Political Calculations
Unexpectedly Intriguing!
July 26, 2016

Each month, Gordon Green and John Coder of the private sector income and demographics analysis firm Sentier Research report on the level of median household income that they estimate from monthly Current Population Survey data published by the U.S. Census Bureau. We've found their estimates to be an invaluable aid for assessing various aspects of the relative real-time health of the U.S. economy.

We use their reports (the latest is for June 2016) to record a nominal estimate for median household income each month, which as future reports are released, we adjust for inflation as measured by the Consumer Price Index for All Urban Consumers in All U.S. Cities for All Items (CPI-U).

Since the beginning of 2016, we've been observing a developing trend for which we now have just barely enough data points to begin making relevant and useful observations, where we find that there are two developing stories. So you can see what we are seeing, here is a chart showing the evolution of median household income in both nominal and real terms from January 2000 through June 2016.

Monthly Median Household Income in the U.S., January 2000 through June 2016

The first and more important story is that nominal median household incomes would appear to have stalled out since December 2015, which is significant because it indicates that the U.S. economy has not been successful in generating higher paying jobs during the last several months.

The second story has to do with the changes in oil and fuel prices, which is greatly affecting the real median household income. In 2015, with those prices falling through much of the year, and particularly in its second half, the effect was to help boost the real incomes of Americans, where those incomes were also growing in nominal terms.

But in 2016, with oil and fuel prices having bottomed and rebounded since the beginning of the year, the effect has been to shrink the real incomes of American households.

Given that 2016 is a presidential election year, you can reasonably expect that whatever trends develop here throughout the year will have an impact on the election's results.


July 25, 2016

The S&P 500 in the third week of July 2016 ran a bit to the hot side for what our future-based model forecast, but still well within the typical volatility that we would expect. In the chart below, we find that investors are largely continuing to focus on the expectations associated with 2017-Q2 in setting current day stock prices. But we also see that our futures-based model is on the verge of a period of time during which we expect that it will be less accurate than it has been in recent months.

Alternative Futures - S&P 500 - 2016Q3 - Standard Model - Snapshot 2016-07-22

For the last several years, we have been developing a dividend-futures based model for projecting future values of the S&P 500, which incorporates historic stock prices to use as base reference points from which to project the future. More specifically, our standard model incorporates actual S&P 500 closing values that were recorded 13 months earlier, 12 months earlier and 1 month earlier than the period being projected.

In using those historic stock prices however, we have a huge challenge in coping with what we call the echo effect, which results when the historic stock prices we draw upon to create our projections are pulled from periods that experienced unusually high amounts of volatility. A good example of the kind of volatility we're looking to address would be the kind the market saw just a month ago from the market's reaction to the Brexit vote, but much more significantly, on the one-year anniversary of what the market experienced during China's meltdown back in August 2015.

To work around that looming challenge and to try to improve the accuracy of our forecasting model during the periods where we know in advance that our model's forecast results will be less accurate because of the echo effect, we're looking at substituting the actual historic stock prices in our model with prices that reflect the historic mean average trajectory of stock prices.

There's more than one way that we might go about that, but our initial idea is to simply replace the projections of our standard model during the that show the echo effect with the trajectory that would apply as if it were paralleling the mean historic trajectory of the S&P 500 as averaged over each of the last 65 years, which may minimize the discrepancies produced by historic noise between our model's projections and actual future stock prices (absent current day volatility events).

What we're doing assumes that the volatility of the past doesn't have much influence over today's stock prices, which itself is something we strongly suspect, but for which the supporting evidence is less definitive. We also don't know yet to what degree this approach will work, but we'll find out during this quarter. If you follow us, we typically post updates to our projections on Mondays, so you can find out how what we're doing is working almost at the same time we do. Here's the first chart where we're featuring this modified model, which we've imaginatively called "Modified Model 01".

