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February 21, 2020

COVID-19 is the name the World Health Organization has given to the highly contagious and deadly new viral infection that has severely impacted China's economy as it threatens to become a pandemic.

The world recently ran an experiment on how potentially contagious the viral infection formerly known as Novel Coronavirus 2019 (or 2019-nCoV) on a cruise ship, which was quarantined in Japan from 3 February 2020 through 19 February 2020. During that period, some 3,711 passengers and crew on board the Diamond Princess were at an elevated risk of exposure to the new coronavirus, as the ship effectively became a 'super spreading' site. In those 16 days, the number of passengers and crew testing positive for the COVID-19 infection grew from 1 to 621. The following chart tracks the cumulative number of passengers testing positive for the COVID-19 infection on each day of the Diamond Princess' quarantine period.

Reported Cases of Diamond Princess Passengers and Crew Testing Positive for COVID-19 Virus Infection by Day

Cruise ships have earned notorious reputations for becoming incubators for contagious diseases given their design, where people are contained in close quarters that provide an environment that is conducive to the spread of diseases. In the case of the Diamond Princess, in addition to sharing these characteristics, the quarantine practices put into effect on the ship after the first passenger was confirmed to have been infected proved to be ineffective in slowing the spread of the COVID-19 viral infection. The measures taken have been described as "an improvisation", including the fiasco of having the wrong masks initially provided to passengers. After the correct face masks were finally provided, the passengers were not adequately trained to fit them properly, impairing their effectiveness.

All these problems combined are why a National Institute of Health official described the ship's attempted quarantine as "ineffective", as the Diamond Princess became the home of the largest cluster of coronavirus cases outside China in the epidemic's earliest phase.

The failed quarantine of the Diamond Princess then gives us an example of how fast the COVID-19 coronavirus might spread in a crowded city with little-to-no effective quarantine procedures in place to slow the spread of the viral infection. But can we really tell anything about how fast it might spread from just 16 days worth of data?

The answer to that question is yes, provided we have a growth model that can provide a good indication of how quickly the disease could spread through an entire susceptible population.

To that end, we can apply the mathematical growth models that have been developed to track the progression of diseases in plants. The following figure illustrates the various growth models that might be employed:

Figure 1. Examples of disease progress curves represented by monomolecular, exponential, logistic, and Gompertz models

The following slideshow gives more background into these models:

Based on what has been learned about the COVID-19 virus, it fits the profile of a polycyclic disease. An exponential model might be used to describe its early phases, but a logistic (or Richards) growth model or a Gompertz growth model will more closely match its full progression.

But which to use? A 2015 paper by Wendi Liu, Sanyi Tang, and Yanni Xiao gives the edge to the general logistic growth model, although a 2017 paper by C.R. Sebrango-Rodriguez, D.A. Martinez-Bello, L. Sanchez-Valdes, P.J. Thilakarathne, E. Del Fava, Patrick Van Der Stuyft (UGent), A. Lopez-Quilez and Z. Shkedy argues in favor of averaging the models' results together.

For our part, we built a tool to model the progression of the COVID-19 virus onboard the Diamond Princess using both the logistic and Gompertz growth models, where we've assumed that all those on the ship would be susceptible to becoming infected if they had remained on board. To use the tool, just select the growth model for which you would like to see the results and enter the number of days you would like to project results for. 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.

Growth Model and Number of Days
Input Data Values
Select Growth Model
Number of Days Since First Reported Case

Projected Spread of Infection
Estimated Results Values
Modeled Percentage of Population Infected

The tool's results are expressed in terms of the percentage of the population affected, which for the Diamond Princess, totals 3,711 individuals.

In playing with the tool with our basic assumptions, we find that virtually all of the passengers and crew would have been likely to have become infected with the COVID-19 coronavirus if they had remained on the ship for more than 60 days, regardless of which growth model we select. The following chart visualizes the growth models' projections, where we find the COVID-19 virus would have been likely to spread to 95% or more of the 3,711 passengers and crew quarantined on the Diamond Princess after 60 days.

