones that seem impossible, but involve the application of mathematical principles, they can reliably deliver a seemingly impossible outcome.

The following video from Mathologer involves much longer exploration of seven examples involving the pigeonhole principle in action, but we've cued it up to feature a card trick where the key to getting the magic to work involves understanding how the randomly selected cards can be ordered to encode a secret message from the magician's assistant to the magician about what card an audience member has selected:

The trick works in part because of the pigeonhole principle, which will seem blindingly obvious once it's pointed out. This second video does that in a little over 30 seconds, but continues for about another eight minutes to present examples of how it can be practically applied:

And that's how you get from a parlor magic trick to the kind of modern lossless data compression we use every day to more efficiently communicate large amounts of data across computer networks!

For most Americans, the coronavirus pandemic has had two dimensions. The first dimension involves the excess deaths per capita recorded during the pandemic. The second dimension involves the direct economic impact from how people and governments responded to the pandemic, which for many, meant job losses.

The analysts of Hamilton Place Strategies came up with a way to visualize both dimensions for all 50 states in a single chart. Here it is!

The chart indicates each state's COVID deaths per capita on the vertical scale, and each state's job loss per capita on the horizontal scale. By showing the national averages for both dimensions, it divides the 50 states into four quadrants.

The lower left hand quadrant is the best one in which to find your state. The states in this sector experienced both low rates of COVID deaths and low levels of job lossses during the pandemic. The best performing states are those that are furthest away from the intersection of the national averages for COVID deaths per capita and job loss per capita, where Idaho, Utah, and West Virginia having the best outcomes (Idaho and Utah with respect to job losses, West Virginia with respect to COVID deaths).

By contrast, the states in the upper right hand quadrant experienced the worst outcomes. Here, the combination of high COVID death tolls and high job losses indicates poor performance. Once again, the states furthest away from the intersection of the national average COVID death toll and job losses are the ones who ranked the worst.

Here, we find four states performing worst than almost all others. Louisiana, New Jersey, Nevada, and New York were the worst performing states in the U.S., with New York having by far the worst outcome of all states for both measures.

States falling in the other two quadrants had mixed outcomes, with high rates of COVID deaths per capita combined with lower than average job losses per capita, or vice versa.

With respect to COVID deaths per capita, Mississippi had the worst outcome in upper left quadrant. For the measure of job loss per capita, Hawaii had the worst performance in the lower right quadrant.

All in all, it's a neat bit of analysis. We wish we had thought to frame the data this way!

Not much has changed over the last two weeks with respect to COVID trends in Arizona. Which is very good news.

That's because of what didn't happen after Arizona's economy fully reopened, which we mark from the lifting of capacity limits on businesses such as bars, restaurants, gyms, and others that would be considered prime territory for spreading coronavirus infections. What didn't happen is significant, because instead of developing a rising trend for COVID-19 cases, hospitalizations, ICU bed usage, and deaths as it did after its first reopening attempt following its first wave of COVID-19, Arizona has instead experienced steady, relatively flat levels for all these measures. What had looked like the potential stalling of a previous trend of improvement is really demonstrating the benefits of the widespread deployment of Operation Warp Speed's vaccines in Arizona. The protections offered by the vaccines are enabling the gains of improvement to be sustained. Even as the kind of activities that would have previously resulted in the reversal of a positive trend for coronavirus infections have expanded.

That's evident in the latest updates to the four charts tracking the trends for each of these measures based on Arizona's high quality data for the numbers of new cases by test sample collection date, hospitalizations by date of admission, deaths by date as recorded on death certificates, and ICU bed usage.

Since our last update, the trend for cases has continued moving sideways, with the trends for both hospitalizations and ICU bed usage now following suit. It will take a little more time to see if the dataset for deaths attributed to COVID-19 will follow the same pattern, but the early indicators are that it will.

The next time we look at Arizona's high quality COVID-19 data, we'll be looking to confirm the answer to a very different question.

