Thursday, April 30, 2020

Projecting Deaths from COVID-19 (another update)

On April 2, I published a blog (here) analyzing available information to put into context the 100,000–240,000 U.S. COVID-19 deaths then being projected. On April 15, in this blog, I cast doubt on the reduction of government projections to “only” 60,000 deaths through August 4[i], suggesting that 100,000 deaths were more likely. The official projection has now been increased several times and as of this writing sits at nearly 73,000. Once again, applying my na├»ve methodology, I think this number is too low.

A chart I have found helpful to visualize the path of U.S. COVID-19 cases is to compare us to Spain, Italy, and Germany, recognizing that Italy started about two weeks before us and Germany and Spain a week after that.

Note: the horizontal axis is time (Italy has 64 days, the other countries fewer.

The most recent two weeks have crushed any chance the U.S. curve would flatten faster than Italy’s. Instead, our path is not even flattening as much as Italy’s did at comparable points in time. We have set our own course and it appears it will remain above Italy’s level of infection.

Fortunately, the death rate experienced in the U.S. is considerably lower than Italy’s. Using the metric developed in earlier posts of dividing total reported deaths by total reported cases a week earlier (in order to reflect an average time between reporting and death, should it occur), the U.S. is now at 7.3%, less than half Italy’s rate. The chart below demonstrates that both rates have been declining very slowly for some time.

Before combining the data from these charts to project future deaths, we need to examine some assumptions.

Why Are U.S. cases as a percentage of population increasing faster than Italy?

Either (1) U.S. testing is more comprehensive than was the case in Italy, resulting in more “benign” cases per capita detected in the U.S. than in Italy. AND/OR

(2) Italy did a better job of controlling the spread of the virus through the strength of and/or compliance with stay-at-home orders, business closures, and similar precautions.

If U.S. testing had significantly increased, yielding many “benign” cases, we would expect mortality rates of those infected to decrease. Over the last two weeks there has been a slight decline in the U.S. from 7.5% to 7.3%. If the explanation for the decreased death rate were entirely due to increased testing, it would mean that about 22,000 of the 412,000 cases reported between one and three weeks ago resulted from increased testing. Adjusting U.S. reported cases by that amount only slightly decreases the slope of the U.S. curve displayed in the first graph.

If next week we see a significant decline in the death rate, we’ll know increased testing is driving the level of newly reported cases. That would be a good thing.

In the U.S., states have imposed various levels of business closings and stay-at-home orders, making it difficult to compare to Italy, which did have different rules for the northern and southern sections of that country. I don’t have data to know how well Italians complied with their government’s rules. Anecdotal evidence in the U.S. shows compliance has been spotty. Some churches remained open despite state rules against crowds larger than ten people Demonstrations occurred in several state capitals protesting the “unnecessary” sheltering in place. Beaches in some states remain busy, where other states have kept them closed.

My current projections

As I write this (the morning of April 30), the U.S. has reported 1,064,194 COVID-19 cases of whom 61,656 have died. If we had no additional cases and the death rate remained at its current level, we’d have 77,000 deaths (4,000 higher than the government’s projections that go out to a later date).

If we continue to track Italy’s path (but recognizing our current level is higher than theirs) we would experience another 290,000 cases, which would yield another 21,000 deaths for a total of 98,000 by May 15. However, I do suspect death rates will continue to decline as they have in Italy. Should they decrease in the U.S. to 7%, the expected deaths by May 15 becomes fewer than 95,000—still much higher than the government’s estimate of 73,000 by August 4.

Italy continues to report new cases, and so will the U.S. We don’t know the effect warmer weather will have on stopping or slowing the spread. It happens for flu, so we can hope. Offsetting that are whatever negative effects may result from states “reopening” their economies by relaxing the disease-preventing rules currently in place.

I’m starting to think 100,000 deaths might prove optimistic, but I continue to hope I’m wrong.

