Political Calculations
Unexpectedly Intriguing!
30 September 2015

In 2013, poor Americans received the equivalent of $412 billion worth of welfare benefits from the U.S. government, which it raised through a combination of taxes, fees and borrowing. The chart below details how that breaks down among the federal government's various welfare programs.

Major Federal Welfare Programs, Fiscal Year 2013

To visualize that data, we experimented with the tools available at IBM's Watson Analytics site, the successor to our old favorite ManyEyes. Here's the treemap we generated:

U.S. Welfare Spending by Program Treemap, FY 2013

If that $412 billion were equally divided among the 86.6 million Americans whose incomes are equal to or less than 138% of the official federal poverty level, they would each receive $4,758.

If we just focus on the top four welfare programs, Medicaid, Supplemental Nutrition Assistance Program (SNAP, or perhaps best known as "food stamps"), Temporary Aid for Needy Families (TANF) and Section 8 Housing Choice Vouchers, a national average of $4,018 is spent to benefit poor Americans, representing 84% of all major welfare program spending.

Data Source

Furchtgott-Roth, Diana. Welfare in America, 1998-2013. Figure 1. Major Federal Welfare Programs, Fiscal Year 2013. Manhattan Institute: Economic Policies for the 21st Century, e21 Issue Brief, No. 3. [PDF Document]. January 2015.


29 September 2015

In several major U.S. cities, police are beginning to use math originally developed to predict earthquakes to fight crime. Or more specifically, the kinds of crime that occur in either series or sprees that tends to be concentrated within a defined region, such as burglaries or gang-related violence.

If you live in Los Angeles there are two things you might feel particularly worried about: earthquakes and crime. It's nice to know, then, that mathematics can help to keep you safe from both. A software system called PredPol, that has been developed by the mathematician George Mohler, the anthropologist Jeff Brantingham, and others, is now being rolled out across multiple jurisdictions of the Los Angeles Police Department and in other cities too. Officers on the ground use it every day.

PredPol stands for "predictive policing". It works by calculating the probability that crimes will be committed in a particular area on a particular day, based on real-time data from the previous couple of days. Police officers are then given prediction maps telling them where the probability is high, so they can put in place extra patrols and hopefully prevent at least some of those crimes from happening.

The initial results of using the math-based approach to directing police activity would appear to have some promise. After being introduced in the Los Angeles Police Department's Foothill Division in 2011, after having seen its violent crime rates rise significantly in 2010 as the city reduced its budget for policing the area, the incidence of crimes fell by 13% in the first four months after the division implemented the PredPol software, while crime elsewhere in the city rose by 0.4%. That reduction came as the city further reduced its policing budget in 2011.

More recently, the LAPD Foothill Division saw a 20% reduction in the level of predicted crimes in the year from January 2013 to January 2014. According to PredPol's marketing, other cities where the predictive crime software has been introduced have reported similar experiences.

+Plus Magazine's Marianne Freiberger describes how the math behind the software works.

To get a feel for how this works, let's concentrate on something that's rife in LA and other big cities too: gang crime. Fierce battles over territory are central to gang violence, and whatever one gang does to another, retaliation is sure to follow. That latter point is what makes gang violence similar to earthquakes: acts of violence come with follow-ups, just as earthquakes come with aftershocks.

Earthquakes can be described mathematically as self-exciting processes. They are events that happen over time as a result of all sorts of complex factors we don’t really understand. So we might as well treat them as random processes. What we do know, however, is that once an earthquake has happened, the chance of another one (an aftershock) goes up, at least in the immediate future. That’s the self-exciting part.

There’s a mathematical technique for dealing with self-exciting sequences of events, called a Hawkes process, which you can also apply to the rivalry between two gangs. The idea is to treat acts of violence between the gangs (it doesn’t matter which way around) as a sequence of events in time. What you are after is a rate function r(t), which essentially measures the chance that a crime happens at time t, with that chance depending on what happened previously (because the process is self-exciting). We usually think of a rate as the number of events over a given time interval, for example the number of crimes we expect to happen per day. In this case, however, the time interval is made infinitesimally small. So you can think of the rate function r(t) as the instantaneous rate at which we expect crimes to happen at time t.

The idea now is to express the rate function as a sum: the first term of the sum is the background rate of crime: that’s the rate at which unprovoked attacks between the two gangs happen, ignoring any retaliations. The other terms in the sum correspond to the amount by which any previous violation between them raises that background rate. These reflect the self-exciting part (the retaliations). The longer ago a particular attack happened, the smaller its contribution to the rate function at time t....

Once you have the parameters, you can use the rate function to simulate crimes between two gangs as sequences of events in time. The crimes happen randomly by chance, but that chance isn’t the same for all times t, rather it’s given by the rate function. By seeing how the simulated patterns of crimes compare to real data you can assess how well your model does at describing reality (there are standard statistical methods for making that comparison). And once you’re happy the model does reasonably well, you can use it to predict what will happen in the real world and, hopefully, intervene.

The same math works for property crimes like burglary as well, where criminal offenders will often case a defined region before their crime sprees to identify their targets of opportunity before working through them in a relatively short period of time.

On a final cautionary note, we can't help but think in reading through PredPol's success stories of when the software is introduced in some areas of a city but not others, which see crime fall where PredPol is directing police activity but also see general crime rates rise elsewhere, that the use of the software might in fact be partially responsible for those increases. Much like squeezing a water balloon in one spot causes it to expand everywhere else, as those seeking to conduct criminal activities moved away from where the police presence has been concentrated. In that sense, what the results suggest is that simply providing an effective police presence provides a deterrent to crime, which is something that doesn't require an investment in software.

But that's not the whole story. It is also important to recognize the budgetary environment in the city of Los Angeles during the period when the software was being introduced, where the money to fund policing activities across the whole city was being reduced. That crime in the area where resources were concentrated was reduced while only expanding rather modestly everywhere else suggests that the predictive crime software does provide a real benefit in making more efficient use of the city police department's limited resources.