Alternative Futures - S&P 500 - 2016Q3 - Modified Model 01 - Snapshot 2016-07-22

Because the context of how far forward investors are looking in time is so important to determining which of the alternative trajectories that the S&P 500 applies, we make a point of recording the headlines that catch our attention for their market moving potential influence each week. Here are the headlines we identified during Week 3 of July 2016, where much of the news cycle was dominated by reports from the Republican National Convention in Cleveland, Ohio. If you're a serious market investor, you should note how none of them have anything to do with any of the political news from the week, which was a non-event as far as the market was concerned!

Monday, 18 July 2016
Tuesday, 19 July 2016
Wednesday, 20 July 2016
Thursday, 21 July 2016
Friday, 22 July 2016

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July 22, 2016
Solenoid Perfectoid Space - Source: MSRI - https://www.msri.org/system/cms/files/83/files/original/141109_Emissary-Fall-2014-Web.pdf

There are some really exciting developments starting to bubble up like perfectoid spaces in mathematics.

Talk about a sentence that we never thought we'd ever write, because:

  1. The concept of perfectoid spaces has only been around since 2010, having been introduced in a remarkable paper by then-grad student Peter Scholze.
  2. They've gone from newly introduced exotic concept to powerful tool in an amazingly short period of time.

It's that second thing that's motivated us to write on the topic today.

Here's the best, simplest description we could find of what they are (we've added the links to good starting point references for the different mathematical fields mentioned):

Scholze’s key innovation — a class of fractal structures he calls perfectoid spaces — is only a few years old, but it already has far-reaching ramifications in the field of arithmetic geometry, where number theory and geometry come together.

By far reaching ramifications, they're referring to the use of the new tool to greatly simplify mathematical proofs, such as Scholze did in rewriting a proof of the Local Langlands Correspondence, which had originally required 288 pages, in just 37 pages.

That's possible because of what perfectoid spaces can do in being able to transform very difficult math into much easier math to do, which was Scholze's breakthrough in the field (we've added some of the links in the following passage again for reference purposes).

He eventually realized that it’s possible to construct perfectoid spaces for a wide variety of mathematical structures. These perfectoid spaces, he showed, make it possible to slide questions about polynomials from the p-adic world into a different mathematical universe in which arithmetic is much simpler (for instance, you don’t have to carry when performing addition). “The weirdest property about perfectoid spaces is that they can magically move between the two number systems,” Weinstein said.

This insight allowed Scholze to prove part of a complicated statement about the p-adic solutions to polynomials, called the weight-monodromy conjecture, which became his 2012 doctoral thesis. The thesis “had such far-reaching implications that it was the topic of study groups all over the world,” Weinstein said.

When we discuss math, we like to focus on the practical applications to which it can be put. In this case, mathematician Bhargav Bhatt, who has collaborated with Scholze on several papers, gets to the bottom line for why perfectoid spaces will matter for solving real world problems (reference links added by us again).

Namely, as perfectoid spaces live in the world of analytic geometry, they actually help study classical rigid analytic spaces, not merely algebraic varieties (as in the previous two examples). In his “p-adic Hodge theory for rigid-analytic varieties” paper, Scholze pursues this idea to extend the foundational results in p-adic Hodge theory, such as Faltings’s work mentioned above, to the setting of rigid analytic spaces over Qp; such an extension was conjectured many decades ago by Tate in his epochmaking paper “p-divisible groups.” The essential ingredient of Scholze’s approach is the remarkable observation that every classical rigid-analytic space over Qp is locally perfectoid, in a suitable sense.

Which is to say that a whole lot of problems that have proven to either be very difficult to solve or have evaded solution by other methods might yield easily to solution by the newly developed mathematical theory of perfectoid spaces. For a field like mathematics, that's a huge deal!

We'll close with Peter Scholze speaking on perfectoid spaces in 2014.


July 21, 2016

We have a new example of junk science today, which might perhaps be better described as bad analysis that checks off one of the more significant boxes in our junk science checklist. Specifically, today's example trips over the checklist category for Inconsistencies, which is where we are most likely to find the effects of deceptive maths and abusive statistics.