Thursday, April 23, 2020

Stock Market Volatility in the Time of Covid-19

To believe newscasters, stock markets rise when there are more buyers than sellers and fall with the converse. To consummate a transaction, there must be both a buyer and seller. It is more proper to say that stock markets rise when more people are motivated to buy shares than sell them at a given price. To balance that optimism, sellers require more money to part with their shares. Similarly, price declines reflect that to induce people to purchase shares, they must lower prices. Whatever the motivations, at the point of transaction, both parties have agreed to a price.

General agreement on the prospects for stocks results in little volatility in prices. As what were expected future profits become actualized, current prices rise to reflect the time value of money. As new information becomes available to estimate future profits, individual stocks will increase or decrease—causing what little volatility there is.

Several methods exist to gauge the stock market’s price volatility. The measure I’ll use for this blog is the daily percentage change in prices of the S&P 500 Index[i]. Because we are concerned only with how much the market changed each day, not whether it rose or fell, we use the absolute value[ii] of the percentage price change.

Historical Averages

For the ten-year period ending April 22, 2020, the average absolute value percentage change was .82%. The current S&P 500 Index is ~2,800. Applying the long-term expectation means that, on average, daily prices change by 23 points. Not every day is the same, and standard deviation[iii] measures the variability around that average. The larger the number, the more the variability. For the 10-year period, that was 1.04%.

So, the two key measures for the 10-year period are .82% average change with a standard deviation of 1.04%.

The 2020 Experience

In the beginning of 2020, the stock market was relatively calm. From January 2 through February 19 (the day the S&P 500 reached its all-time high), the average change was .57% and the standard deviation during that time was  .44 (or .50 when comparing those thirty-three daily results to the long-term average change). This calm trading behavior suggests everyone seemed to think they had the temperature of the market.

That stability has changed markedly since the record high. In the forty-four trading days since (from February 20 through April 22, 2020), the average percentage change has exploded to 3.62% with a standard deviation of 2.73 (or 3.91 when comparing those daily results to the long-term average change!). The expected daily change of 23 points has exploded to an actual average of 101. Not only has the daily percentage change more than quadrupled, the variability of the daily change has also skyrocketed.

Meaning What?

Yeah, fascinating for the number geeks, but what does that mean? My interpretation is that until we have clarity on two issues, everyone is shooting in the dark. Each daily statistic shines a penlight worth of knowledge into a mammoth cave worth of unknowns, and yet the markets react: hence massive volatility. Issue number one is how much damage are businesses experiencing? First quarter reports will come out soon. They reflect half a quarter of boom times and the rest of responding to Covid-19 shelters-in-place. Corporations will not be providing forward guidance about the second quarter or later. This data will only partially answer the first question. The Federal Reserve continues to prop upthe economy and Congress continues to throw money (and ballooning deficits beyond anyone’s imagination just two months ago) at the problem.

And still we do not know what the short-term damage will be.

Worse, we have no certainty about what the longer-term damage will be. Today’s weekly unemployment new claims data are projected to be 4.5 million[iv], yielding 26.5 million new claims during the month. The unemployment rate will exceed 15%.

Initial words from pundits suggested a V-shaped recession: quick decline and rapid recovery because financial imbalances did not cause the problem, and the economy was so strong before the Covid-19 damage. The decline part is correct. I am not optimistic about the quick recovery.

Our chances of screwing things up seem much larger than our opportunity to do it exactly right. The U.S. approach has been to focus primarily on keeping businesses solvent so they can resume operations once governments raise the green flag. It won’t have been enough for some retail operations and many restaurants, which is why there is pressure to reopen as soon as possible. But, reopening businesses too early gives the virus an opportunity to re-accelerate, causing renewed and longer shutdowns. Delaying reopening causes rank-and-file employees to dip further into savings or go further into debt, neither option allowing them to spend at previous levels.

In short, an economy that is 70% driven by consumer spending can’t bounce back to previous record-low unemployment without everything returning to normal. Unless Covid-19 magically disappears or treatments become highly effective, I don’t see a quick restart.