That's a winning story in anybody's anti-crime playbook.

Update 17 September 2019: The PredPol algorithm discussed above is not living up to its initial promise. In practice, it appears to have a Garbage-In-Garbage-Out (GIGO) problem. (Apologies for not linking to our update earlier!)


Freiberger, Marie. Crimes and earthquakes. +Plus Magazine. [Online Article]. 11 August 2015. Accessed 29 August 2015.

International Association of Crime Analysts. (2011). Crime pattern definitions for tactical analysis (White Paper 2011-01). Overland Park, KS. [PDF Document].

McNeely, Jim. Your Home Security - Never Before Revealed - How Burglars Case Homes. [Online Article]. 13 July 2011. Accessed 29 August 2015.

National Science Foundation: UC Mathematical and Simulation Modeling of Crime Project - https://www.nsf.gov/news/news_images.jsp?cntn_id=116357&org=NSF

Image Credit: National Science Foundation: UC Mathematical and Simulation Modeling of Crime Project.

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28 September 2015

For the S&P 500, the week ending 25 September 2015 went pretty much as well expected, as the index' value remained well within the range we indicated it most likely be a week ago.

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot on 25 September 2015

Really, the most interesting day of the week was Friday, 25 September 2015, when stock prices opened the day up thanks to Janet Yellen's speech the evening before, in which she indicated that the Fed would seek to raise interest rates before the end of 2015-Q4.

But then, something overrode that expectation after 2:08 PM that day, and the S&P actually closed lower for the fourth consecutive day, as whatever was plaguing health insurers and pharmaceutical companies throughout the day caught up to the bigger market-cap players in those industries.

Speaking of which, four consecutive down days is something that the market has only a 1.3% (or a 1 in 73) chance of doing.

And while the range we indicated left plenty of room for the market to have one or more up days, our model suggests things should be a little bit better through the end of the month. At least in the absence of a significant change in the expected future dividends that are the fundamental driver of stock prices or an outburst of market moving noise, where the worst outcome would be news that drove investors to focus upon 2016-Q1 for whatever reason.

Most likely, unless new information resolves the current split in the forward-looking focus of investors, the actual trajectory of stock prices will fall somewhere between the trajectories indicated for a strong focus on either 2015-Q4 or 2016-Q1. Janet Yellen tried her best, but alas, fell short.

And with that, we won't be discussing the S&P 500's actual trajectory during the next couple of weeks, as we'll be jumping ahead in time to check back in with the index after 2015-Q4's earnings season is officially underway, and also because we already have.

Tenses are difficult, aren't they?

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25 September 2015

Have you ever had a hands-on project and needed to draw perfectly parallel lines by hand? Or needed to lay out a circle without a compass? Or to bisect something other than a right angle without a protractor? Designer, builder and occasional TV host Jimmy Diresta shows how:

As a bonus, you'll also finally find out why the end of your retractable tape measure has that little tiny niche in it and what you can do with it!


24 September 2015

October is often the most volatile month for U.S. stock prices. The reason why that's the case is because fourth quarter earnings season, which begins each year in the second week of October, is the time that publicly-traded U.S. firms announce if they are doing better or worse than expected for the year.

It's called the October Effect, and from the data we have at this point of time, it looks like 2015 will be a year in which the market may be prone to crashing during the month.

We're looking at two specific industrial sectors of the stock market to make that assessment: manufacturing and oil.

For manufacturing, Mike Shedlock has put together a quick roundup of the latest Bloomberg news service reports, which we've linked here for convenience, covering the home regions of the Philadelphia, New York, Dallas, Kansas City, and Richmond branches of the U.S. Federal Reserve.

The one consistent theme in each of these surveyed regions is that the manufacturing sector of the U.S. economy is considerably underperforming analyst expectations.

Meanwhile, there hasn't been much noise from the U.S. oil industry lately, as the falling prices that had troubled the industry beginning in mid-2014 had stabilized earlier in the year, but which have resumed falling sharply during the last two months.

And though we won't hear much from the industry until Schlumberger takes the lead on reporting its earnings on 15 October 2015, the following Reuters article regarding the French national oil producer Total may provide a preview of what to expect:

French oil major Total has cut its capital and operating expenses again in response to low oil prices and trimmed its ambitious output growth targets but reassured the market that its dividend was safe.

The cost cutting deepens previous steps taken by Total to withstand the oil price rout and is similar to measures taken by rival majors. So far only Italian firm Eni has cut its dividend among oil majors, most of whom see the payout to shareholders as the chief factor supporting share prices.

"We cannot control the price of oil and gas but we can control our costs and allocation of capital," Chief Executive Officer Patrick Pouyanne told investors in London on Wednesday.


Total said in a presentation to investors and media in London that it would reduce capex to $20-21 billion from 2016 and to $17-19 billion per year from 2017 onwards compared with $23-24 billion in 2015 and a peak of $28 billion in 2013.

The important information to take away here is that the troubles in the oil industry and manufacturing industry are not independent of one another. Larger than previously expected reductions of capital investments in the oil industry, driven by the need for oil industry companies to control their costs to remain profitable in the face of falling revenues resulting from falling global oil prices, is spilling out of the sector into the manufacturing industry through much fewer than expected orders for new equipment.

If, like Total, U.S. firms can cut back their costs of business without reducing their dividends, U.S. stock prices will simply follow their current slowly falling trend, as companies in more than one sector of the market have their profit margins squeezed in the current revenue environment. But, if they're not able to cut their costs by enough to avoid significant dividend cuts, particularly at the largest market cap weighted firms in the U.S. oil industry, then we can expect an outsized and negative response in U.S. stock prices.

Most announcements coming out of the troubled oil industry will be occurring during the last half of October 2015, which will be the most likely period in which negative volatility will rear its ugly head in the stock market.

