Political Calculations
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31 May 2019
Retirement Savings

What are the odds that your investment in the S&P 500 will last as long as you need in retirement?

The answer to that question depends upon the answers to three additional questions:

  1. What percentage of the balance of your funds invested in the S&P 500 you plan to withdraw from your retirement accounts each year?
  2. How long will your retirement last?
  3. What returns will the S&P 500 deliver over time?

The S&P 500 and its predecessor indices have been around long enough where we have historic data we can use to answer the last question, where we can assume the future will be similar to what has occurred in the past. That leaves the remaining factors, which have been addressed by Wade Pfau in his 2015 update to the 1998 Trinity Study, which estimated what a safe withdrawal rate would be for a variety of retirement portfolios made up of stocks and bonds with historic data from 1926 through 2014.

We've approximated the results of Pfau's math as it would apply for having 100% of your money invested in the S&P 500, where you can estimate the odds that the portion of your retirement nest egg invested in the S&P 500 will last as long as you might need to fund your retirement. If you're reading this article on a site that republishes our RSS news feed, click here to access a working version of this tool! (Alternatively, here's static snapshot of the tool with its results for the default data).

S&P 500 Investment Withdrawal Data
Input Data Values
Inflation-Adjusted Annual Withdrawal Rate
Expected Duration of Withdrawals [years]

Probability Your Retirement Fund Will Last
Calculated Results Values
Estimated Odds of Success

If you're like an average American, you can reasonably expect to live at least 15 years after you retire, so we've set that figure as the shortest period of time you can select in the tool. Meanwhile, the math assumes that you will adjust how much you might withdraw each year to account for the effect of inflation, where you would maintain a steady "real" withdrawal rate from your S&P 500 investment in retirement.

What the tool doesn't address is whether that percentage you might withdraw from your investment will provide the amount of income you would like to spend, where even if you might be successful in sustaining your S&P 500 investment, you might find yourself on the wrong end in the investing equivalent of one of Zeno's paradoxes as the balance of your retirement fund dwindles over time. Ultimately, the figure you have to work with will be set by the total you've accumulated in your investment before you might retire, where the following tools explore different ways to arrive at your personal retirement savings target.

We may come back at a future date to develop a tool that can accommodate having different percentages invested in stocks and bonds. If Pfau's data is any indication, there is a blend of the two types of investment vehicles that can produce better odds of success for a retirement fund that will last as long as your retirement than just the "stocks only" scenario we considered in this tool.

Meanwhile, if you'd like to get a better sense of some of the analysis that drives the math behind this tool, Paul Merriman works through a historical example with real life numbers and returns.

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30 May 2019

In April 2019, the initial raw data for median new home sale prices in the U.S. spiked sharply upward, rising to a new record high value of $342,200 - a nearly 12% increase over the second estimate of $305,800 for March 2019's median new home sale price.

Meanwhile, median household income in the U.S. likewise rebounded in April 2019 after having dipped in early 2019, rising to a new nominal high value of $64,019.

Calculating the trailing twelve month averages for both data series to smooth out month-to-month volatility, then finding the ratio of median new home sale prices to median household income, we find that new homes are nearly the most affordable that they have been since November 2013, the last time the median new home sold in the United States cost just under 5.1 times the income earned by a typical American household. The following chart shows the evolution of that affordability measure from December 2000 through April 2019, where we find the peak of "unaffordability" was reached just a little over a year ago, in February 2018.

Ratio of Trailing Twelve Month Averages for Median New Home Sale Prices and Median Household Income, Annual: 1967 to 2017 | Monthly: December 2000 to April 2019

In the next chart, we're showing the monthly data for trailing twelve month average for U.S. median new home sale prices from December 2000 through April 2019, plotted against the trailing twelve month average of U.S. median household income over the same period of time, which shows the relative improvement in affordability seen since April 2018 has come through a combination of declining new home sale prices and rising household incomes. April 2019's preliminary figures potentially mark a reversal in the recent trend for declining new home sale prices.

U.S. Median New Home Sale Price vs Median Household Income, Annual: 1999 to 2017 | Monthly: December 2000 to April 2019

What's driving the apparent rebound? If we were to pick one potential factor, it would be the rapid decline in U.S. mortgage rates that has taken place since they peaked in mid-November 2018, where they have now dropped nearly three quarters of a percent to just above 4.1% in April 2019.

30-Year Conventional Fixed Mortgage Rates in U.S., April 1971 through April 2019

The question now is whether that rebound represents either a sign of life or a dead cat bounce for the new home sales market in the U.S.?


Freddie Mac. 30-Year Fixed Rate Mortgages Since 1971. [Online Text]. Accessed 30 May 2019.

