On 24 September 2018, mathematician Michael Atiyah announced that he believed that he had cracked the Riemann Hypothesis at the Heidelberg Laureate Forum, which if his proof holds, would represent a very big deal. Not just because the proof would come with a one million dollar price from solving one of the Clay Mathematical Institute's millennium problems, or because it describes the distribution of prime numbers, but also because it would automatically prove a lot of other mathematical hypotheses that rely on the Riemann hypothesis being valid for their contentions to hold.

For more information about what the Riemann Hypothesis is, we recommend viewing either Numberphile's 17-minute video or 3Blue1Brown's 22-minute long video on the topic, both of which are well done but offer different strengths in presentation. What we found interesting in Atiyah's announcement is that he claims the proof came about because of work he was doing (leaked here?) to analytically derive the fine structure constant from physics, which is fascinating in and of itself.

In the following video from the University of Nottingham's Sixty Symbols project, Laurence Eaves provides a blissfully short 5-minute long explanation of the significance of the fine structure constant, which is the measure of the strength of the electromagnetic force governing how electrically-charged elementary particles interact.

The three fundamental constants that are combined in the fine structure constant are:

• The elementary charge of an electron (e)
• Planck's constant, divided by both 2 and pi (h)
• The speed of light (c)

If we include pi, there are technically four universal constants in the formulation. It's estimated to be very nearly equal to 1 divided by 137, where if it were exactly equal to that ratio, would really be extraordinary because the value 137 happens to also be a Pythagorean prime number. As it happens, the denominator in the fine structure constant is currently estimated to be 137.035999138..., so it's close, but not quite.

Not long ago, thanks to a botched drink order, we had our first experience with the new style plastic "adult sippy cup" lids that Starbucks (NYSE: SBUX) announced would replace plastic straws for all its iced beverages back on 9 July 2018.

Starbucks promoted the new lids as a way to reduce the amount of plastic waste that ends up in the world's oceans, where the company's press release featured the comments of environmental activist Nicholas Mallos:

“Starbucks’ decision to phase out single-use plastic straws is a shining example of the important role that companies can play in stemming the tide of ocean plastic,” said Nicholas Mallos, director of Ocean Conservancy’s Trash Free Seas program. “With eight million metric tons of plastic entering the ocean every year, we cannot afford to let industry sit on the sidelines.”

Starbucks' adult sippy cup lids are being first rolled out in the North American cities of Seattle, Washington and Vancouver, British Columbia, even though neither city, nor any city in North America, nor the entire continent of North America, is a major source of plastic waste that enters the world's oceans each year. At present, neither Starbucks nor the Ocean Conservancy has indicated how they will reduce the total volume of plastic trash entering the world's oceans from the places that are primarily responsible for the practice.

It's already been remarked that the new plastic lids use more plastic than the combination of plastic straws and the "flimsier" plastic lids that they are replacing, as can be seen in the following investigative report:

What hasn't yet been much remarked upon is that the thicker plastic used in Starbucks' adult sippy cup lids makes them less effective at their primary purpose: containing the iced beverage within its cup without spilling.

The thicker plastic makes the lid design more rigid than its predecessor, which makes it much easier to pop off the top of the cup with a very light amount of pressure, applied either to the lid or to the upper portion of the body of the plastic cup. The previous flat lid design didn't have that problem, because it was much more flexible, allowing it to remain attached to the cup when handled similarly.

If you get one, try the following experiments for yourself, each of which represents very common ways that these kinds of beverages are handled by consumers, particularly if they are drinking them on the go, such as in a car:

• Apply a light amount of pressure at a single point on the underside of the lid where it is attached to the cup.
• Pick the cup up by the lid at several points around the lid and squeeze gently.
• Hold the plastic cup near the top, but not touching the lid, and squeeze gently.

In each case, you should discover that the lid pops off much more easily than the old-style flat lid design does, greatly increasing the risk of spills. Although our experiments currently involve a sample size of just one cup, where perhaps Starbucks' inattentive baristas [1] randomly provided us with an extraordinarily poor lid/cup combination, our first experience suggests that Starbucks' new adult sippy cup lids are not ready for prime time as they would appear to be less effective as lids than the design they will replace.

The funny thing is that if Starbucks would rather that customers pop the tops off their iced beverages when they consume them, the practice of drinking them on the go be damned, they could have simply eliminated the plastic straws and kept their existing plastic lids, which are actually designed to be used as coasters when consumers choose to drink their iced beverage from a lid-free cup. That's something else at which the Starbucks' new lid design also fails.

[1] Remember, we only got the cup because they botched our drink order, where they chose to provide us with an altogether different beverage than the one we ordered. We chose to go along with it because it came with the new cup and lid design, which we wouldn't have had the chance to play with if they had gotten our order right. For us, it's additional evidence that the company is increasingly troubled, where it is perhaps skimping on employee training as well as product testing as part of a series of poorly considered cost reduction strategies in trying to boost its bottom line.