That assumes that the U.S. Federal Reserve or other central banks (most notably the People's Bank of China) will not seek to shore up the future outlook for businesses by announcing new rounds of quantitative easing or adopting other economic stimulus measures as they have done in ways that also boost stock prices on previous occasions.

If so, that will be quite a reversal of the direction of the policies that they currently have in place.

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23 September 2015

Each summer, American farmers harvest millions of bushels of wheat. But those bushels don't head straight to the market for sale - the wheat is first processed, transforming it from an agricultural product into the non-durable goods that consumers can actually buy at the markets where they shop.

Two years ago, Katie Taube of KSN-TV told the story of how wheat goes from field to flour.

WICHITA, Kansas — Now that the Kansas wheat harvest is over, much of that grain is going to Horizon Mill in Wichita for flour production.

“Sometimes if it’s really busy we can do anywhere from 90 trucks a day,” says truck dump operator, Charlene Johnson.

How much wheat is that really? After describing what the mill does to transform the wheat into consumable flour, Taube details what they do to move the pure flour they've milled onto the next stage of its journey to become the products you buy in your local grocery store.

The pure flour then fills two 50,000 pound holding tanks before getting loaded onto trucks.

“It takes about 20 minutes from when I start a load to go through everything and get loaded in the truck,” says bulk loader Jason Clark.

The trucks are regulated for cleanliness.

And if a 50,000 pound truckload isn’t enough, there’s options.

“We can load anywhere from 180,000 to 210,000 pounds of flour on a rail car,” says Jason.

Doing some quick math, since a single bushel of wheat can produce as much as 42 pounds of flour, each single truckload of wheat flour being shipped out represents approximately 1,190 bushels of wheat. Since a large semi can carry 910 bushels of wheat, we find that about 76% of each truckload of wheat into the mill is actually converted to flour that is shipped out.

At up to 90 trucks per day, that works out to be 81,900 bushels of wheat arriving daily which, if it could all be milled in one day before being shipped out to its next stage of production, would add up to 3.44 million pounds of wheat per day, which would take 69 trucks to deliver.

Considering a different metric, since a 5 pound bag of flour is a pretty standard size U.S. consumers can buy at a typical grocery store, at that peak production rate, that's the equivalent of 687,960 bags of flour.

But a large portion of the wheat that arrives daily during harvest season is stored, where it is milled into flour at other times of the year to better match the demand of consumers for wheat flour. Even so, it's still an enormous daily operation that impresses the people who work at milling bushels of wheat into flour with its scale and scope.

Even people who’ve worked at Horizon Mill for more than a decade still appreciate the process that feeds people across the world.

“To see the wheat and everything it’s just neat and how they make it, it’s nice yeah,” says Charlene.

The Horizon Mill plant in Newton packages smaller quantities of flour, like the sacks of Wal-Mart brand flour you see at the store.

More than two-million pounds of flour are produced every single day at Horizon Mill.


InvestorWords. Non-durable Good Definition and Examples. [Online Text]. Accessed 14 August 2015.

Taube, Katie. KSN.com. From Field to Flour; How Kansas Grain Feeds the World. Online Article]. 23 July 2013. Accessed 14 August 2015.

Tennessee-Tombigbee Waterway Shipping Comparisons. [Online Text]. Accessed 14 August 2015.

Tom Morton harvests wheat on his farm near Oxford, Kan., Friday, June 13, 2003 - Source: http://photos.state.gov/libraries/usinfo-photo/39/week_5/020107-farming-500.jpg

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22 September 2015

Up until a week ago, if a publicly traded U.S. company was announcing it was cutting its dividends, we would have almost automatically assumed, based on what we've observed since the first quarter of the year, that it was an oil industry-related firm.

But now, we can't automatically make that assumption because for the first time since late 2013 and early 2014, we've seen a significant increase in the number of Real Estate Investment Trusts (REITs) announcing that they will be cutting their dividends.

In fact, of the eight firms we counted as taking such action in the last week (via Seeking Alpha's Market Currents, filtered for dividends, and the WSJ's dividend declarations database, five were REITS.

The reason that's significant is because a number of REITs are especially sensitive to interest rate hikes, with the announced dividend cuts lagging several months behind when interest rates have risen.

In fact, from late 2013 all the way up to November 2014, after which the U.S. oil industry claimed the title of being the most distressed sector of the U.S. economy, and a brief increase at the end of first quarter of 2015, we really haven't seen very many REITs listed among the U.S. firms announcing dividend cuts until the past week.

Here's the short list: Hatteras Financial (NYSE: HTS), Invesco Mortgage Capital (NYSE: IVR), Ellington Residential Mortgage REIT (NYSE: EARN), American Capital Mortgage (NASDAQ: MTGE), and New York Mortgage Trust (NASDAQ: NYMT). Going back to the beginning of the month, we would need to add Capstead Mortgage (NYSE: CMO). The last REIT to declare a dividend cut before that was Western Asset Mortgage Capital (NYSE: WMC) back on 19 June 2015. Going back to the beginning of the first quarter, we find that 18 REITs have announced dividend cuts during the 2015, with both Capstead Mortgage and American Capital Mortgage having done so twice.

We'll conclude this post by updating our real-time chart reporting the relative health of the U.S. economy in 2015 as measured by the cumulative number of U.S. firms announcing that they are cutting their dividends by the day of the quarter.

Cumulative Announced Dividend Cuts in U.S. by Day of Quarter

It would appear that after six weeks of relative quiet, recessionary conditions are making their presence within the U.S. economy felt once more.

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21 September 2015

Scott Sumner considers the immediate reaction of stock prices to the Fed's announcement that it would not hike short term interest rate hikes following its two-day meeting ending on 17 September 2015 last week, but has a problem in understanding it:

But I have trouble seeing what Yellen said that would have made markets more bullish around 2:40 made more bearish after 2:50.

We can help. To help put the reactions into their proper context, we can draw upon the invaluable resource of the WSJ's live blog of the Fed's announcement and Janet Yellen's press conference that afternoon.

