Political Calculations
Unexpectedly Intriguing!
September 2, 2015

We've previously written that the only time we get really ever get excited about what's going on in the stock market is when it changes by 2% or more from the previous day's closing value.

That threshold is based on our statistical study of the volatility of stock prices, where we found that the percentage change of the S&P 500 from one trading day to the next fit pretty neatly inside a normal distribution, where:

  • 78.8% of all day-to-day percentage changes were within 1 standard deviations of the mean, about 10.6% higher than what would typically be expected for a perfect normal distribution.
  • 95.3% of all day-to-day percentage changes were within 2 standard deviations of the mean, almost right in line with what would typically be expected for a perfect normal distribution.
  • 98.6% of all day-to-day percentage changes were within 3 standard deviations of the mean, about 1.1% less that what would typically be expected for a perfect normal distribution, but still pretty close.

For bell curve fans, all those numbers mean two things:

  1. Small changes in stock prices are much more likely to occur than would be the case if their variation were the result of purely random factors.
  2. Big changes in stock prices from one day to the next are pretty unusual events.

So that brings us to yesterday, 1 September 2015, where for most of the day, stock prices were about 2-2.5% below where they had previously closed, before they suddenly dipped to be 3.5% lower before recovering to close at 3% lower in the last 37 minutes of trading.

And that was really pretty uninteresting because that final closing value would be exactly what our model of how stock prices work forecast it would be provided investors were setting stock prices according to the expectations they have for the current quarter, 2015-Q3.

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot 1 September 2015

Now, here's the thing about how our model works. What you see in our model as day to day variation for the alternative trajectories that stock prices are likely to take when investors are focused on a particular future quarter is based upon historic stock price data. We then factor in the change in the growth rate of dividends per share for each indicated future quarter for which we have dividend futures data, which you see as the vertical separation between the various trajectories.

For our standard model, for each day's forecast value, we use the historic stock prices that were recorded 13 months earlier, 12 months earlier and 1 month earlier as our base reference points from which we project future stock prices.

But in our rebaselined model, which we use when the historic price data for our standard model contains too much volatility to provide the most accurate forecast possible, we substitute the historic stock prices from different points in time and adjust our calculations accordingly. In forecasting each day of 2015-Q3 since 28 June 2015, we've been using the historic stock prices from 25 months earlier, 24 months earlier and 1 month earlier.

S&P 500 Index Value (Historic Data Base Reference Points) Used in Rebaselined Model Forecast Projections, 2015

So when we see that today's stock prices are largely matching our forecast changes, as we basically have for all but three of the last 26 trading days, what we're seeing is that stock prices are directly echoing the events of 25 months ago, 24 months ago and 1 month ago.

Here's the multi-million dollar question: Why is that? We would only reasonably expect stock prices to fall somewhere within the range of values we forecast, where the actual trajectory of stock prices should be continually cutting across our forecast trajectories and the echoes of historic noise they capture, not paralleling them. Especially with the record levels of volatility that the market has shown recently.

But it's not, which would mean that other factors are at work. Our best guess is that those factors are somehow tied to options contracts and investments with two-year long maturities and expiration dates, where the confluence of interactions between investments initiated 25 months ago, 24 months ago and 1 month ago is compelling stock prices today to follow the course it is. Throw in a three-day long quantum shift in focus on the part of investors, and we have our recipe for explaining why stock prices have behaved as they have.

Or rather, why our model of how stock prices work has surprisingly managed to work as well as it has in the current stock market climate.

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September 1, 2015
Checkbook - Source: Virginia Department of Education - http://www.doe.virginia.gov/instruction/economics_personal_finance/

Are you tired of paying your your mobile phone bill every month? What if you could get your carrier to pay it for you?

Believe it or not, there's a way that you could actually make that happen. All you need to do is to buy the company!

Or rather, you need to buy enough shares of stock in the company to cover the cost of your monthly bills through the dividends you might earn as a partial owner of the business. But how many shares would that take?

Our latest tool answers that question! We've plugged in the quarterly dividend and share price data as it might apply to an average monthly bill for Verizon (NYSE: VZ), but you're more than welcome to substitute the data that applies to your own mobile service provider. Or for that matter, any company that bills you monthly that also pays dividends to its shareholders!

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!

Monthly Bill Data
Input Data Values
Your Monthly Bill [$USD]
Investment Data
Current Share Price [$USD per Share]
Quarterly Dividend [$USD per Share]
Dividend Income Tax Rate [%]

Shares Needed to Pay Bills with Dividends
Calculated Results Values
Annual Amount of Monthly Bills
Number of Shares Needed to Provide Enough Dividend Income to Cover Bills After Taxes
How Much Will Those Shares Cost You to Buy Today?

If you think about it, this is really the sort of thing that you're trying to accomplish for when you're not working any more through your retirement investments.

But nobody said you had to be retired before you could start working your way toward that objective.


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August 31, 2015

From time to time, we'll conclude our more remarkable posts with the phrase "Welcome back to the cutting edge!" We're going to do that again today.

