# Intuition for Understanding Fractions

If you were to ask an adult to pick the point where their education in math started to go off the rails, more often than not, they will identify the point where fractions made their first appearance, often around the fifth grade.

In the image below, we see how one fifth grade student in Maryland ran into some trouble describing why the given fractions and mixed numbers should be put in the order they put them, even though they got that part of the answer correct.

Meanwhile, if you were to ask when they began to find doing math hard, they will probably identify the point in time where instead of equals signs, they started seeing inequality symbols, which comes after fractions are introduced, where the combination with fractions can prove to be pretty problematic, if not outright traumatic.

The good news is that it's never too late to develop the intuition that applies to both concepts, if we draw on the wisdom of renown maths professor Israel Gelfand, as conveyed by Edward Frenkel in Love and Math: The Heart of Hidden Reality:

"People think they don’t understand math, but it’s all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he won’t be able to tell you. But if you rephrase the question: what is better, 2 bottles of vodka for 3 people or 3 bottles of vodka for 5 people, he will tell you right away: 2 bottles for 3 people, of course."

That might work for adults, but if you're dealing with kids, the same insight still works if you substitute the vodka with cookies. Which if you think about it, can open the door for algebra for the adult student if you can get them to make that abstract connection....

# Cumulative Dividend Cuts At The Midpoint of 2019-Q2

We're just past the midpoint of the second quarter of 2019, where the pace of dividend cuts that have been announced to date in our near real-time sampling of these declarations is well ahead of the same point of time a year earlier in the second quarter of 2018. The following chart illustrates the cumulative number of dividend cuts by day of quarter for both 2018-Q2 and 2019-Q2, where we find that the cumulative number in 2019-Q2 is running near the threshold that would indicate recessionary conditions are present within the U.S. economy:

Here's the working list-to-date of our sampling through the midpoint of 2019-Q2, where the first part of our list focuses on firms that pay variable dividends to their shareholders, where changes in dividend payments automatically follow from changes in their revenues and earnings:

If you noticed, two of these firms appear in this listing twice, because they pay dividends to their shareholders monthly and have decreased their dividends in both April and May 2019.

The second part of the listing consists of firms who set the level of their dividends independently of their revenues and earnings, where reductions are purposefully set by their boards of directors.

We count 41 individual dividend cuts through the middle of 2019-Q2, with 22 announced by firms in the oil and gas sector, 13 in the financial sector (in which we group Real Estate Investment Trusts), and 4 from mining industry firms. Of the remaining two firms, one is in the chemical industry and one is a technology firm.

### References

Seeking Alpha Market Currents. Filtered for Dividends. [Online Database]. Accessed 22 May 2019.

Wall Street Journal. Dividend Declarations. [Online Database]. Accessed 22 May 2019.

# The 13 States Where Existing Home Sales Are The Strongest

We've began tracking existing home sales over the last several months, using Zillow's seasonally adjusted price and sales volume data to estimate the total aggregate valuation of these sales at the regional and state level in order to get a sense of the relative health of the real estate markets in these geographies.

Many of these markets have shown signs of having peaked in or around March 2018 for this equivalent measure of market capitalization, but thirteen states have, within the first quarter of 2019, seen their real estate markets for existing homes reach new highs. The following chart reveals the 13 states whose real estate markets have been the strongest in 2019, showing the trends for aggregate existing home sales in each from January 2016 through the latest data available for each in either February or March 2019.

Perhaps the most remarkable of these states is Washington, which had seen the market cap for its existing homes fall by 16% from a peak in March 2018 through October 2018, which has since rebounded strongly to reach a new peaks in February and March 2019, which we believe is attributable to a rapid decline in U.S. mortgage interest rates, which has made the high prices of the state's existing homes more affordable in recent months. Other states have shown a similar pattern to Washington over this period of time, including New York, Virginia, Massachusetts, and Ohio.

Other states have shown less volatility as the aggregate value of their existing home sales have grown to new heights, including Arizona, Michigan, Tennessee, Indiana, Alabama, Nebraska, Delaware, and Alaska.

The following charts shows our estimates of the peaks in the aggregate value of existing home sales in these thirteen states, and indicates the month in the first quarter of 2019 when it reached those record value.

These estimates are based on preliminary data, where Zillow's data is subject to revision as their sources update and report more complete information.

# Spring 2019 Snapshot of Expected Future S&P 500 Earnings

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

The earnings outlook for the S&P 500 through the end of 2019 has continued to deteriorate since our previous edition, where the projected trailing year earnings per share for the index in December 2019 has fallen to \$150.96 per share from the \$154.67 forecast three months earlier.

At the same time, we're getting our first look at Standard & Poor's projections for the S&P 500's earnings per share through 2020, which as of the data published on 15 May 2019, shows the S&P 500's trailing year earnings per share growing to \$167.97.

The last three months have seen the biggest downdraft in the projected growth of the S&P 500's earnings per share since the earnings recession of 2015-Q3 through 2017-Q2, which we've illustrated with the vertical light-red hashed lines where projected earnings in 2019 have fallen since our last update.

Given the deterioration in projected earnings per share in the nearer term, the current projection for trailing year earnings in 2019-Q4 looks conspicuously optimistic, where we would anticipate it will be revised significantly downward to be closer in line with the trend leading up to it by the end of the year.

As for what factors are eroding those projected future earnings, Lance Roberts has been drawing from the same data sources as we do to recap some very interesting analysis and forecasting:

Let me review what we said previously about the impact of a trade war on the markets.