Typically, it takes about 2-4 minutes for stock prices to react to news crossing the wires that investors were not previously expecting. With that in mind, note the following report that was posted at 2:36 PM EDT, which would be the news that would influence the bullish reaction at 2:40 PM:

WHEN TO RAISE? Ms. Yellen is mostly just recapping the official statement in her opening remarks, but she did issue this tidbit for when the FOMC will raise rates:

“When it has seen some further improvement in the labor market and is reasonably confident that inflation will move back to its 2 percent objective over the medium term.”

The global economic weakness right now seems to be the key to what’s damaging their confidence that inflation will move back toward 2%.

And then at 2:47 PM, one of the WSJ's team of reporters covering the event posted the news that drove the market's bearish reaction at and after 2:50 PM:

THE OUTLOOK: Ms. Yellen confirmed that global economic uncertainty was a key factor prompting the Fed not to raise interest rates today, even though the Federal Open Market Committee considered it.

“I don’t want to overplay the implications of these recent developments,” she added, saying they “have not fundamentally altered” the Fed’s outlook for the economy. But clearly they altered the Fed’s outlook enough not to move today, after communication from the central bank spent much of the year building toward today’s meeting.

Now, let's move into some basic theory to understand why these particular reactions occurred....

Going into the announcement, the Fed confirming that they would begin hiking short term interest rates as expected would have produced the "zero" result - stock prices would react by essentially being flat, or trading within a relatively narrow range of noise in the absence of other news.

But, if it looked to investors like the Fed only would delay the rate hike to begin in 2015-Q4, stock prices would begin to rise. On the other hand, if it were further delayed to 2016-Q1, they would actually fall.

These specific outcomes are dependent on two main factors: what stock prices are today and what investor's rational expectations are for the change in the year-over-year growth rate of dividends per share that will be realized at discrete points of time in the future. The chart below, which we originally posted a week ago, shows where stock prices were at the end of the previous week, and what stock prices would alternatively be if investors focused exclusively upon either 2015-Q3, 2015-Q4, 2016-Q1 or 2016-Q2 in setting today's stock prices.

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot on 2015-09-11

Meanwhile, the relative separation that we observe between these alternative trajectories is what determines the potential magnitude of changes in stock prices when investors shift their focus from one point of time in the future to another.

In the weeks leading up to the announcement, investors had either focused upon 2015-Q3 or 2016-Q1, with the latter being consistent with the expectation that a rate hike would be delayed to 2016-Q1 at the earliest because of a deterioration of the global economic outlook.

We know that because coming into Thursday, 17 September 2015, with little exception over previous weeks, investors had been focused on 2015-Q3 in setting stock prices. The "little" exception of course was a sudden shift in investor focus to 2016-Q1 and back to 2015-Q3 in late August 2015, as investors considered the impact that a negative change in China's economic outlook might have on the Fed's expected monetary policies.

After the announcement, the consensus was that the Fed had kicked the can down the road, but only to the next quarter - 2015-Q4. Consequently, stock prices drifted slightly higher in response. The WSJ's live blog of the event confirms the assessment that they had begun looking at 2015-Q4 as the period in which the Fed might be most likely to begin hiking short term interest rates:

STILL APPETITE FOR RATE HIKE THIS YEAR: The Fed didn’t raise rates today, but most Fed officials still want to raise interest rates by the end of the year. Their interest rate projections show that 13 of 17 policy makers see higher rates at the end of the year. Three officials want to wait until next year. One official actually wants to cut rates and make them negative. It looks like the Fed skipped the rate increase today only to immediately put it back on the table.

That expectation gained steam during the press conference, as Janet Yellen's recap the Fed's announcement emphasized that understanding, which set the expectation that the next action on their part would be in 2015-Q4.

That changed however after she began taking questions at 2:47, where it quickly became very clear that the global economic outlook was going to be a major factor in setting the timing of their plans for a future rate hike. That pushed out investor expectations of the likely timing of any future rate hike to the first quarter of 2016, and consequently, stock prices fell on that unexpected bit of news, which showed up in stock prices some 2-4 minutes later.

To confirm that this news was unexpected, see the following quote from a Citi analyst's reaction to the Fed's announcement (via ZeroHedge):

The Federal Open Market Committee (FOMC) decision to stay pat reveals a new monetary policy rule in place—one that amplifies the importance of international and financial market developments.

We did not believe the FOMC would take such a limited risk scenario involving China, which is not part of their baseline outlook, and delay a rate increase that arguably is warranted by domestic conditions. Indeed, we have noted that the last time international economic and market developments stopped the Fed from raising rates was in 1997-1998 when LTCM, Russia, and the Asian crisis caused disorderly markets that were global and systemic. Current volatility conditions are not at all similar to those of 1998.

The new FOMC reaction function—one that assigns greater importance to global and international financial market developments—will require some time to assess and understand.

Now what? China's growth uncertainty will not diminish quickly and the EM fallout will take time to assess. The Chinese authorities have no track record of successfully dealing with such a structural slowdown, nor a track record of not exacerbating such a well-anticipated economic weakness. Also, excess supply conditions in commodity markets depressing EM growth and US inflation likely will not dissipate quickly.

The September FOMC meeting was a real "bunker buster" insofar as it has challenged our understanding of Federal Reserve policymaking and the inputs that matter most.

We see then that the Fed really did introduce quite an element of uncertainty into the market, which is why we would now appear to have something of a "split" focus between future quarters: 2015-Q4 and 2016-Q1. (Note: The Citi analyst quoted at ZeroHedge went on to indicate they were in the latter camp, which means that they're focusing on the expectations associated with 2016-Q1 in making their investment decisions today.)

From a volatility standpoint, given the amount of vertical space between the likely trajectory of stock prices for investors focusing on either of these two future quarters, we can now reasonably expect that there will be quite a bit of volatility in the near term, which is due to the quantum-like characteristics of how stock prices behave.