How to Distinguish "Good" Science from "Junk" or "Pseudo" Science
Aspect Science Pseudoscience Comments
Inconsistencies Observations or data that are not consistent with current scientific understanding generate intense interest for additional study among scientists. Original observations and data are made accessible to all interested parties to support this effort. Observations of data that are not consistent with established beliefs tend to be ignored or actively suppressed. Original observations and data are often difficult to obtain from pseudoscience practitioners, and is often just anecdotal. Providing access to all available data allows others to independently reproduce and confirm findings. Failing to make all collected data and analysis available for independent review undermines the validity of any claimed finding. Here's a recent example of the misuse of statistics where contradictory data that would have avoided a pseudoscientific conclusion was improperly screened out, which was found after all the data was made available for independent review.

The following analysis shows the importance of the work that is often done in near-anonymity to replicate and validate the results of analysis where unique findings are made, which is only possible when the data behind the analysis is available. Unfortunately, today's example of junk science won't be the last time we'll be discussing an example in this category, thanks to the special efforts of a repeat offender.

Let's get to it then, shall we?

Everyone knows about lies, damned lies, and statistics. The quote has been attached to Mark Twain who apparently attributed it to British Prime Minister Benjamin Disraeli. It remains among popular clichés because there is universal truth to it, a sort of caveat emptor lying in the background whenever one consumes an argument. Nowhere is that more the truth than economics and finance, disciplines almost (nowadays) entirely populated with statistics and very little else.

Given the rather extreme nature of the times, extreme statistics are more prevalent perhaps than at any other point. They run the spectrum, as do human intentions, from the purely mistake to the malicious. The better stats, as the best lies, are often difficult to discern because they contain a great deal of truth; requiring a great deal of further analysis and scrutiny to unpack the error or mistake. Sometimes, however, it takes very little effort (reflecting both on the numbers and the person wielding them).

Prominently displayed on the front page of Yahoo! Finance recently was an article whose purpose was just so barely disguised. You can and should read the whole piece, but the gist is essentially that we shouldn't worry about very high valuations to the current stock market because valuations aren't so simple. The expert quoted in the article declares that PE's at this point, well above 20x, "do not contradict the bullish case for stocks." The reason is low inflation and related low interest rates; an argument proposed and reiterated many, many times before.

There are statistics for this view, including a neat chart showing the relationship between PE's for the S&P 500 and their coincident inflationary circumstances (represented by the 1-year change in the CPI).

Inflation vs. S&P 500 P/E Ratio (Jan. 1965 through Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Yahoo.jpg

Using Robert Shiller's data for the historical S&P 500, inflation, and earnings, I recreated the same chart with very nearly the same results.

PE vs. Inflation (Jun. 1965 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Yahoo-65-16.jpg

Running a simple, exponential regression (a polynomial regression finds a better fit, but raises the objection of being fitted), you do find a relationship that argues in favor of the proposition; inflation and PE's are to some degree negatively correlated.

PE vs Inflation with Regression (Jun. 1965 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Regress-65-16.jpg

Because I found the same as projected in the article, I can confidently declare it nonsense. I did not test for statistical significance in the regression because it simply wasn't necessary; this argument falls apart long before the math.

This is simply a case of, at best, circular logic or, at worst, intentional obfuscation. The first clue is the time frame itself, starting right on the cusp of the Great Inflation. Given the much further history of Shiller's data, we need not be so discerning. Going back further to the 1870’s provides a much different result.

PE vs Inflation (Jan. 1872 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Full.jpg

The regression using this full dataset is far, far less compelling. You don’t even need the regression to see the distribution – the densest area of the scatterplot above is between 0% and 5% inflation and 10 and 20 times earnings.

PE vs Inflation with Regression (Jan. 1872 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Full.jpg

There is still, however, some mathematical relationship even though the R-squared is especially low. If we perform our own transformations in framing the time period, this apparently inverse correlation is revealed more clearly. If we instead end with only through the last part of the Great Inflation, to December 1979, we actually find very little to support the hypothesis.

PE vs Inflation (Jan. 1872 to Dec. 1979) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-1872-1979.jpg

There is actually very little reasonable correlation between inflation and PE's to this point in history; a slightly detectible hint but without a whole lot of variation. Notably absent are those more extreme, higher valuations that perform the upward transformation in the original regression. Moving forward in time to December 1994, we find some indication of a greater cluster starting to move up the axis (the Great "Moderation"), but still nothing like the original premise.

