As of the end of 2019, the total market capitalization of the S&P 500 was $26,759,686,786,884. Or if you prefer, approximately $26.76 trillion!

That's 14.8 times the value of the S&P 500's market capitalization at the end of 1988-Q1, when the index' market cap stood at $1.81 trillion. From 1988-Q1 to 2019-Q4, the S&P 500's total market capitalization has doubled three times, completing its first doubling period in 7 years from 1988-Q1 to 1995-Q1, taking another 2.5 years to double again by 1997-Q3, and then another 16 years to double a third time in 2013-Q3.

Measured a little differently, the market cap of the S&P 500 as a percentage of the U.S. Gross Domestic Product at the end of 2019-Q3, the most recent quarter for which we have a somewhat finalized estimate, was 114.7%. That's close to the highest the S&P 500's total market cap has been since the days of the Dot-Com Bubble, when that figure peaked at 126.8% in the first quarter of 2000.

We won't know until the end of March 2020 how the S&P 500's market cap compares to the size of the U.S. economy through the end of 2019, when the estimate for the United States' GDP in 2019-Q4 is somewhat finalized.

References

Silverblatt, Howard. Standard & Poor Index Earnings and Estimates. [Excel Spreadsheet]. 16 January 2020. Accessed 23 January 2020.

U.S. Bureau of Economic Analysis. GDP and Personal Income Interactive Data. National Income and Product Accounts. Table 1.1.5. Gross Domestic Product. [Online Database]. Accessed 23 January 2020.

The S&P 500 (Index: SPX) completed the Lévy flight event it began last week, with investors fully shifting their forward-looking focus to 2020-Q4 in setting current day stock prices, as expected.

As of the close of trading on Friday, 24 January 2020, the level of the S&P 500 was 3,295.47.

The shift in focus was completed as the outbreak of a new SARS coronavirus in China came to dominate headlines during the week. Here are the market-moving headlines we noted during the holiday-shortened trading week of January 2020:

Tuesday, 21 January 2020

• Oil market shrugs off Libya crisis amid ample global supply
• Bigger trouble developing in Asia, Eurozone
• Risk assets fall as Chinese virus triggers anxiety
• China virus scare sends shudder through European luxury goods sector
• China's Baoshang Bank to be taken over by local governments, state firms
• South Korea posts slowest annual GDP growth since financial crisis
• Euro zone companies cut loan applications for first time in six years: ECB
• Germany likely to lose the most from trade diverted by U.S.-Sino deal
• Trump says Fed has lowered rates too slowly
• Wall Street falls as China virus reaches the U.S.

Wednesday, 22 January 2020

• Oil slides 2% as glut forecast, China virus overshadow Libya disruption
• U.S. home sales surge to near two-year high; supply at record low
• Trump says Fed raising rates was a mistake: CNBC
• Stocks edge up, oil drops as China virus worries abate

Thursday, 23 January 2020

• Oil falls 2% as specter of China virus threatens fuel demand
• Bigger trouble, stimulus developing in Asia:
• Japan exports shrink for 13th month in further blow to economy
• China central bank to lower funding costs, prevent debt and inflation risks: adviser
• S&P 500 gains, Nasdaq hits new high as investors eye earnings, coronavirus
• Coronavirus fears weigh on global equity markets

Friday, 24 January 2020

• Brent logs worst weekly loss in a year as China virus fears swell
• Take Five: When China sneezes
• Early signs of rebound in Eurozone?
• Euro zone economy remains weak but green shoots emerging: PMIs
• ECB's Lagarde says uptick in inflation 'really minor'
• And Japan? Slowing contraction in Japan factory activity eases fears of recession: flash PMI
• The S&P 500 has worst day since October as virus fears mount

Elsewhere, Barry Ritholtz lays out a short list of the positives and negatives he found in the past week's economics and market-related news. Between us and him, did we catch them all during the MLK holiday-shortened trading week?

Artificial intelligence, or AI for short, is creeping into all sorts of real world applications. Want to order cat food from Amazon? Ask Alexa via your smart speaker! Want to take the drudgery out of driving on a long road trip? Have your self-driving car do the driving for you!

Now, if you followed the links in the preceding paragraph, you've not only found stories involving how people are using AI-equipped devices today, you've also found some cautionary tales where machine learning hasn't been as up to the tasks to which it has been put, and certainly not as advertised. Some of these stories are kind of funny. Others have very tragic endings.

That's because many of the most successful AI systems that have been developed to date have limitations that aren't well understood. A recent article in Quanta explores some of those limitations and how researchers are turning toward mathematical physics to address them:

The revolution in artificial intelligence stems in large part from the power of one particular kind of artificial neural network, whose design is inspired by the connected layers of neurons in the mammalian visual cortex. These “convolutional neural networks” (CNNs) have proved surprisingly adept at learning patterns in two-dimensional data — especially in computer vision tasks like recognizing handwritten words and objects in digital images.