That volatility will be highly dependent upon new information entering the market, as stock prices move rapidly from one expectation level to another as investors shifting their forward-looking focus from 2015-Q4 to the more distant future and less positive future of 2016-Q1 and back again in response to news events.

Keep in mind that this is not something new. We have already tracked one such Levy flight this year, and the Fed has created an environment where we may well see others in upcoming weeks until investors might have sufficient reason to stabilize their focus on one particular point of time in the future.

That is assuming that there will be no changes in the fundamental driver of stock prices: rational expectations of the amount of dividends that will be paid out in future quarters, which have been remarkably steady through most of the year to date. If and when that might change, the likely trajectory for stock prices will change dramatically, as we've previously observed back in late 2008 and 2009, and more recently in December 2012 and 2013.

And as for what to expect this week, in the aftermath of these events, and not considering any new information that what we have at the close of trading on 18 September 2015, here you go:

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot on 2015-09-18

[Update 9 October 2015: Changed "hand" to "have" in paragraph preceding chart. Damn you autocorrect!]

In the chart above, we show that each of the alternative future trajectories is showing the effect of the "echo" of the "China crash" of late August 2015. This apparent outcome is an artifact of our using historical stock prices in our model of how stock prices work. Because this event was such a short term event however, we've shown a shaded rectangle that "bridges" across the echo to indicate where we would expect to find the trajectory of stock prices otherwise.

And though we expect that trajectory to be slightly negative, with the current split focus of investors, stock prices will tend to rise on news that focuses investors on 2015-Q4, which would be consistent with positive economic news, and will fall if they focus upon 2016-Q1, which will likely be consistent with the incidence of negative economic news.

As far as we know, we're the only ones who have developed a theory of how stock prices work that is even capable of considering not just the future time focus of investors, but differences between different camps of investors, where we've basically been able to reduce the challenge of describing stock price behavior to be a simple problem in terms of the math of quantum kinematics. As you can tell from the discussion above, it can be complex to explain, given that the stock market is a complex system, but not difficult to understand.

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18 September 2015

Want to see how to combine a box fan and a window screen with a squirt bottle filled with a 50-50 rubbing alcohol/water mixture into a highly effective mosquito corpse collection device?

You've come to the right place, because Instructables' NightHawkInLight is sharing his take on Green Power Science's Dan Rojas' mosquito population control technology!

HT: Core77.


17 September 2015

We had a big day behind the scenes here at Political Calculations yesterday, as we updated four of our most popular tools!

First up, with the release of the U.S. Census Bureau's income distribution data for 2014, we generated nonlinear regressions of the latest data for U.S. men, women, individuals, families and households to update our two most frequently visited posts:

What Is Your Income Percentile Ranking?

Originally posted on 17 September 2014, coinciding with the release of the U.S. Census Bureau's income distribution data for 2013, we updated the tool to now span all years from 2010 through 2014.

What Is Your U.S. Income Percentile Ranking

First posted on 20 September 2013, when the income distribution data for 2012 was brand new, we've updated this tool to find what your income percentile would be for the years cover the years from 2011 through 2014.

We also generated cumulative income distribution charts for 2014, which we've animated. Each frame will last for three seconds, with the first showing the results for individuals, followed by the frame for families, and then U.S. households, before repeating the cycle.

Animation: U.S. Cumulative Income Distribution for Individuals, Families and Households in 2014

All in all, it took us about an hour to do all of those updates. So, since we had extra time, and because the U.S. Bureau of Labor Statistics released the Consumer Price Index for All Urban Consumers for August 2015 yesterday as well, we also did our regular monthly update of our next two most-visited tools!

The S&P 500 At Your Fingertips

Our signature tool that allows you to calculate the rate of return, both with and without the effects of inflation and with and without the reinvestment of dividends, for an investment in the S&P 500 stock market index or its predecessor indices and components, between any two months since January 1871.

Investing Through Time

Using the same raw data that's behind our S&P 500 At Your Fingertips tool, this is our tool that will let you work out how any investment you might have made between any two months since January 1871 would have fared.

So, if you didn't like your income percentile, at least now you have some idea of what it might take to invest your way up in the rankings.

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16 September 2015
Pension Plans - Source: http://www.bls.gov/opub/btn/volume-3/an-analysis-of-multiemployer-pension-plans.htm

Imagine this scenario. You work for a company that has previously committed to provide you with a traditional defined benefit pension after you retire, but now wants to lock in its costs for those benefits by offering you a choice. You can:

  1. Take a one-time lump sum payment, representing the present value of the pension benefits it has made on your behalf, which you can then use to invest for your retirement through your own Individual Retirement Account (IRA).
  2. Take an immediate annuity, in which your employer takes the lump sum and sets you up to receive monthly payments for life beginning now from an annuity provider it selects based on whatever annuity option you select.
  3. Let it ride, where you may keep your defined benefit pension.

To be frank, the main reason that your employer is offering you these options is because they don't know how much it is going to cost them to provide you with a guaranteed benefit like a traditional pension. Defined benefit pensions were developed at a time when pension investment managers could count on relatively risk-free investment options for decent returns, which have increasingly become difficult to identify over the last decade.

For your employer, falling short means having to take money away from things that benefit the business, like new investments that help generate more revenue to keep the business in business going forward.

For you, choosing your company's pension buyout offer means taking on the risks that they otherwise would have to take on your behalf. That risk was always there, but now will no longer be hidden from you.

But the question is now this: can you do a better job in managing that risk and your retirement than your employer? And to answer that question, we've built the following tool, which you can use to work out how well your employer thinks they would be able to do. Just enter the indicated information that your employer will have provided to you in our tool below, and we'll run some quick estimates of the rates of return your employer believes they can obtain.

If you're accessing this article on a site that republishes our RSS news feed, click here to access a working version of our tool.