Sentier Research. Household Income Trends: April 2019. [PDF Document]. Accessed 30 May 2019. [Note: We've converted all data to be in terms of current (nominal) U.S. dollars.]

U.S. Census Bureau. Median and Average Sales Prices of New Homes Sold in the United States. [PDF Document]. 23 May 2019. Accessed 30 May 2019.


29 May 2019

The U.S. Treasury yield curve inverted between the 10-Year and 3-Month durations last week once again last week, shrinking the average spread between these two treasury securities over the last 90 days to 0.09%, its lowest level since early-to-mid-2007 when the yield curve signaled that a future recession would be likely to start sometime between then and early-to-mid-2008.

Through 28 May 2019, that combines with a much lower average level for the Federal Funds Rate over the last 90 days of 2.41% than was recorded back in mid-2007 to place the odds the U.S. economy will enter into a recession sometime between 28 May 2019 and 28 May 2020 at nearly one-in-twelve, or a little over an 8% probability, as shown in the latest update of the Recession Probability Track.

U.S. Recession Probability Track Starting 2 January 2014, Ending 28 May 2019

The Recession Probability Track is based on Jonathan Wright's 2006 paper describing a recession forecasting method using the level of the effective Federal Funds Rate and the spread between the yields of the 10-Year and 3-Month Constant Maturity U.S. Treasuries. If you would like to run your own recession probability scenarios, please take advantage of our recession odds reckoning tool which, like our Recession Probability Track chart, is based on Jonathan Wright's paper.

For example, the probability of recession we've discussed above does not take into account the amount of additional tightening that the Federal Reserve has achieved through its quantitative tightening policies which, if they had occurred in the form of interest rate hikes as some analysts have argued, would add add another three hundred basis points to the effective level of the Federal Funds Rate. Running our recession odds tool to consider that scenario with the same spread between the 10-Year and 3-Month treasuries, it finds that this shadow rate would coincide with a probability of recession occurring before June 2020 of 36.5%, which would be better than 1-in-3 odds.

We don't know how real an effect the shadow rate might have for predicting the probability of recession in the future, but it does provide an example of the kind of scenarios you can consider using the tools we've developed over the years.

Using the tools is really easy. Plug in the most recent data available, or whatever data would apply for a future scenario that you would like to consider, and compare the result you get in our tool with what we've shown in the most recent chart we've presented, which would be the official probability we obtained from using the available nominal data. Meanwhile, the links below present each of the posts in the current series since we restarted our series tracking the probability of recession in the U.S. back in June 2017.

Previously on Political Calculations


28 May 2019

Global financial markets experienced something of a "volatile shift" on Thursday, 23 May 2019, sending bond yields falling as the yield of the 10-Year Treasury dropped below the yield of the 3-Month Treasury as the inversion of the U.S. treasury yield curve suddenly expanded.

For the S&P 500 (Index: SPX), that shock prompted investors to once again draw in their focus from 2020-Q4 toward the nearer term futures of 2019-Q3 and Q4, where the prospects of a Federal Reserve rate cut in 2019 increased in response. The following chart from the CME Group's FedWatch Tool shows are now betting on future rate cuts happening sooner rather than later, which is a change in their forward-looking expectations since last week.

CME Group FedWatch Tool - Probabilities of Federal Funds Rate Changes at Selected Upcoming Federal Reserve Meetings - Snapshot 24 May 2019

Meanwhile, our spaghetti forecast chart shows the impact for the S&P 500, where we now find the level of the index falling about halfway between the levels the dividend futures-based model on which it based indicates would apply if investors were either focused exclusively on 2020-Q4, as they were as recently as the week before, or on 2019-Q3/Q4, for which our model forecasts nearly identical trajectories for the level of the S&P 500.

Alternative Futures - S&P 500 - 2019Q2 - Standard Model - Snapshot on 24 May 2019

That brings up an interesting possibility. What if the dividend futures-based model we use in forecasting the alternative futures for the S&P 500 captured stock market investors reacting to the volatile shifts before bond market investors caught on to it? As you can see in the chart above, it shows the shift taking place as a growing deviation from the trajectory the model indicates the S&P 500 would have taken if investors had remained tightly focused on the future quarter of 2020-Q1 in setting stock prices beginning from a week beforehand, which could potentially explain why stock prices then didn't fall by as much as the "violent treasury move" in the bond markets suggests they should have when that adjustment finally arrived.

That may be attributable to the higher-than-average level of new information feeding into the market during the trading week ending on Friday, 24 May 2019, where the last day of the trading week ahead of the U.S. Memorial Day holiday was the slowest news day for finding market moving headlines during the week that was.