Reported and Modeled Percentage of 3,711 Passengers and Crew Testing Positive for COVID-19 While In Quarantine Onboard the Diamond Princess Cruise Ship

In reality, it's more likely that not all passengers would have been susceptible to the COVID-19 virus, but that's the conservative assumption to make for any new virus until we learn more about it.

We should also note that the data for the cumulative number of infected passengers and crew may not be representative of the true rate of spread of COVID-19. Japan's national health laboratories only had the capacity to run 300 tests per day during most of the quarantine period, where the daily numbers reported may well have been understated.

Speaking of which, here are our sources for the cumulative daily numbers of infected passengers and crew on the Diamond Princess:

Reported Cases of Diamond Princess Passengers and Crew Testing Positive
for COVID-19 Virus Infection During Its Quarantine Period
Date Number Tested Positive Source of Figure
03 February 2020 1 Princess Cruise Ship Temporarily Delayed for Coronavirus Testing
04 February 2020 10 10 Test Positive for Coronavirus Aboard Carnival's Diamond Princess
05 February 2020 20 20 people test positive for coronavirus on board Carnival’s Diamond Princess cruise in Japan
06 February 2020 41 Coronavirus cases triple to 61 on cruise ship quarantined in Japan, with 41 more reported
07 February 2020 61 Oregon woman infected with coronavirus quarantined in Japan
08 February 2020 67 Diamond Princess cruise ship has 67 passengers who have tested positive for coronavirus onboard, Japan's Health Minister announced
09 February 2020 69 Inferred from 10 February 2020 report.
10 February 2020 135 Diamond Princess cruise ship coronavirus cases double to 135; Marysville woman still healthy
11 February 2020 174 Japan confirms 39 new virus cases, 174 total on cruise ship
12 February 2020 174 No reports indicating change in number of positive test results for COVID-19 infection.
13 February 2020 218 44 more on Diamond Princess cruise ship test positive for COVID-19
14 February 2020 218 No reports indicating change in number of positive test results for COVID-19 infection.
15 February 2020 285 Travis Air Force Base Prepares For Coronavirus Airlift Of Diamond Princess Passengers
16 February 2020 355 Virus spreads on ship in Japan, American passengers set to disembark
17 February 2020 454 99 more coronavirus cases reported on cruise ship docked in Japan
18 February 2020 542 Japan says 88 more virus cases confirmed on quarantined ship
19 February 2020 621 79 New Cases Of Coronavirus On Quarantined Japan Cruise Ship Take Toll To 621

Since Japan's official quarantine ended on 19 February 2020, two Diamond Princess passengers who became infected with the COVID-19 coronavirus have died.


Wendi Liu, Sanyi Tang, and Yanni Xiao. Model Selection and Evaluation on Emerging Infectious Disease Data Sets including A/H1N1 and Ebola. Computational and Mathematical Methods in Medicine. 2015; DOI: 10.1155/2015/2017105.

SEBRANGO-RODRÍGUEZ, C., MARTÍNEZ-BELLO, D., SÁNCHEZ-VALDÉS, L., THILAKARATHNE, P., DEL FAVA, E., VAN DER STUYFT, P., LOPEZ-QUILEZ, A., SHKEDY, Z. (2017). Real-time parameter estimation of Zika outbreaks using model averaging. [PDF Document]. Epidemiology and Infection. (2017), 145, 2313–2323. DOI: 10.1017/S0950268817001078.

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February 20, 2020

Every three months, we take a snapshot of the expectations for future earnings in the S&P 500 (Index: SPX) at approximately the midpoint of the current quarter, shortly after most U.S. firms have announced their previous quarter's earnings.

While the earnings outlook for the S&P 500 slipped somewhat since our Fall 2019 snapshot, based on the data available as of 14 February 2020, trailing year earnings for 2019-Q4 have rebounded strongly over 2019-Q3, marking the end of a very short-lived earnings recession.