Your Pension Buyout Offer
Input Data Values
Your Current Age
Your Age at Retirement
One Time Lump Sum Pension Buyout Offer
Monthly Annuity Payment Beginning at Your Current Age
Monthly Pension Payment Beginning at Your Retirement Age If You 'Let It Ride'

Pension Buyout Considerations
Calculated Results Values
The Average Rate of Return You Have to Beat Before You Retire
The Immediate Annuity's Interest Rate

In our tool's results above, the average rate of return that you would need to beat represents the rate that your employer would have to obtain in investing the amount of your lump sum payment today to be able to provide your monthly pension payment after you've retired, without having to add any extra money to make up any shortfalls.

To put that rate of return in some context, the average rate of return for investments in the S&P 500 of any duration is 9.4%, which does not account for the effects of inflation over time. Then again, neither does your employer's promised pension payment.

And of course, stock market returns can be volatile, especially in the short term. See our Remapping the S&P 500's Performance Since 1871 tool for a quick summary of the best, worst and average rates of return ever provided by investments in the S&P 500 stock market index and its predecessor indices and components to get a sense of just how volatile that might be over the period of time between the present and when you might retire.

Meanwhile, the immediate annuity's interest rate is the annualized rate of return that your employer can obtain in taking the lump sum and setting you up with monthly annuity payments. While this would be a sure thing, where the payments will last as long as you live, or as long as the annuity option you select lasts, it also will never be adjusted to account for the effects of inflation over time.

As a final note, this tool applies to defined pension benefits that are fully funded, where your employer regularly sets aside sufficient funds to ensure its pension plan can fully satisfy all its obligations to the company's future retirees. For underfunded pensions, and particularly public sector pension plans, you would need to also consider just how seriously underfunded your pension plan may be in making your choice, as your pension plan's manager may not be capable of generating the kind of returns on its investments that will be needed to keep the plan from going into default when it comes to making its full promised payments to you in retirement.

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15 September 2015

Back in December 2014, we picked up on a change in business strategy by a number of U.S. home builders, where several such as D.R. Horton (NYSE: DHI), Lennar (NYSE: LEN) and Pulte (NYSE: PHM) were going to focus a much larger portion of their business in 2015 on builing more affordable, entry level homes.

With data just over halfway through the year, we can see some very clear effects of that strategy of obtaining profits from volume over profit. First, in terms of affordability, the growth of median new home prices has stalled out at roughly $290,000 with respect to the estimate of median household income reported by Sentier Research in each month since February 2015, even though median household income has continued to increase.

U.S. Median Trailing Year New Home Sale Prices vs Trailing Year Median Household Income, December 2000 through July 2015

Taking a step back and looking at the big picture for median new home sale prices, or rather, their trailing twelve month average to account for the effects of seasonality in the raw data reported by the U.S. Census Bureau, we confirm that the recent runup in median new home sale prices appears to be topping out.

Trailing Twelve Month Average of U.S. Median Trailing Year New Home Sale Prices, December 1963 through July 2015

Next, we estimated the equivalent market capitalization of all new homes built in the U.S., using the U.S. Census Bureau's historical records of new residential sales and their average sale price. We find that the market capitalization of all new homes sold in the U.S. has continued to increase, even as their prices have stalled out, which means that their increasing market cap is being driven by an increasing number of sales.

Market Capitalization of New Homes Sold in the U.S., December 1975 through July 2015

We should note that the U.S. Census Bureau's monthly data for average new home sale prices only extends back to 1975.

On the whole, the stabilization of new home sale prices matched with an increasing volume of sales represents the healthiest possible scenario for the U.S. real estate market. As such, the U.S. real estate market currently represents a source of strength for the U.S. economy.


14 September 2015

Going by the closing value of the S&P 500 on each trading day of the week ending 11 September 2015, nothing much unexpected happened during the week. Assuming, of course, that investors remain closely focused on the current quarter of 2015-Q3 in setting today's stock prices.

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot on 2015-09-11

Now, here's where things start to get interesting. The Federal Reserve's Federal Open Market Committee (FOMC) meets on the 16th and 17th of this upcoming week, where on 17 September 2015, the Fed will confirm, for once and for all, whether it will begin almost immediately hiking short term interest rates in the U.S. or whether it will delay its long expected action.

The Fed's pending decision is the reason why investors have been so strongly focused on 2015-Q3, where the expectations associated with the quarter have been largely driving U.S. stock prices, with little exception, for the last several months. We base that assessment on how closely actual daily closing stock prices have tracked along with the alternative future trajectory our model has been projecting for 2015-Q3, particularly on days coinciding with Federal Reserve announcements.

The only major exception to that strong focus occurred in the period from 19 August 2015 through 26 August 2015, when concerns about China's economic situation led investors to shift their forward looking focus briefly to 2016-Q1, taking the S&P 500 on a Lévy flight from 2,079.61 down by 10.1% to bottom at 1,867.61 before recovering to 1,987.66 on 27 August 2015. Or as we like to describe it, a short quantum random walk.

Speaking of which, after the FOMC concludes its two-day meeting on Thursday, 17 September 2015, there will be absolutely no reason for forward-looking investors to continue focusing any portion of their attention on the current quarter of 2015-Q3 for much more than one more day. With the dividend futures contract for 2015-Q3 set to expire on the third Friday of the month, 18 September 2015, investors will soon be compelled to shift their forward-looking attention to another point of time in the future, no matter what.

If the Fed wants to do a good job in managing future expectations, it will direct investors to focus upon either 2015-Q4 or 2016-Q2, thereby avoiding another Lévy flight-driven episode for stock prices and thus offering a much greater degree of relative stability for U.S. stock prices than the potential alternative scenario of investors suddenly focusing their attention again on 2016-Q1. According to our model of how stock prices work, if that were to happen, stock prices would rapidly decline on the order of seven percent below the other most likely trajectories they would otherwise follow, plus or minus three percent (if we account for the typical level of day-to-day volatility in stock prices, and in the absence of other news that might affect investors expectations of the future).