Previously on Political Calculations

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

• Improving COVID Trends Bottom and Flatline in Arizona
• Surge of Migrants, Lifting of Business Capacity Limits Change Arizona COVID Trends
• COVID-19 in Retreat in Arizona With Vaccines Gaining Traction
• The Ebb and Flow of COVID-19 in Arizona's ICUs
• Arizona's Plunging COVID-19 Caseloads and the Vaccines
• Arizona Enters Downward Trend for COVID-19 After Second Peak
• Arizona Passes Second COVID-19 Peak
• A Tale of Two States and the Coronavirus
• COVID-19 Questions, Answers, and Lessons Learned from Arizona
• The Deadly Intersection of Anti-Police Protests and COVID-19
• 2020 Campaign Events Drive Surge in Arizona COVID Cases
• Arizona Arrives at Critical Junction for Coronavirus Cases
• Arizona To Soon Reach A Critical Junction For COVID-19
• Getting More Than Care from Arizona's COVID ICU Beds
• Arizona's Decentralized Approach to Beating COVID
• Going Back to School with COVID-19
• Arizona Turns Second Corner Toward Crushing Coronavirus
• Arizona's Coronavirus Crest in Rear View Mirror
• The Coronavirus Turns a Corner in Arizona
• A Delayed First Wave Crests in the U.S. and a Second COVID-19 Wave Arrives
• The Coronavirus in Arizona
• A Closer Look at COVID-19 Deaths in Arizona
• The New Epicenter of COVID-19 in the U.S.
• How Long Does a Serious COVID Infection Typically Last?
• How Deadly is the COVID-19 Coronavirus?
• Governor Cuomo and the Coronavirus Models
• How Do False Test Outcomes Affect Estimates of the True Incidence of Coronavirus Infections?
• How Fast Could China's Coronavirus Spread?

References

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 20 April 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]. Updated 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.

The Wall Street Journal recently reported on the apparent effectiveness of the Operation Warp Speed COVID-19 vaccines:

The U.S. Centers for Disease Control and Prevention has identified a small cohort of approximately 5,800 cases of Covid-19 infection among more than 66 million Americans who have completed a full course of vaccination.

These so-called breakthrough cases, which are defined as positive Covid-19 test results received at least two weeks after patients receive their final vaccine dose, represent 0.008% of the fully vaccinated population.

Officials said such cases are in line with expectations because the approved vaccines in the U.S. are highly effective but not 100% foolproof.

For judging the effectiveness of a vaccine, that's the wrong measure. What we really want to do is compare how well the vaccines protect the portion of the public who have been fully vaccinated with the portion of the population that has either not been vaccinated or has only been partially vaccinated against COVID-19.

So we ran some rough numbers to find out. The following chart reveals a back-of-the-envelope estimate of how well the COVID-19 vaccines are so far working in the U.S.

At first glance, the Operation Warp Speed vaccines would appear highly effective.

Running Through the Rough Numbers

The first COVID-19 vaccincations of the U.S. public began on 14 December 2020.

On 15 December 2020, the U.S. Census Bureau estimated the size of the U.S. population on 1 April 2020 to be 332,601,000. The Census Bureau based this estimate on demographic analysis, independently of the actual 2020 U.S. Census results, where they estimated the actual population of the U.S. would fall in between a low estimate of 330,730,000 and a high estimate of 335,514,000.

As of 8 April 2021, 66,203,123 Americans (about 19.9% of the population) had been fully vaccinated for COVID-19. Using these figures, that would mean roughly 266,398,000 Americans would be considered either unvaccinated or partially vaccinated on that date [1].

From 15 December 2020 through 8 April 2020, the CDC reported a total of 14,232,649 new COVID-19 cases in the U.S. [2]. If 5,800 is the number of "breakthrough" cases among the 66,203,123 fully vaccinated Americans, subtracting 5,800 from 14,238,649 let's us arrive at the estimated number of cases among the "less-than-fully-vaccinated" population of 14,232,849.