PE vs Inflation (Jan. 1872 to Dec. 1994) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-1872-1994.jpg

It isn’t until we add the latter half of the 1990’s and the dot-com bubble that these “positive” valuation outliers suddenly appear (the rest of them don’t show up until, ironically, the Great Recession when earnings fell very far in coincidence to disinflation and even negative inflation). This is, of course, wholly unsurprising.

PE vs Inflation (Jan. 1872 to Dec. 2000) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-1872-2000.jpg

But there is more to the deception, which is why the Great Inflation period was included. If we isolate just age of asset bubbles, the relationship once more disappears almost entirely.

PE vs Inflation (PE Bubble) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Bubble-1.jpg

PE vs Inflation (PE Bubble with Regression ) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Bubble-Regression.jpg

A regression function that plots almost vertically means that PE valuations have moved around almost totally independent of the CPI. In other words, without including the Great Inflation period and its immediate aftermath to fill in the bottom right there is again no mathematical significance between inflation and PE's. In isolation, the market valuation since 1995 just doesn't bear any resemblance to inflation, leaving it as a function of some other independent condition (such as monetary agency). It is only by included the “other” extreme of low valuations and high inflation of the 1960’s and 1970’s that gives this assertion of causation the thin veneer of validity.

But that is hardly the same scheme as what was proposed. What these figures show is really much different; from 1965 forward, the most that can be said is that there were generally lower valuations as high consumer inflation raged before the 1980’s. After 1995, there was generally much higher valuations and lower inflation. It does not follow, then, that valuations are determined by inflation – at all. Causation would appear to be among the “error” terms or more likely independent variables left out entirely, which is what the full data set suggests. There is no data suggesting what valuations would do with very high inflation (recorded in the CPI) after 1995 because it hasn't happened; likewise with low inflation during especially the 1970’s.

These are cases, then, that must be taken in isolation, not as a universally-applied “rule” or even suggestion. To add one is a blatant misuse of correlation, again an indictment first suggested by starting with and only including the period after January 1965. Including the Great Inflation and its opposite extreme muddies the interpretation because you can't immediately discern the separate circumstances as separate. To claim that low inflation after 1995 supports high valuations is tantamount to wholly biased selectivity; there is no evidence to prove (or disprove) the assertion, an invalidation in statistics as well as basic logic. All the math shows is that there was low inflation.

That is really what the full data tells us, with one very important contextual addition. Comparing the years without the dot-com bubble and finding very little relationship means that it is only through the high valuations of the dot-com era (and to a lesser extent more recently) that gives this idea its apparent (and still wrong) relevance. That would mean the original premise contained in the article is using the incident high valuations of the dot-com bubble because they occurred during a period of low CPI inflation to propose that high valuations today aren't threatening because we still find low CPI inflation. It essentially advises that the last big stock bubble justifies why we shouldn't be worried about another one.

That was Twain's, as Disraeli's, point all along. If you have a strong argument you don't need to resort to bad math to make it; bad math is instead used, often intentionally, to obscure the weakness.


Snider, Jeffrey P. Valuation Fallacies. Alhambra Investment Partners. [Online Article]. 18 July 2016. Republished with permission.

Shiller, Robert. U.S. Stock Markets 1871-Present and CAPE Ratio. [Excel Spreadsheet]. Accessed 18 July 2016.

Political Calculations. How To Detect Junk Science. [Online Article]. 19 August 2009.


July 20, 2016

Nearly a month ago, we presented our "most likely" prediction for how the U.S. Bureau of Economic Analysis will revise the U.S.' Real Gross Domestic Product on Friday, 29 July 2016.