Considering what lies ahead for stock prices even if the Fed is successful in directing the focus of investors to 2015-Q4 or, as we've recommended, 2016-Q2, which would have greater practical utility than we had originally recognized, we would strongly encourage the voting members of the FOMC to follow our advice. We don't believe that it is either desirable or necessary to wipe out an additional $1.3 trillion of market capitalization from the S&P 500, even if done temporarily.

This is one of the very rare occasions where we can predict with absolute certainty when a shift in the forward looking focus of investors will occur. Which future quarter they will settle their forward-looking attention upon, and thus, the level of today's stock prices, can still be influenced.

And unlike in 2008, the FOMC won't be able to say that they didn't understand in advance what the consequences of their forward guidance might be.

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11 September 2015

As often as we generate charts as part of our analysis, and as often as we use automated tools to generate them, there's actually quite an art that goes into making them. Today's is no different, other than we're going to push the envelope beyond what we've done before as we resume and update a story we've been following by retelling how it goes and how we expect it will go in a single picture.

Residual Distribution for Weekly Seasonally-Adjusted Initial Unemployment Insurance Claims, 31 May 2014 - 29 August 2015

It would seem that OPEC's "miserable failure" will likely have measurable negative consequences in the eight states indicated.

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10 September 2015

Believe it or not, there is good news coming out from China regarding the state of its economy. According to trade data collected and reported by the U.S. Census Bureau on the value of goods and services transacted between the two nations, the year-over-year growth rate of China's imports from the United States has increased into positive territory.

Year Over Year Growth Rate of Exchange Rate Adjusted U.S.-China Trade in Goods and Services, January 1986 - July 2015

In the chart above, we see that in both June and July 2015, the growth rate of U.S. exports to China has moved up out of the range that is consistent with contractionary forces being at work within China's economy. We should note that June's figure shown in our chart above is a little more positive than we had previously indicated, as we've corrected a data entry error in our records for that month.

Also, when we look at global atmospheric carbon dioxide levels, of which China is the leading producer in the world, we find that the decline in CO2 that began in conjunction with China's Third Plenum leadership meeting, in which the nation's leaders acted to put the brakes on its robust economic growth of previous years in favor of steering the nation's economy to grow more slowly, has largely stalled out.

Trailing Twelve Month Average of Year-Over-Year Change in Parts per Million of Atmospheric Carbon Dioxide, Jan 1960-Aug 2015

That reversal would confirm that what we see in the trade data is real, as it suggests that China's economic slide may also begun to reverse in the period from June 2015 onward.


Those two consecutive months of positive year-over-year changes came just before the government-run People's Bank of China devalued the nation's currency with respect to the U.S. dollar in early August 2015.

In practice, what that means is that in the near term, it will be relatively more expensive for China to import goods from both the U.S. and also from other regions of the world where the value of its currency declined as a result of the devaluation. At the same time, goods produced in China will be less costly for those in these other regions to acquire, which would give Chinese exporters a relative competitive advantage.

And by relative, we mean about a 2% difference if we look simply at the change in the official exchange rate between the U.S. dollar and the Chinese yuan from July to August 2015.

It will be interesting to see how the trade data evolves in response to the change. Coming at the time it did in August 2015, when nearly every good that will be recorded as having either been exported from either the U.S. to China or from China to the U.S. during the month was already in transit between the two nations, given the typical three-week long trip for cargo ships to cross the Pacific Ocean, we suspect that when the Census Bureau posts its trade data for U.S. exports to China, it will likely be "inflated" by the full 2% of the devaluation - initially making it appear that China's economy grew more robustly in August 2015 than it will really have done.

The early word on China's imports in August 2015 from its official trade statistics, which should really only be considered seriously for providing an indication of the direction of China's economy, is not good:

China’s imports fell more sharply, by 14.3 percent in yuan terms, compared to 8.1 percent in July, with falling commodity prices seen as one factor.

The fall in imports left the country’s overall foreign trade for the month down 9.7 percent from a year earlier, but also meant that China’s trade surplus for the month was markedly up, by 20.1 percent year-on-year, to 368 billion yuan, or about $58 billion, compared to the average of about $43 billion for the first seven months of the year.

Given how GDP is calculated, that surge in China's trade surplus with the rest of the world in August 2015 will likely give China quite a boost for the month and quarter. Funny how China's own reported levels of imports and exports both fell at the same time, suggesting an economy that's undergone contraction.

Data Sources

Board of Governors of the Federal Reserve System. China / U.S. Foreign Exchange Rate. G.5 Foreign Exchange Rates. Accessed 9 September 2015.

U.S. Census Bureau. Trade in Goods with China. Accessed 9 September 2015.

National Oceanographic and Atmospheric Administration. Earth System Research Laboratory. Mauna Loa Observatory CO2 Data. [File Transfer Protocol Text File]. Accessed 8 September 2015.


09 September 2015

Yesterday, the Wall Street Journal reported on the growing controversy of a chart produced by Josh Bivens and Lawrence Mishel of the Economic Policy Institute and its meaning. Let's dive right into the center of the storm.

In case you missed it, there’s a chart making the rounds that has come to represent, for some, all that is wrong with the American economy.

The top line shows worker productivity growing by 72.2%, or 1.33% per year, between 1973 and 2014. The bottom line shows median workers’ hourly compensation increasing by 9.2%, or 0.2% annually, over that same period. The gap between them more or less symbolizes the big empty space in workers’ wallets.

EPI: FIGURE A - Disconnect between productivity and a typical worker's compensation, 1948-2014

The chart, part of a broader research series from the left-leaning Economic Policy Institute, has struck a chord. Hillary Clinton tweeted a version of it following her first major economic policy speech in July, and has clearly leaned on EPI research in calling for policies that boost wages.

But the chart—and its data, methodology and conclusions—has become a flashpoint.