The U.S. Department of Education has updated its statistics on the number of student loan defaults occurring within three years of a borrower beginning repayment. The latest data covers borrowers who began making payments on their student loans during the U.S. government's 2015 fiscal year, which ran from 1 October 2014 through 30 September 2015, who have subsequently stopped making scheduled payments for a prolonged period of time without making arrangements to either defer them or to seek relief from them during the following three years.

The following chart shows the number of student loan borrowers who have defaulted within three years after starting to make payments in each fiscal year from 2009 through 2015 according to the type of four year degree-granting institution they attended, covering proprietary (or for-profit) universities, public universities, and private (or non-profit) universities.

For student loan borrowers who attended four-year degree granting institutions and began making payments during the U.S. government's 2015 fiscal year, 531,653 went on to default on their student loan debt over the next three years. Of these, 51% attended public universities, 34% attended proprietary (or for-profit) institutions, and 15% attended private universities.

The next chart shows the percentage of student loan borrowers for each type of institution that began repaying their student loans, but went on to default on them within the following three years.

We find that although public universities account for the largest number of defaulting student loan borrowers, a larger percentage share of students who attend proprietary (or for-profit) institutions have consistently defaulted on their student loans.

The final chart reveals the average annual cost of college tuition and fees for each type of institution, which is based on data from the 2016-17 academic year, which is the closest we could get to 2015 for all three types of four year degree-granting institutions. The $9,670 value shown for public institutions applies for state residents eligible for in-state tuition rates, where the average public university tuition and fees for out-of-state residents is $24,820.

Since March 2010, when President Obama signed legislation putting the U.S. government into the student loan business, most of these defaults represent money borrowed from the U.S. government.

Today, about 90 percent of loans made to students and their families are from the federal government, which does not follow the same lending standards required of financial institutions. The federal government holds around $1.4 trillion in student loans on its books and is currently seeing a double digit delinquency and default rate.

10.3% of student loan borrowers who started making payments on their debt to the federal government in 2015 have defaulted. That figure has come down and stabilized over the last several years, but is still a double-digit problem for the demographic group with the lowest rate of unemployment in the U.S. economy. Meanwhile, many who are making payments on their student loans aren't getting very far in paying them down.

Just as alarming as the high number of defaults on federal student loans is that less than half of new borrowers are able to put a dent in their principal balance within three years of entering repayment.

Currently, the U.S. government makes it very difficult, if not nearly impossible for borrowers to have their student loan debts discharged through bankruptcy proceedings, which is pretty much what you would expect for any creditor who has the power to write the rules to benefit itself by forcing the repayment of any loan that it has either guaranteed or issued.

If it cannot be discharged in bankruptcy and the money borrowed is owed to the government, it isn't debt. It's taxes. The sooner that's fixed by transforming student loans back into debt, among other reforms, the better it will be for everyone involved.

References

U.S. Department of Education. Official Cohort Default Rates for Schools, by Institution Type. [PDF Documents: 2009-2011, 2012-2014, 2013-2015]. 26 September 2018. Accessed 13 October 2018.

College Board. Trends in Higher Education. Average Published Undergraduate Charges by Sector and by Carnegie Classification, 2017-18. [Online Document. 17 November 2017.

It's been several months since we last considered the deteriorating situation for the future of dividends at General Electric (NYSE: GE), where we wrote that either GE or its dividend, and quite possibly both, were set to shrink.

Four months and one CEO later, and that statement holds even more true today, where we believe that it is no longer a question of "if", but of "when" and "by how much".

On 12 October 2018, GE announced it would delay the release of its fourth quarter financial statements until the end of the month to allow the company's new CEO, Larry Culp, to complete his "initial business reviews and site visits".

At the same time, we're coming up on the one year anniversary of when GE's then new CEO, John Flannery, slashed its quarterly dividend in half, from $0.24 per share to $0.12 per share, so it's a good time to look at what's changed for investors, which we can do by looking at just one number: the company's market capitalization.

When GE declared its last quarterly dividend of $0.24 per share on 7 September 2017, GE's market cap was nearly $208 billion. Exactly one year later, when declaring its fourth quarter dividend payment for 2018, GE's market cap was $108 billion, which is pretty close to where it stands today, just over a month later. That missing $100 billion goes a long way toward explaining why GE now has a new CEO.

That decline also gives us an indication of how much GE's new manager may be looking to cut the company's dividend. The following chart shows the relationship between GE's market cap and its aggregate dividend payouts for each quarter since 12 June 2009.

Given the historical relationship captured in the chart, at GE's current day market cap of $108 billion, we would anticipate a 35-40% reduction in the size of the company's dividends, from $0.12 per share to about $0.07 per share, which for all practical purposes, is already baked into the company's average share price over the five weeks. Culp could announce this change today and there would be minimal impact to the company's stock price.