Forecasts for S&P 500 Trailing Twelve Month Earnings per Share, September 2014-December 2021, Snapshot on 14 February 2020

Looking past the earnings data for 2019-Q4 that is still in progress for being reported, we see very little change projected for earnings through the end of 2020, where forecast trailing year earnings per share dipped slightly from the $161.95 per share projected on 11 November 2019 to $162.22 per share in this snapshot.

Meanwhile, Standard and Poor has extended their earnings forecast for the S&P 500 out through the end of 2021, with the trailing year earnings per share in the fourth quarter of that year initially set at $176.20.

In the next snapshot, we'll simplify the chart by resetting the horizontal axis to start with December 2016.

Data Source

Silverblatt, Howard. Standard & Poor. S&P 500 Earnings and Estimates. [Excel Spreadsheet]. 14 February 2020. Accessed 17 February 2020.

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February 19, 2020

The number of dividend cuts announced through the midpoint of the first quarter of 2020 is generally on track with the number that had been declared by this point of time in the first quarter of 2019. The following chart shows how the cumulative total of dividend cuts in 2020-Q1 compares with the year-ago quarter of 2019-Q1, where the pace of dividend cuts in 2020-Q1 falls well within the "relatively healthy" portion of the chart.

Cumulative Total of Dividend Cuts in U.S. by Day of Quarter, 2019-Q1 vs 2020-Q1, Snapshot on 14 February 2020

Through 14 February 2020, we've counted a total of 24 dividend cuts announced through our two near-real time sources of dividend declarations, Seeking Alpha and the Wall Street Journal. We've broken that full list up into two different categories, one for firms that pay variable dividends to their shareholders, with the amount of the dividends directly linked to their revenues and earnings, and the other for firms that fix the amount of their dividend payments independently of their business performance.

Here's the first part of the list of dividend cuts announced by the variable dividend paying firms through the halfway point of 2020-Q1.

Eight of these firms hail from the oil and gas industry, where the number of firms is consistent with the typical month-to-month noise we see among variable dividend payers, which is often tied to the fluctuating prices of oil and gas. Of the remaining firms, two are in the mining industry, one is a technology firm, and one is in the financial industry.

Here's the list for the firms that set their dividends independently of their earnings and cash flow:

Seven of these firms are in the U.S. oil and gas industry, but this list is significant in that several are midstream producers, whose businesses involve transporting oil and gas from wells (upstream) to end users (downstream), usually through pipelines, where the firms are cutting their dividends to address high debt loads on their books, which is an indication they are not seeing the revenues they had hoped to gain by investing in their infrastructure.

Beyond that total, we count two firms in the manufacturing sector of the U.S. economy, two are real estate investment trust, and there is one firm each from the mining and technology sectors.

Of these, the two manufacturing firms U.S. Steel (NYSE: X) and Spirit AeroSystems (NYSE: SPR) because we're starting to see some of the anticipated fallout from the global recession in the automotive industry, where we would advise paying close attention to debt-burdened firms like Ford (NYSE: F), and also to firms affected by Boeing's ongoing problems in the aerospace industry, which is now rippling through the company's supply chain, and which may take years to recover, even if Boeing (NYSE: BA) soon receives FAA approval to resume production of its troubled 737 MAX commercial transport aircraft.


February 18, 2020

The U.S. Federal Reserve has something of a love-hate relationship with its latest liquidity injection policy. The Fed keeps having to supply money markets with more and more liquidity, which has contributed to boosting the S&P 500 (Index: SPX) to four new record highs in the last week, but Fed officials are signaling they really want to stop.

That may be why investors appear to now be focusing strongly on 2020-Q4 in setting today's stock prices, as suggested by the dividend futures-based model that underlies our alternative futures spaghetti forecast chart for stock prices:

Alternative Futures - S&P 500 - 2020Q1 - Standard Model - Snapshot on 14 Feb 2020

This brings us to something we missed in the data in the previous edition of our S&P 500 chaos series, where we took a cautious note in reading the week's data:

This is where we have to add a note of caution, because we're dealing with a rapidly evolving situation in the markets. If you look at the alternative futures chart above, if investors shift their attention fully toward 2020-Q3 in setting current day stock prices, the S&P 500 could continue to rise by as much as 250-300 points. But, if China's and the Fed's liquidity injections work to stabilize markets as intended, the FedWatch tool's probability estimates may only have caught investors in the process of shifting their focus more fully back toward 2020-Q4, which is consistent with the S&P 500's recent trajectory, which would also mean that stock prices are within a few percent of where they might go.