Monday, 20 May 2019
Tuesday, 21 May 2019
Wednesday, 22 May 2019
Thursday, 23 May 2019
Friday, 24 May 2019

That's far from all the news affecting markets and the U.S. economy during the week. If you're looking for a bigger picture than the items we highlighted, check out Barry Ritholtz' listing of the week's five positives and five negatives that he found among the week's markets and economy-related news!

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24 May 2019

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.

School Improvement in Maryland - Grade 5 Mathematics - Sample Student Responses - Source: http://mdk12.msde.maryland.gov/assessments/k_8/grade5_math_sampleresponses.html

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."

 - Israel Gelfand

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....

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23 May 2019

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:

Cumulative Dividend Cuts Announced in U.S. by Day of Quarter, 2018Q2 vs 2019Q2 Year to Date, Snapshot 22 May 2019

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.


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

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


22 May 2019

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.

Estimated Market Cap of Existing Home Sales, 13 State Markets With Peaks in 2019-Q1, January 2016-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.

Estimated Total Valuation of Existing Home Sales Market, States Reaching New Peak Value During 2019-Q1

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


21 May 2019

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.

Forecasts for S&P 500 Trailing Twelve Month Earnings per Share, 2014-2020, Snapshot on 15 May 2019

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.”

Real Investment Advice - Lance Roberts - A Trade War Would Wipe Out Tax Cut Boost

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.

Real Investment Advice - Lance Roberts - Downside Revisions Wipe Our Tax Cut Benefits

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.

Real Investment Advice - Lance Roberts - Trade War Impact to Earnings Estimates

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.


20 May 2019

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.

Alternative Futures - S&P 500 - 2019Q2 - Standard Model - Snapshot on 17 May 2019

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.

CME Group - Federal Funds Rate Change Probabiblities Expected at Vairous Upcoming FOMC Meeting Dates - Snapshot on 17 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.

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17 May 2019

How many cats are prowling outside in your neighborhood? Or in your city? Or in your country?

That's a remarkably difficult question to answer, where the Wall Street Journal indicates the best estimates scientists have of the outdoor population of Felis catus, better known as the domestic house cat, are very far from being either accurate or precise:

In the U.S., estimates range from 40 million to 60 million; 30 million to 80 million; and 20 million to 120 million.

"It's a huge window," said Tyler Flockhart, an ecologist with the University of Maryland Center for Environmental Science. "And they're not even estimates. They're expert guesses based on very limited data."

At the end of the day, he said, scientists have to shrug and say this is the best information they have.

It's an important question to answer because Felis catus is a predator species, one whose prey includes birds and small mammals. To the extent that these hunted species overlap the list of endangered or threatened species, knowing the number of outdoor cats would better define the extent to which the populations of endangered animals are negatively impacted by their hunting habits, which in turn, could lead to more effective conservation efforts.

The WSJ article goes on to describe an effort to get an accurate count of the population of outdoor cats in the District of Columbia, which uses motion sensing cameras to conduct a census of the local cat population during a set period of time.

Accounting for the outdoor cats is the most complex part of the research. The project uses cameras to count cats in a given area over a certain period. Then, using a mathematical formula, the project extrapolates the total number of cats in the area by seeing what portion of the photographed cats show up on camera again.

The article provides the following infographic to describe the math developed by U.S. Geological Survey's Andy Royle to more accurate estimate the population of cats in the surveyed region from the sampling of images obtained by the network of motion-sensing cameras:

WSJ: Math to Estimate Population of Cats in Region from Sampled Images

We built the following tool to do that math, so if you want to estimate the size of a population you're interesting in tracking from a sample of it observed over a limited period of time, you can do the same math. If you're accessing this article on a site that republishes our RSS news feed, you can choose to either click through to our site to access a working version of the tool or to view a static screen shot of the tool with its results for the default input data.

Population Observed in Area During First Period
Input Data Values
Number of Observed Members of Population
Population Observed in Area During Second Period
Number of Observed Members of Population
Number of Previously Observed Members of Population

Projected Population
Calculated Results Values
Estimated Size of Population

The results of running the tool with the default input data confirms the results presented in the WSJ's infographic, but the cool thing about it is that the math can be applied to estimate the size of other difficult-to-measure populations, such as the endangered species that are believed to be negatively impacted by predatory house cats. Or even the total unsheltered members of a region's homeless population, whose numbers are currently counted in the U.S. during a single night in January each year by community canvassers.

Alone, such a canvassing approach is affected by the limitations of the canvassers, who might miss significant portions of the homeless population during the single period where they perform their count, resulting in an undercount in the official figures. Adopting a dual-period measurement approach could provide a better indication of how accurate the canvassers single-period counts are while also leading to a better overall estimate of the total homeless population using this kind of math.

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About Political Calculations

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:

ironman at politicalcalculations

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