“While many have believed a ‘trade war’ will be resolved without consequence, there are two very important points that most of mainstream analysis is overlooking. For investors, a trade war would likely negatively impact earnings and profitability while slowing economic growth through higher costs.”

While the markets have indeed been more bullishly biased since the beginning of the year, which was mostly based on “hopes” of a “trade resolution,” we have couched our short-term optimism with an ongoing view of the “risks” which remain. An escalation of a “trade war” is one of those risks, the other is a policy error by the Federal Reserve which could be caused by the acceleration a “trade war.”

In June of 2018, I did the following analysis:

“Wall Street is ignoring the impact of tariffs on the companies which comprise the stock market. Between May 1st and June 1st of this year, the estimated reported earnings for the S&P 500 have already started to be revised lower (so we can play the “beat the estimate game”). For the end of 2019, forward reported estimates have declined by roughly \$6.00 per share.”

The red dashed line denoted the expected 11% reduction to those estimates due to a “trade war.”

“As a result of escalating trade war concerns, the impact in the worst-case scenario of an all-out trade war for US companies across sectors and US trading partners will be greater than anticipated. In a nutshell, an across-the-board tariff of 10% on all US imports and exports would lower 2018 EPS for S&P 500 companies by ~11% and, thus, completely offset the positive fiscal stimulus from tax reform.”

Fast forward to the end of Q1-2019 earnings and we find that we were actually a bit optimistic on where things turned out.

The problem is the 2020 estimates are currently still extremely elevated. As the impact of these new tariffs settle in, corporate earnings will be reduced. The chart below plots our initial expectations of earnings through 2020. Given that a 10% tariff took 11% off earnings expectations, it is quite likely with a 25% tariff we are once again too optimistic on our outlook.

Over the next couple of months, we will be able to refine our view further, but the important point is that since roughly 50% of corporate profits are a function of exports, Trump has just picked a fight he most likely can’t win.

A more cynical interpretation of the politics involved is that the tax cuts bought the U.S. economy and stock market the space needed to accommodate the bipartisan-supported trade war, which is now being spent down.

It's a good thing that stock prices track along with expected future dividends per share and not expected future earnings per share, otherwise investors would already be in a world of hurt. If expected future dividends start significantly eroding, watch out below.

### Data Source

Silverblatt, Howard. Standard & Poor. S&P 500 Earnings and Estimates. [Excel Spreadsheet]. 15 May 2019. Accessed 19 May 2019.

# S&P 500 Goes On Volatile Ride With Fed Rate Cut Timing At Stake

The S&P 500 (Index: SPX) experienced an interesting level of volatility during the third week of May 2019, as investors shifted how far forward in time they're looking into the future twice during the week.

We consider an "interesting level of volatility" as being whenever the closing daily value of stock prices changes by more than 2% from the previous trading day's closing value, for statistical reasons, where the action on Monday, 13 May 2019 definitely qualified as such. As it happens, we were uniquely positioned to analyze the event, where we provided special coverage for it since the change in stock prices was accompanied by a change in investor expectations for the future, which prompted investors to shift how far forward into the future they were looking.

The quick summary of what happened on Monday, 13 May 2019 is that investors shifted their forward-looking focus from the distant future quarter of 2020-Q1 back toward the nearer-term future of 2019-Q4. Because several Federal Reserve officials had been communicating that it would cut interest rates if U.S. economic growth looked like it might suffer from the U.S.-China trade war, China's weekend announcement that it would launch new retaliatory tariffs against U.S. goods sharply increased the probability that the Fed would cut rates in or by 2019-Q4, which prompted investors to shift a portion of their forward-looking focus from 2020-Q1 to 2019-Q4. The rest can be explained simply by the math behind how stock prices work.

Picking up from that point, chart above reveals that investors next shifted their forward-looking attention back toward 2020-Q1, which was prompted by new information related to the strength of the U.S. economy, an easing of trade war-related worries, and a statement by a Fed official that they saw no need to change U.S. interest rates at this time.

By Thursday, 16 May 2019, the flow of news was such that investors had shifted their forward-looking attention back toward 2020-Q1 more fully, where the S&P 500 went on to end the week within the range of values our dividend futures-based model indicates would apply for when investors are largely focused on that future quarter.

That occurred even though investors are still placing better-than-even odds the Fed will cut interest rates well before the end of 2019, according to the CME Group's FedWatch Tool, where the probabilities table indicates investors are pushing out their expectations for the timing of a Fed rate cut to occur later than what they were betting the future would be on Monday, 13 March 2019. Here's the picture of those probabilities as of the close of trading on Friday, 19 May 2019.

We can reasonably expect interesting levels of volatility in stock prices to continue while investors shift their attention back and forth between these two future periods of time as the timing of the Fed's next interest rate move is at stake. And though these kinds of dynamics mystify former Treasury secretaries who labor under Keynes' antiquated animal spirits-based pagan belief system, they're really all you need to understand why stock prices have been behaving as they have at this time.

Here's our wrap-up of the major market-moving headlines from the trading week ending on 17 May 2019.

Monday, 13 May 2019
Tuesday, 14 May 2019
Wednesday, 15 May 2019
Thursday, 16 May 2019
Friday, 17 May 2019

There were more U.S. markets and economy news than that during the week that was, which Barry Ritholtz categorized into seven positives and seven negatives.