Many supply chains will not seamlessly restart because Covid-19 is affecting various parts of the world in different manners. Most spring events with large gatherings are canceled. Many are already canceling summer events, and planners are already canceling some fall events. Each of these has run-on effects for the hospitality industries and airlines. All this yields more uncertainty.

Which means, volatility will remain high for some time until the economy’s future becomes clearer. That resolution will determine whether the stock market is over-valued or under-valued.

[i] All data based on information provided by
[ii] The absolute value of a negative number is determined by changing the negative sign to a positive sign. E.g. the absolute value of -1 is +1
[iii] Standard deviation is the square root of the variance. Variance is defined as the sum of the squares of the difference between each individual value and the mean of values, that total divided by the number of values

James M. Jackson authors the Seamus McCree series. Full of mystery and suspense, these thrillers explore financial crimes, family relationships, and what happens when they mix. Furthermore, a novella is the most recent addition to the series. You can sign up for his newsletter and find more information about Jim and his books at

Wednesday, April 15, 2020

Projecting Deaths from COVID-19 (an update)

On April 2, I published a blog (here) analyzing available information to put in context the 100,000–240,000 U.S. deaths then being projected. More recently, the government has reduced projections to 60,000[i]. That’s a sizeable difference. What’s up?

The modification from the initial range resulted from two major components: how many would become infected in the U.S. and what percentage of those affected would die. Dr. Fauci, in announcing the reduction to 60,000 projected deaths, suggested the decrease came about because much of the country embraced the shelter-in-place and social distancing.

Flattening the Curve

In the previous blog, I compared the U.S. response to controlling the novel coronavirus to the efforts of Italy, Germany and Spain[ii]. Because of Germany’s massive early testing, the slope of their infection growth is the lowest. Spain is worst because they continued to allow massive public gatherings for a longer period than the other countries. Italy, which experienced infections earlier, was in the middle. The U.S., which experienced large numbers of infected two weeks after Italy and one week after Spain and Germany, continues to follow a path close to Italy, but slightly worse.

Covid-19 reported cases per million

We’ve lost our opportunity to be like the Germans. Our infection rate per million population has already exceeded theirs, even though we are a week earlier in the curve. We are doing much better than Spain. The U.S. still has the potential to bend its curve so it will not experience the same infection levels as Italy.

One piece of (comparative) good news is that for several days the number of new cases in the U.S. has decreased from its worst day. This peak occurred a week earlier in the curve than the peak happened for Italy, suggesting our social distancing has helped. The tail, however, is long.

Italy’s worst day was March 21 when they reported 6,557 new cases. That gave them 53,578 total infected. Yesterday (April 14), their cases stood at 162,488. That means more that twice as many people were reported infected in Italy after their worst day than before it. Yesterday, Italy reported nearly 3,000 new cases. Their tail continues to lengthen.

German’s worst day was March 22 with 6,933 new cases. That gave them 57,695 total infected. Yesterday they stood at 132,210. With a significantly flatter curve than Italy, they experience a multiplying effect of 1.3 cases after the peak for every pre-peak case.

Spain reached their high a few days later. On March 26 they reported 8,271 new cases, totaling 57,786. Their total yesterday was 174,060. Matching Italy, they had more than twice as many people infected after their peak than before it.

The U.S. experienced its highest reported cases on April 4, with 34,196. At that date we had 311,413 total cases. Yesterday we had reached 613,886 (nearly double) with 26,945 new cases that day. We are not experiencing Germany’s tapering; we continue to track Italy’s experience. If that remains the case, we can expect another 300,000 infected in April, bringing us to over 900,000 by the end of the month.

What’s happening with death rates?

In the previous blog, I suggested a method to estimate the death rates of reported cases: take total deaths and divide by reported cases a week earlier. Excluding China (because of their likely under-reporting of deaths), I estimated on April 2 a ratio of 12.8%.

Updating that calculation to April 14, yields 123,259 total worldwide deaths (excluding China). Total reported infected on April 7 (excluding China) were 1,352,655. The ratio is 9.11%. This decline is welcome news. I suspect the reasons for the decline combines wider testing catching many more “light” cases and possibly better treatment.