That's how you get the numbers we used to calculate the percentages in the chart. 5,800 breakthrough cases among 66,203,000 fully vaccinated Americans works out to be a percentage of 0.0088%.

Meanwhile, the 14,232,849 newly reported cases among the 266,398,000 unvaccinated or less-than-fully vaccinated portion of the U.S. population during the period of time vaccinations have been available for the U.S. public represents 5.3% of that portion of the population.

Based on this rough reckoning, it would appear the vaccines are working very well in limiting the spread of new infections from the strains of SARS-CoV-2 coronavirus active within the United States [3].

Notes

[1] None of this back-of-the-envelope analysis considers the number of Americans who already had and recovered from COVID-19, who have gained at least partial if not full immunity to the infection for at least some period of time as a result. As of 8 April 2021, that potential additional total is 30,181,371 (30,737,477 cases minus 556,106 deaths). We're also not considering the 46,843,488 Americans the CDC reports have received at least one dose of the COVID-19 vaccines as of 8 April 2021 either, who it would consider partially vaccinated.

We opted to not consider these additional categories because the CDC has not indicated how many of the fully or partially vaccinated portions of the population in the U.S. has previously tested positive for SARS-CoV-2 coronavirus infections. By grouping them in the unvaccinated or partially-vaccinated category however, our rough estimates understate the relative benefits of vaccination. Even so, the apparent relative benefit is massive.

[2] This figure almost certainly includes the results of positive COVID-19 test results whose samples were collected days and weeks before the Operation Warp Speed vaccines began to be introduced to the U.S. public. The CDC does not report test results by sample collection date, which would provide higher quality information.

[3] We're also not considering political factors that have affected how the U.S. vaccination program has been rolled out by various state governments.

There's not much new in the S&P 500 (Index: SPX) this week, so it looks like the index kept drifting upward to new highs on its momentum.

Here's how that looks on the latest update to the alternative futures chart:

We're also reaching the point where we can test one of the assumptions behind the redzone forecast shown on the chart. When we first locked it in several weeks ago, we assumed investors would begin shifting their forward-looking focus from 2021-Q2 out to the more distant future of 2021-Q4 during April 2021.

That assumption is looking really iffy right now. Instead of starting to shift their forward time horizon to the more distant future as we has assumed would happen this month, investors would appear to have strongly locked into their focus on 2021-Q2.

Given the small differences in the expectations for the growth rate of dividends in 2021-Q2 and 2020-Q4, we see that the redzone forecast range has so far captured most of the trajectory for the S&P 500. But that trajectory has also progressively run to the low side of the projected range. The actual trajectory is much more consistent with what would be expected if investors were maintaining a strong focus on 2021-Q2, so the question becomes why?

We think the ongoing strong focus on 2021-Q2 may be related to the surge of inflation now hitting the U.S. economy, which is raising questions of how long it will be before the Fed has to react to it. That concern is pulling investors forward-looking attention in toward the near term.

The growing concern of rising inflation and the Fed's likely response to it is reflected in the week's market-moving news headlines, where the first step in that response looks like it will involve tapering the Fed's purchases of U.S. government-issued bonds.

Monday, 12 April 2021

• Signs and portents for the U.S. economy:
• U.S. budget deficit hits record high for March as aid swells outlays
• Oil rises on U.S. vaccine rollout, Middle East tension
• Fed minions
• Fed's Powell: U.S. economy at an 'inflection point' - CBS '60 Minutes'
• Analysis - A tale of two tapers: This time is different for a Fed focused on jobs
• Fed's Rosengren says U.S. economy should see significant rebound this year
• Bigger inflation developing in Japan, COVID lockdown restrictions in India:
• Japan wholesale prices rise for first time in more than a year, stoked by commodities surge
• Businesses in India's richest state choke under new COVID-19 curbs
• Positive recovery signs seen in China exports to world, UK shops reopen:
• China's exports, imports seen staying buoyant in March: Reuters poll
• Shopper numbers jump 218% as England reopens economy
• Wall Street ends lower as investors await earnings, inflation data