Let's recap what we forecast, picking things up from after we described how we went from estimating the "maximum potential" size of the revision to the "maximum likely" size of it, before we drilled down to what we think will be the "most likely" amount by which real GDP will be revised through the fourth quarter of 2015:

Previously Reported and Revised Real GDP, 2005-Q1 Through 2015-Q4, per BEA Regional Data released on 2016-06-14, Revised to Account for 'Overseas' GDP, with Date Correction - was 14 June 2015, now corrected to 14 June 2016 - previous chart here: https://2.bp.blogspot.com/-EzKqOVcLGC4/V2XJce71MhI/AAAAAAAANkk/uxCWYmwSK98c6baRUFRi1-NmNArdwz1qgCLcB/s1600/Political-Calculations-2016-GDP-Revision-Projection-spanning-2005Q1-to-2015Q4.png

But the "maximum likely" revision of -1.4% of previously reported GDP through 2015-Q4 is not the "most likely" size of the upcoming revision to the nation's GDP will be, because the BEA's plans for the revision of the national level GDP data will only cover the period from 2013-Q1 through 2016-Q1.

That means that it will miss the discrepancy that opens up in 2012-Q3 and 2012-Q4 between the just-revised state level GDP and previously indicated overseas federal GDP and its previously recorded national level GDP. That discrepancy is just over $55.1 billion in terms of constant 2009 U.S. dollars in 2012-Q4, which itself is over 24% of the full $225.7 billion discrepancy that our previous calculations indicates between the pre-revised national level real GDP and the post-revised state level GDP data through 2015-Q3.

Because the BEA won't be including that $55.1 billion portion of the discrepancy from 2012, the "most likely" size of the revision that it will report at the end of July 2016 is therefore -1.1%, which is 24% less than the "maximum likely" revision of -1.4% we previously calculated.

After the BEA's annual revision of GDP for the 50 states and the District of Columbia on 14 June 2016, there is only one factor left that can affect the amount by which the BEA will actually revise the nation's total real GDP next week - the contribution of overseas federal military and civilian government activities, or as we've described it, the "hidden GDP of war".

There are three scenarios in how that one factor can play out:

  1. If that contribution is greater than what the BEA has previously indicated, the amount by which real GDP through 2015-Q4 will be adjusted will be smaller. So instead of being reduced by 1.1% as we've projected to be "most likely", it would instead be reduced by a smaller percentage, or in the very unlikely case that contribution is much, much greater, real GDP through 2015-Q4 could be adjusted upward. For this scenario to occur, it would mean that the U.S. government was much more engaged in fighting wars overseas in a way that adds to the nation's GDP than it has previously indicated. This is the "under" scenario.
  2. If that contribution is less than that the BEA has previously indicated, the amount by which real GDP through 2015-Q4 will be adjusted downward will be larger, going in the direction of what we calculated would be the maximum likely revision. For this scenario to occur, it would mean that the U.S. government was engaged in less "productive" military and civilian government activities overseas than it has previously indicated. This is the "over" scenario.
  3. If the contribution is the same as what the BEA has previously indicated, then we'll see the "most likely" scenario we calculated be the actual result. Real GDP through 2015-Q4 would be decreased by about 1.1% from the level that was recorded earlier this year on 29 March 2016. This might be considered the "null" scenario.

To make that question more interesting, we asked our most dedicated readers [1] to click through and answer a SurveyMonkey poll, which we've now closed. The results of that poll are presented in the following chart.

SurveyMonkey Poll Results

As you can see, our poll produced a 40-40-20 split. 40% of the poll participants indicated they thought Scenario #1 was more likely, 40% predicted Scenario #2 would be a reality, and 20% believed in the Scenario #3 "no change from our forecast outcome" outcome.

While those results seem nearly split down the middle, what they really indicate is that the majority of the poll participants believe that the actual adjustment to real GDP through 2015-Q4 will be different from our "most likely" forecast for the size of the July 2016 national revision. What is equally split down the middle is the direction in which it will be adjusted, with no clear collective prediction emerging from our poll.

Where is Philip Tetlock when you need him?


[1] We had problems with generating working code to embed the survey directly in our post, so we were stuck with providing a link for readers to click through to participate in the survey. That's the sort of hassle that only the most dedicated readers would endure, so we greatly appreciate the extra effort on the part of all the participants who registered their own prediction for how this one aspect that will affect the actual size of the upcoming GDP revision. Thank you!


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