How one interprets the mass of historical data we have on workers’ productivity, wages and growth has profound consequences for which economic policies one might pursue. Most economists agree that productivity is essential for raising living standards, and that the superrich have seen their incomes skyrocket. The devil is in the details.

The economists behind the chart have now come out with guns blazing, releasing a vigorous defense of their work that decries critics’ attacks as “baseless.” The briefing paper by Josh Bivens and Lawrence Mishel, “Understanding the Historic Divergence Between Productivity and a Typical Worker’s Pay,” calls wage stagnation for the majority of American workers “a bald fact.”

So is it?

The WSJ article then goes on to take in the viewpoints of a number of other economists, including such players as Scott Winship, Robert Gordon, and Robert Lawrence, who point out a number of the problems with the data and analysis used to produce the chart.

But there's a more fundamental problem with both the data and the analysis, which these critics have only barely touched upon. Bivens and Mishel got the math wrong. Badly.

Not their actual calculations, mind you. Their problem lies deeper in a seriously flawed methodology - one that students in hard sciences, such as physics or engineering, are specifically trained to avoid.

But you don't have to take our word for it. Russian geophysicist Ivan Kitov was intrigued enough by Bivens and Mishel's results that he reviewed their work the same way any Doctor of Physics and Mathematics might review the work of a student submitting a term paper or a final exam in an undergraduate level class.

As you read the following, keep in mind that English is not Dr. Kitov's first language and that being Russian, he doesn't have any stake in the political arguments involved, which would only apply to the U.S. He may be as close as we can get to a genuinely neutral arbiter - although as you'll find out, not one who tolerates incompetent analysis well.

In terms of physics, democratic (might be not only) economists are ignorant. I would recommend learning some basic notations from thermodynamics before using any specific units. The physical concepts of ensemble and closed system seem to be too difficult for economic science.

My story is simple. Through "Economist's View" I found a graph in The Fiscal Times comparing the evolution of productivity and hourly compensation. This figure is not too complicated; it's rather too misleading.

Democrats claim that money leak from "workers" to "wealthy", whatever it means. This is not true; this just demonstrates the (hopefully not deliberate) misuse of simple notations. Roughly, hourly compensation is calculated as a ratio of total wage and salaries and total hours worked. Indeed, if to ignore the increase in employment/population ratio since 1950, and especially since the late 1960s, one gets something as shown in the figure below. Real GDP per capita and labor productivity ($ per hour as reported by Total Economy Database borrowed from the Conference Board website) follow similar paths. Wages and salaries (as published by the BEA) divided by employment (same database) deviate from these two curves since the 1970s, as in the above figure.

The next graph shows the ratio of employment and total population since 1950. This ratio has been increasing from the 1960s. Effectively, more and more people are involved in real economy, but unfortunately for them they share the same real GDP. On average, one person gets smaller and smaller share of the cake - and we see that compensation per hour increases slower than GDP per capita and productivity.

When compensated for the difference in the total population and employment growth, the green curve is back to its true position. Rich do not rob "workers". Instead the employment has been increasing over time. In that sense, declaring the decrease in hourly compensation as evil, democratic economists are strongly against increasing employment, i.e. against workers.


Never normalize values to fluctuating portion of a closed system. This always gives a biased (wrong) result. Also, it is always a formal mistake and negative mark on exam (in physics).

It is also a prime example of what Paul Romer has called economics' "mathiness" problem, where highly deficient analysis is too often generated for the sake of pursuing a highly politicized agenda in the media, where journalists who lack sufficient training in the sciences are exploited into advancing the biased analyst's political agenda.

In this case, Bivens and Mishel's fundamental error has not just created a controversy within the field of economics, it is actually setting back positive progress in the field. Worse, the policy prescriptions being advanced to "correct" Bivens and Mishel's identified "problem" by U.S. policy makers buying into their fundamentally flawed analysis would, if adopted, actually set back the economic interests of the very people the political "solution" claims to help.

All for a story that doesn't stand up to scrutiny. We can do with a lot less of those in this political season.

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08 September 2015

With the news last Friday, 4 September 2015 that the employment situation in the U.S. economy was not as bright as had been expected, once again opening the door to the possibility that the U.S. Federal Reserve might pull back from its plans to begin hiking short term interest rates by the end of this month, it shouldn't come as a surprise to any of our readers that the S&P 500 fell from where they would be if they were closely focused on 2015-Q3 in setting the value of stock prices in the direction of where they would be if they focused on 2016-Q1 instead.

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot 2015-09-04

But not so significantly as to be distinguishable from the typical level of noise for U.S. stock prices. Yet. We'll see how the month plays out....

In the mean time, now that stock prices have somewhat stabilized, let's take a quick look at how the future through the end of 2015 is shaping up.

Alternative Futures - S&P 500 - 2015 - Rebaselined Model - Snapshot 2015-09-04

In this chart, we assume that there will be no significant net erosion of expected future dividends per share. If there is a net erosion, we can expect that these likely trajectories based on how far ahead investors are looking in time will appear somewhat optimistic. Conversely, they will appear to be pessimistic if there is a positive change in the expected growth rate of dividends per share.

That kind of dynamic is why October will likely be a volatile month for the stock market. Especially since September 2015 was so quiet, even though the same conditions that preceded the "oil spike" shown in the chart below took hold once again during the month....

Monthly Number of Public U.S. Companies Announcing Dividend Cuts, 2004-01 thru 2015-08

We somewhat know in advance that 2015-Q4 will likely not be a positive one for U.S. oil and energy companies, unless they can show that the rate at which their future business is getting worse is starting to decelerate and reverse. The big question yet to be answered is how many other companies will take advantage of the opportunity of the upcoming earnings season to adjust their own dividend targets to be easier to hit.

Because if there is ever a right time for a CEO to make such an announcement, it is when their peers at other companies are annoucing that they are cutting their own dividends. They are a lot like startled starlings that way.

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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:

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