But, that 35-40% lower dividend payment is for a General Electric that still has its health care division, which it has been planning to spin off. Without it, GE will need to cut its dividend by more than that percentage, because it won't have the revenues, earnings, and cash flow that it provides to the company to sustain a dividend reduced by only 35-40% from today's level.

We think then that it's very likely that once the new CEO's review of the company's operating and financial situation is complete, GE will suspend its dividend altogether. The change would help preserve what has been the company's increasingly distressed cash flow, which some analysts have indicated is not sufficient to cover both GE's current quarterly dividend of $0.12 per share and its operating requirements.

Other analysts believe that GE's dividend is safe. Based on the information we have today, we are not in that camp.

References

Dividend.com. General Electric Dividend Payout History. [Online Database]. Accessed 14 October 2018.

Ycharts. General Electric Market Cap. [Online Database]. Accessed 14 October 2018.

Yahoo! Finance. General Electric Company Historical Prices. [Online Database]. Accessed 14 October 2018.

The second week of October 2018 was one of the most interesting for the S&P 500 (Index: SPX) in quite some time.

For our purposes, to qualify as interesting, the S&P 500 needs to change in value by 2% or more on any given day, and Week 2 of October 2018 had two days that met that simple threshold, Wednesday, 9 October 2018, when it fell by more than 3% and Thursday, 10 October 2018 when it continued to fall by another 2%.

In doing so, investors moved the market by shifting their forward-looking focus from 2019-Q1 toward the more distant future of 2019-Q3. Through the end of the week on Friday, 12 October 2018, the level of the S&P 500 in our dividend futures-based model indicates that investors are splitting their attention between these two quarters, putting a slightly heavier weighting on the nearer term future of described by the expectations associated with 2019-Q1 than they are for 2019-Q3.

Why focus on 2019-Q3 at all? Starting with basic fundamentals, the dividend futures for the S&P 500 associated with this upcoming quarter have been flat at $14.00 per share since 12 July 2018, where they represent a deceleration in the year-over-year rate of growth of trailing year dividends per share for the index. As such, the expectation that the rate of growth of S&P 500 dividends, and by extension, U.S. economic growth, will slow during this future quarter has been baked into investor considerations for quite some time.

Since there has been no change in these fundamental expectations, we can rule out any growing fear of a stalling stock market and economy at this time as a causal factor behind the S&P 500's latest Lévy flight event. Ditto for any news items related to the ongoing low-level trade war between the U.S. and China, which for all the noise in the news it has generated since it began earlier this year, has not produced a noticeable impact on dividend futures to date.

What has changed very recently however is investor expectations of a Fed rate hike in 2019-Q3, which would explain why investors would focus on this particular point of time in the future at this point of time in the present. With the U.S. economy continuing to grow strongly, and with the lowest official unemployment rate since the late 1960s, the probability that the Fed will continue its series of interest rate hikes in this quarter has very recently surged above 50% according to interest rate futures. This change in investor expectations has also coincided with a period of heightened volatility in intraday stock price values, which peaked with the U.S. stock market's Lévy flight event on 10 October 2018. The following chart shows the probabilities indicated by the CME Group's FedWatch tool for upcoming rate hikes as of the close of trading on 12 October 2018.

We see that investors are currently giving better than even odds of a quarter percent or greater rate hike occurring when the Fed meets on 19 December 2018 (2018-Q4), then again on 20 March 2019 (2019-Q1), and again on 18 September 2019 (2019-Q3).

Since the week's Lévy flight event prompted us to feature a special mid-week edition of our weekly S&P 500 Chaos series, we only have two additional days of news headlines to catch up on. Here's the rest of the week's market-moving news....

Thursday, 11 October 2018

• Oil falls 3 percent as equity markets drop, inventories climb
• U.S. 30-year mortgage rate hits seven-and-a-half year peak: Freddie Mac
• Trump calls 'loco' Federal Reserve 'too aggressive'
• Call 'em crazy, but Fed officials likely to keep raising rates
• Wall Street tumbles again, world equities at one-year low
• S&P tumbles as investors shun risk

Friday, 12 October 2018

• Oil turns lower as weaker demand outlook weighs
• Wall St. rebounds with technology stocks leading the way
• Global stocks rebound but S&P 500 posts biggest weekly loss since March
• Most S&P 500 stocks are deep in correction territory

Looking for a bigger picture of the week's major economics and markets news? Barry Ritholtz' has outlined the week's positives and negatives. As a special bonus, he also wrote one of the better analytical pieces of the week: The Stock-Market Meltdown That Everyone Saw Coming! Absolutely essential reading, and the only other piece we know of that even mentioned properly mentioned random walks in describing what happened with stock prices in the aftermath of the week's Lévy flight event.