What we missed is that the reason investors would now be fixing their focus more tightly on 2020-Q4 in setting current day stock prices is because they are betting that this distant future quarter will see the Fed cut short term interest rates for a second time in 2020. According to the CME Group's FedWatch tool, investors are now giving a 46% probability they will follow a quarter point rate cut in 2020-Q3 with another in 2020-Q4.

CME Group FedWatch Tool Probabilities of Federal Funds Rate Changing at Future FOMC Meeting Dates, Snapshot on 14 February 2020

Consequently, unless the arrival of new information leads investors to alter that expectation, we think the liquidity operations that Fed officials hate will be with us for quite some time longer than they would like.

In any case, here are the more significant market-moving headlines we found in the past week's news stream:

Monday, 10 February 2020
Tuesday, 11 February 2020
Wednesday, 12 February 2020
Thursday, 13 February 2020
Friday, 14 February 2020

Over at the Big Picture, Barry Ritholtz succinctly summarizes all the positives and negatives he found in the past week's economics and market-related news.

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February 14, 2020
Wedding Party - Alasdair Elmes - Unsplash

Happy Valentine's Day! By all accounts, today is the second most popular day of the year for couples to become engaged after Christmas Day, where if you find yourself among the large numbers of those who recently have become engaged, you have begun a journey where you will soon be planning your wedding.

With the average cost of a wedding falling between $20,000 and $30,000 in most states, a wedding and reception can be very expensive. Since how expensive your wedding will actually be is tied to how many guests might attend, it will be key to sort that number out early in your planning, since it will affect almost every other aspect of your big day.

You could simply use the count of invitations you will send out, taking care to include any children or plus-one's your invited guests might have, but that number will almost certainly be too high. If you use that total body count to plan around, you'll end up with a lot of wedding waste, paying too much for both facilities and food you'll never enjoy.

We can help you get more bang for your wedding buck! Our latest tool is based on Offbeat Bride's Catherine Clark's magic wedding math, in which she describes how to estimate guest list numbers using a simple equation. Just enter the indicated information about your wedding and invited guests in the following tool, and it will give you a reasonable number to use in planning your wedding as you select everything from where the ceremony takes place to how big a venue you need to book for the reception and even to how much wedding cake you'll be serving for dessert. If you're accessing this tool on a site that republishes our RSS news feed, please click through to our site to access a working version of the tool!

Wedding Guest Numbers
Input Data Values
Number of Local Guests
Number of Out-of-Town Guests
Are you having a destination wedding where nearly all guests must travel?

Wedding Guest Planning Numbers
Calculated Results Values
Lower Estimate of Invited Guests Who Will Actually Attend
Upper Estimate of Invited Guests Who Will Actually Attend

Catherine Clark provides the following insights about each category of guests:

Your local guest numbers

Local guests are far more likely to come to your wedding. We'd suggest thinking 80-85%. If you have a hard maximum due to venue restrictions, you may want to err on the side of 85-90% just to be safe. Don't forget to count plus-ones and children, if they're invited.

Your out-of-town guests guest numbers

If out-of-towners aren't coming in internationally, you'll mostly be focusing on how close they are to you and if they've got the means to come, financially. If money isn't a big issue, account for about 70-75%.

For our tool's results, we've indicated a range that covers these ranges of values, where using the upper estimate will give you some safety margin in your planning, so you won't get caught short. As you get closer to your wedding date, you can then fine tune your planning as the number of RSVPs you receive will replace our tool's estimates.

One last thing. Congratulations!

Image credit: unsplash-logoAlasdair Elmes

Previously on Political Calculations

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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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