Where are individual countries right now? Using total reported deaths and infections (not adjusting for the week delay between report and death), Italy’s death rate is currently 13.0% (up from 12.1% on April 2); Spain has reached 10.5% (up from 9.2% on April 2), and the U.S. has climbed to 4.4% from 2.5% on April 2.

Unfortunately for the U.S. our rate of testing (9,260 per million population) is well below the three comparison countries (Spain - 12,833; Germany - 15,730, Italy - 17,758). Iceland is the world-leader with 106,490 per million of population! Given that our current testing protocols[iii] are designed specifically to exclude those most likely to recover (not too sick, not elderly or otherwise at risk), our death rate is unlikely to be much better than the world at large. I will change that assessment as a larger percentage of cases derive from countries with inadequate hospital facilities (India, Turkey, and most African countries are still in the early part of the infection curve). Their future inclusion will, I fear, drive up the worldwide death rate. For now, however, their effect on the overall rate is minor.

Applying the current 9.11% rate to the projected 900,000 U.S. cases through April yields 82,000 deaths.

Given the experience of other countries, there is no reason to expect that Covid-19 infections will magically stop on May 1. A percentage of those later infections will also die. Perhaps the original 100,000 will prove accurate after the counting is complete.

I hope Dr. Fauci’s estimate is correct, and mine is overstated. My overstatement could arise from two areas.

The U.S. does not follow Italy’s trend line and develops fewer than the 900,000 cases I projected before May 1. This will be great news—unless the reason for the decline is a continued inability to test all the people we should.

The U.S. death rate proves to be lower than the current worldwide estimate. This could arise because the U.S. health system finds more effective treatments than were available to other countries. We can hope for this great blessing. We also could experience a lower death rate because we accelerate testing and catch more infected patients earlier, thereby allowing healthcare to provide better care. Sadly, testing has not increased. As illustrated in the chart prepared by the CDC and available on their website[iv], despite promises, the U.S. rate of tests done in April are only slightly higher than those performed at the end of March.

CDC Covid-19 Lab Tests

I have my fingers crossed that I am wrong.

Friday, April 3, 2020

Projecting Deaths from Covid-19

In my blog on Covid-19 last week (here), I suggested we could use rates of reported cases per million of population to standardize numbers across countries and gauge the trajectory of infections based on those under the gun for a longer period. Thursday, April 2, we recorded the one-millionth case, and the official death toll crossed 50,000. That day alone the world recorded nearly 6,000 deaths and almost 80,000 new cases.

Graph: Covid-19 Reported Cases per Million Population

 The chart above is an update of the one I prepared last week. It shows the growth in cases per million for Italy, Germany, and the U.S. During the week, Italy’s rate has moderated. Germany, reaping the benefits of significant early testing, has dropped below the rate experienced by Italy at the same equivalent period. The only positive spin for the U.S. is that it could be worse; we could track Spain (see below).

Same chart with Spain added

What can we learn from Germany and Spain?

Let me be clear: I don’t know what’s going on. I am speculating based on news stories and reported statistics. The number of reported cases per million of population became significant for Germany about a week after Italy (and at the same time as Spain). Germany reacted by shutting down sports and other large gatherings and instituted widespread testing. Spain allowed a rally of 120,000 people in Madrid to celebrate Women’s Day on March 8[i] (Day 3 on the above chart).

While the huge gatherings in Spain had an effect, the biggest difference was the speed in which testing rolled out. Spain, like the U.S. required central approval before administering a test. Germany’s s decentralized system experienced no such roadblocks. The result is Germany tested sooner and more widely, identifying a larger percentage of the infected earlier in their infection. This allowed for quicker quarantining of the infected, reducing exposure.

There are also cultural differences between Germans and Spaniards. Germans have a strong form of government and tend to be rule-followers. That’s not the case in Spain, whose central government let a week or more go by before they imposed the same social distancing requirements as Germany. Spaniards did not take the matter seriously until people started dying in large numbers. By then it was too late to stop the first acceleration of cases we see illustrated in the graph above.