Tuesday, 13 April 2021

• Signs and portents for the U.S. economy:
• U.S. consumer prices post biggest gain in 8-1/2 years as economy reopens
• Oil rises after robust China data but J&J vaccine pause weighs
• China's robust exports, surging imports boost economic recovery; outlook challenging
• Fed minion says inflation is under control, Fed to sit on hands:
• Fed's Harker says he does not anticipate inflation running out of control
• Fed's Harker says central bank will 'hold steady' for now
• BOJ minion big on weak yen:
• BOJ's Kuroda says weak yen promises to benefit Japan's economy
• Tech stocks push S&P 500 to record close, buoy Nasdaq

Wednesday, 14 April 2021

• Daily signs and portents for the U.S. economy:
• U.S. import prices increase solidly, seen temporarily boosting inflation
• Fed minions seem a lot more worried about inflation than they previously claimed to be, expect strong growth but slower jobs recovery:
• Powell: QE taper likely 'well before' interest rate increase
• New York Fed's Williams: Fed has tools to deal with high inflation
• Clarida: If inflation expectations 'drift up persistently,' Fed would need to respond
• U.S. economy gaining momentum as consumers ditch the winter blues, Fed says - amazing what lifting lockdowns can do for growth!
• Fed's Kaplan: will be 'a while' until U.S. reaches full employment
• Bigger stimulus developing in Eurozone, Canada:
• European Union unveils recovery fund financing plan
• EU to borrow around 150 billion euros annually for recovery fund
• ECB will act on unwarranted rise in borrowing costs, its VP says
• Canada to go big on budget spending as pandemic lingers, election looms
• Wall Street ends mixed despite bumper bank earnings

Thursday, 15 April 2021

• Daily signs and portents for the U.S. economy:
• U.S. business inventories rise solidly in February
• U.S. retail sales post largest gain in 10 months; weekly jobless claims fall
• Fed minions say not time yet to start pulling back on U.S. money printing, want to stop being so racist:
• Fed's Daly says not time for taper, still far from goals
• Fed's Daly: need to see 'repeated months' of good data
• Fed's Mester not too concerned about inflation getting too high
• Fed's Mester says U.S. economy could grow by 6% or more in 2021
• Economy far from central bank's goals but outlook brightening, Fed's Mester says
• Bostic: U.S. should study ways to offset wealth impact of systemic racism
• Bigger trouble where COVID still reigns:
• Peru economy contracts 4.18% in February amid COVID-19 second wave
• German economy probably shrank 1.8% in first quarter due to lockdown, institutes say
• Slow vaccine rollouts biggest risk to euro zone economy
• BOJ's Kuroda warns of lingering pandemic pain for economy
• S&P 500, Dow hit record highs on upbeat earnings, strong retail sales

Friday, 16 April 2021

• Daily signs and portents for the U.S. economy:
• Pandemic destroyed fewer U.S. businesses than feared, Fed study shows
• U.S. housing starts near 15-year high; consumer sentiment rises moderately
• Oil nudges lower but set for weekly gain on demand recovery hopes
• Fed minions more worried about inflation than they've been letting on:
• Fed's Waller says U.S. economy 'ready to rip' but inflation will level off
• Fed's Kaplan wants to reduce easing at 'earliest opportunity'
• Explainer: U.S. repo market flirts with negative rates as Fed seeks to absorb excess cash
• Positive growth signs in China, also signs of slowing:
• China's GDP jumps record 18.3% but post-COVID recovery seen losing steam
• Factbox: Has China's $16 trillion economy fully recovered?
• Wall Street ends week positively; S&P 500, Dow hit record highs
• Graphic: U.S. bond, equity funds lure money inflows as bond yields drop

Meanwhile, the debonair Barry Ritholtz listed seven positives and five negatives he found in the past week's markets and economics news.