But when applied to data sets without a built-in planar geometry — say, models of irregular shapes used in 3D computer animation, or the point clouds generated by self-driving cars to map their surroundings — this powerful machine learning architecture doesn’t work well. Around 2016, a new discipline called geometric deep learning emerged with the goal of lifting CNNs out of flatland.

Now, researchers have delivered, with a new theoretical framework for building neural networks that can learn patterns on any kind of geometric surface. These “gauge-equivariant convolutional neural networks,” or gauge CNNs, developed at the University of Amsterdam and Qualcomm AI Research by Taco Cohen, Maurice Weiler, Berkay Kicanaoglu and Max Welling, can detect patterns not only in 2D arrays of pixels, but also on spheres and asymmetrically curved objects. “This framework is a fairly definitive answer to this problem of deep learning on curved surfaces,” Welling said.

Already, gauge CNNs have greatly outperformed their predecessors in learning patterns in simulated global climate data, which is naturally mapped onto a sphere. The algorithms may also prove useful for improving the vision of drones and autonomous vehicles that see objects in 3D, and for detecting patterns in data gathered from the irregularly curved surfaces of hearts, brains or other organs.

That's pretty cool stuff! If gauge theory sounds vaguely familiar, it may be because mathematician Karen Uhlenbeck made the news last year when she was awarded the Abel prize in mathematics, in part for her work in the field. If you're not already familiar with the concept of gauge invariance, or equivariance as physicists prefer to call it, the following video provides a blissfully short introduction:

If you want to know more about gauge equivariant convolutional networks and how they apply to deep machine learning, Michael Kissner's easy guide is a good place to begin exploring the topic.

Getting back to the main story, the math behind gauge CNNs are showing real promise in the applications to which they have been placed:

A gauge CNN would theoretically work on any curved surface of any dimensionality, but Cohen and his co-authors have tested it on global climate data, which necessarily has an underlying 3D spherical structure. They used their gauge-equivariant framework to construct a CNN trained to detect extreme weather patterns, such as tropical cyclones, from climate simulation data. In 2017, government and academic researchers used a standard convolutional network to detect cyclones in the data with 74% accuracy; last year, the gauge CNN detected the cyclones with 97.9% accuracy. (It also outperformed a less general geometric deep learning approach designed in 2018 specifically for spheres — that system was 94% accurate.)

Beyond weather monitoring, gauge CNNs may find use in advancing how AI-vision systems used in self-driving vehicles see the world, with their capabilities of processing what these systems are seeing in three-dimensions improving their safety performance.

The future is seemingly determined to have self-driving cars and other AI-powered devices in it. Having those things work well enough to be unremarkable is the real challenge.

Image credit: David Anderson

Existing home sales gained strength in the fourth quarter of 2019, with the estimated market capitalization of the existing home market in 49 states for which we have data appearing to have finally surpassed its previous March 2018 peak in November 2019.

State level data for existing homes sales lags the national data, which reports indicate leapt to their highest level in nearly two years in December 2019. Looking at recent trends for the five largest states for existing home sales, we find uptrends in Texas, Florida, New York and New Jersey, which we find has been prompted by increases in both the number of sales and in sale prices.

Given what has been reported for the national level data, we'll be excited to see what the data for these markets will look like through December when that data becomes available next month.

We've taken the available state level data and have built up regional level data from it. The next two charts show the aggregate value of existing home sales for the U.S. Census Bureau's Midwest and Northeast regions from January 2016 through November 2019:

The next two charts show the same data for the for the U.S. Census Bureau's South and West regions from January 2016 through November 2019.

The aggregated state level data confirms growing strength in the Northeast and South regions for the U.S. existing home market. In the Northeast, while New Jersey had the biggest gains, all states but Maine showed month-over-month increases. In the South, South Carolina and Louisiana lagged behind the general growth that took place in all the other states in the region in November 2019, where Maryland and the District of Columbia turned in very strong performances.

Our analysis is based on the existing homes sales and price data published by Zillow's research team, where they also provide data that drills down into the metropolitan level. Check it all out if you get the chance!

Two years ago, we announced the end of a relative period of order in the U.S. stock market. Two years later, there are signs that the chaotic period that followed may now be coming to an end. The following chart showing the daily value of the S&P 500 versus the index' trailing year dividends per share points to that possibility:

We're a bit reluctant to start drafting the statistical equilibrium thresholds that apply during relative periods of order in the U.S. stock market, mainly because the new order now taking form has arisen only because the U.S. Federal Reserve began buying large quantities of short-term debt securities issued by the U.S. Treasury in its return to a quantitative easing-like policy in October 2019, which is something it really doesn't want to do, but has to because it badly misjudged the markets' needs for liquidity.

How long that might last remains to be seen. For our part, we'd like to see a more typical level of 'orderly' volatility in stock prices before we overlay any statistical thresholds based on the developing period of relative order in the market.