With a country-wide lockdown enforced by police with roadblocks and drones, and nationalization of private hospitals, Spain has clamped down. Its trajectory will eventually decrease, but the delay will cost tens of thousands of lives.

What of the U.S.? Are they just trying to scare us with the projections of 100,000 to 240,000 U.S. dead?

Compared to Germany and Spain, the U.S. had an additional week’s time to prepare for the Covid-19 onslaught. Our federal government pissed it away, leaders convincing themselves that we had taken all the measures we needed by shutting our borders to those arriving from infected areas of China.

Unlike Germany, where the federal government acted deliberately, our federal government has been reluctant to exert control, leaving it up to states and municipalities to respond as they see fit. This has led to a rolling set of policies that react to local conditions after the problem has already grown large. That’s too late to dampen the curve quickly. Even today, when the positive effects of social distancing are understood, states like Florida still allow church services, which they deem essential services[ii].

This nonuniform response will continue to lead to rising case numbers. The same Florida governor who refused to close beaches during Spring Break issued a requirement for those travelling from New York to self-quarantine for fourteen days,[iii] as though the virus weren’t already spreading in his state.

So yes, given the spectacularly slow response by many state and local governments, I suspect health officials are trying to scare us into complying with requests/demands to stay at home. We’re doing much better than Spain, but not nearly as well as Germany. As it stands now, we’re not even matching Italy.

But isn’t the death rate for Covid-19 under 1%?

Does that mean we’ll have 10 to 25 million people infected? Later today, I project, we’ll exceed a quarter of a million people reported infected in the U.S. With all the social distancing ten million or twenty-five million seems unlikely in the near term. It’s unclear what assumptions the studies used to arrive at their death figures.[iv] Much depends on the duration covered, policies employed (and followed), and the death rates assumed.

The studies that showed death rates below 1% were based on data from China, which has come under question based in part on the number of urns being shipped to Wuhan province.[v] [vi]

What we do and don’t know about death rates.

The only way to know the mortality rate for a disease is to test everyone to determine who had the disease and divide that number into those who died from the disease. In fact, we’ll never know the factual answer. Some very smart people with sophisticated models will make their best estimates, which is where the 100,000 to 240,000 deaths came from.

What we know as of April 2, 2020

Excluding China, there have been 49,848 reported deaths and 933,344 reported cases of Covid-19. That’s a death rate of 5.3%. That’s low, because even if there were no more reported cases, we still expect more of those already infected to die.

An early study showed that on average two weeks passed between onset of first symptom and death. For a SWAG (some wild-assed guess), let’s assume the average reported case occurs seven days after the first symptom. If the 14-day period from first symptom to death holds up, then reported deaths came from the population whose illnesses were reported before March 26. Again removing China from the reported cases, that leaves nearly 50,000 worldwide deaths arising from 390,000 reported cases. That ratio is 12.8%!

Is that possible? Italy’s current death rate is 12.07% of reported cases. Spain, which started a week later than Italy, is already up to 9.2%.

But Germany has a 1.3%. rate. The lower rate is because the denominator includes many “healthy” sick discovered as part of Germany’s more extensive testing. Most of these additional individuals will recover (lowering the mortality rate compared to countries who didn’t know these types of individuals were ill).

Our testing rates are more comparable to Italy than to Germany, and so of those already reported, we should expect a higher mortality. (We’re already reached 2.5% and it’s climbing.) For us, experiencing 100,000 deaths may result from as few as one million reported cases—and we have already reached 250,000 cases.

It’s up to each of us.

Our previous actions, or lack thereof, have baked in the number of cases of Covid-19 the U.S. will experience over the next week to two weeks. What happens after mid-April depends on how each of us acts. Will you be responsible, or will your behavior kill others?

Your choice.
* * * * *

James M. Jackson authors the Seamus McCree series. Full of mystery and suspense, these thrillers explore financial crimes, family relationships, and what happens when they mix. False Bottom, the sixth and most recent novel in the series is set in the Boston area. You can sign up for his newsletter and find more information about Jim and his books at