On a final note, while investors may now be focusing on 2021-Q2, they can only do so until the quarter runs out. No matter what, investors will have to shift their forward-looking focus to some other point of time in the future and that will have to happen sometime before the third Friday of June 2021 when the dividend futures contracts for 2021-Q2 expire. Since the differences in the changes expected for the year over year growth rate of the index' dividends per share are relatively small, it's unlikely we'll see a large scale Lévy flight event when that happens.

Unless, of course, something else changes to affect the expectations for the future or the Fed's willingness to stay on its current policy path.

How much data flows through the series of tubes that make up the Internet?

Bernard Marr gives an answer that applied for 2019 in the following under two minute video:

Now, bonus question! How much does all the data that can flow through the Internet's tubes weigh?

That's a harder question to answer, but it didn't stop TopTrending from running the numbers in the following six and half minute video:

The thing to keep in mind in these numbers is that the Internet is about moving information, not storing it. 6.75 ounces is the physical weight of all the electrons that represent the estimated physical capacity of the amount of data that can flow through the internet as we know it today in a year. It also doesn't consider how that data might be moved in the future to get around those physical constraints.

But for now, that figure is also a little over one dry ounce more than the estimated weight of all the particles of SARS-CoV-2 coronavirus in the world.

Ever since we put the S&P 500 at your fingertips, we've explored a lot of different ways to visualize that treasure trove of U.S. stock market data as represented by the S&P 500 (Index: SPX).

But until today, we've never presented the historic yields for the index. The following chart fills that gap in our visualizations of the S&P 500's data, showing the index' monthly trailing year earnings yield and its trailing year dividend yield from January 1871 through March 2021:

As a general rule, dividends have represented anywhere from half to two-thirds of the earnings of S&P 500 companies.

Both the S&P 500's earnings and dividend yields have fallen over time, with the most significant downward shift occurring in the 1990s. This shift coincides with the arrival of the Dot Com Bubble and the modern era of the Federal Reserve's monetary policies, which have set U.S. interest rates on a long term falling trend.

Those long term trends are punctuated by periodic spikes in the data. Spikes in either data series tend to indicate crashing stock prices rather than surging earnings or dividends.

If you would like to sample the raw data behind these values, our S&P 500 At Your Fingertips tool can provide you with the values of the S&P 500 or its predecessor indices, their trailing year earnings per share, and their trailing year dividends per share for any month from January 1871 through the last month.

The global economy appears to have begun recovering after entering into a double dip recession in December 2020, which looks to have bottomed in February 2020.

That assessment is based on the latest data on the changing concentration of carbon dioxide in the Earth's atmosphere recorded at the remote Mauna Loa Observatory. The trailing twelve month average of the year-over-year change in atmospheric CO₂ levels has begun to rise again, indicating a return to net economic growth for the Earth's economy beginning in March 2021.

We have to emphasize "net" economic growth since the change is not uniform across the globe. Many nations, particularly in the Eurozone, continue to experience recessionary conditions from government-imposed lockdowns as they see rising rates of infections combine with the fiasco of their failure to acquire adequate supplies of COVID vaccines.

As long as that situation continues, the global recovery will be much slower than the regional recoveries now underway.

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.

• Double Dip Global Coronavirus Recession Sees Second Bottom
• Net Global GDP Lost to Coronavirus Pandemic Tops $13.6 Trillion
• Global Double Dip Coronavirus Recession Deepens
• Global Economy Enters Double Dip Coronavirus Recession
• Global Economy Teeters on Double Dip Recession
• World GDP Lost Due to Coronavirus Reaches $12 Trillion
• Cumulative World GDP Loss From Coronavirus Pandemic Tops $11 Trillion
• Estimates of World GDP Lost to the Global Coronavirus Recession
• Finding Human Fingerprints in Atmospheric CO2
• The Coronavirus and Atmospheric CO2 in April 2020
• The Coronavirus, Atmospheric CO2, and GDP