The reason we'll do that today is because of a new paper that was published just 20 days ago that describes cognitive decision making as the collapse of a quantum superstate. Phys.org's Christopher Packham provides the background for the application of "Quantum Random Walks" to decision making.

Decision making in an enormous range of tasks involves the accumulation of evidence in support of different hypotheses. One of the enduring models of evidence accumulation is the Markov random walk (MRW) theory, which assigns a probability to each hypothesis. In an MRW model of decision making, when deciding between two hypotheses, the cumulative evidence for and against each hypothesis reaches different levels at different times, moving particle-like from state to state and only occupying a single definite evidence level at any given point.

But the Markov random walk theory, based in classical probability theory, runs into problems when confronted with the emerging research consensus that preferences and beliefs are constructed, rather than revealed by judgments and decisions. An international group of psychological researchers now suggests a new model called the quantum random walk (QRW) theory that specifically posits that preferences and beliefs are constructed rather than revealed by judgments and decisions, and they have published the results of an experiment that support this theory in the Proceedings of the National Academy of Sciences.

By contrast with MRW, the new theory assumes that evidence develops over time in a superposition state analogous to the wave-like state of a photon, and judgements and decisions are made when this indefinite superposition state "collapses" into a definite state of evidence.

That new theory has a direct practical application, because it describes much of the behavior we've directly observed in how investors collectively set stock prices.

To see what we mean, let's update and animate alternative futures chart, which projects the likely trajectories that stock prices will follow based upon how far forward in time investors are collectively looking when they make their current day investment decisions, where we'll pick up the action beginning one month ago.

Animation: Alternative Trajectories - S&P 500 - 2015Q3 - Rebaselined Model - 28 July 2015 through 28 August 2015

Each of the alternative future trajectories in the chart above represent a specific hypothesis, which is given by the acceleration, or change in the year over year growth rate, of the trailing year dividends per share expected to be paid out by the S&P 500 by the end of the indicated quarter.

At the beginning of the animation, we see that investors were tightly focused on 2015-Q3 on 29 July 2015, which makes sense because investors had strong reason to believe that the U.S. Federal Reserve was on track to begin hiking short term interest rates by the end of the quarter in September 2015, thanks to the Federal Open Market Committee's meeting and announcement issued that day. Thus, the trajectory indicated for 2015-Q3 represents the hypothesis that the Federal Reserve would hold to that policy.

Over the next week, the closing value of the S&P 500 closely tracked that trajectory, until moving higher on Monday, 10 August 2015, boosted by the speculative prospect that China, which announced disappointing economic data that day, would soon act to provide new stimulus measures for that nation's economy.

Stock prices remained elevated throughout the rest of that week as China made good on that speculation, as it announced the surprise devaluation of its currency on 11 August 2015 and by other measures that carried through 17 August 2015. Throughout this period, stock prices remained elevated just above the upper edge of the typical range of day-to-day volatility of stock prices that we would expect would apply for investors remaining focused on 2015-Q3.

Stock Market Crash - Source: http://www.federalreserve.gov/aboutthefed/cls-timeline/timeline/timeline_main.htm?04

That positive speculation began to deflate on 18 August 2015 as China's stock market began to decline, as China's government began to back off from enforcing its previous extraordinary measures to arrest its decline earlier in the summer.

That action also coincided with the two-year anniversary of the so-called "taper tantrum" in the U.S. stock and bond markets, which would appear to be relevant since we used historical stock prices from this period as the baseline from which to project the likely trajectories shown in our chart above. Which we began doing on 28 July 2015 because the period was much less volatile that the one-year ago period that we would normally use to forecast the future likely trajectories of stock prices in our standard model of how stock prices work.

What happened next is now the stuff of forecasting legend. Based on the echo of that two-year old event, our model anticipated that stock prices would begin falling, even if investors remained focused on 2015-Q3 in setting stock prices. And through the week ending 21 August 2015, the level of stock prices was fully consistent with investors remaining focused on 2015-Q3.

But then, on Monday, 24 August 2015, stock prices closed far lower than would be consistent with investors remaining focused on 2015-Q3 alone. Instead, stock prices plunged to a level that was much more heavily weighted toward 2016-Q1, which would be consistent with the hypothesis that the Federal Reserve would back off its plans to hike short term interest rates in the U.S. until that time at the earliest based on the continuing deterioration in China's stock markets.

On Tuesday, 26 August 2015, a sizeable rally in the U.S. stock market throughout much of that day "went up in smoke", as stock prices closed that day at a level that was fully consistent with investors having shifted their forward looking focus to 2016-Q1, in effect, collectively betting that a September 2015 rate hike in the U.S. would now be off the table. Coincidentally that day, Federal Reserve Bank of New York president William Dudley said that a September 2015 rate hike was "less compelling".

The downward swinging pendulum of investor expectations for when the Fed would seek to hike interest rates reversed on the next day with the release of positive economic news, giving more strength to the hypothesis that the Fed would hike rates in 2015-Q3. Overall however, stock prices moved to be about halfway between the levels that would be fully consistent with either 2015-Q3 and 2016-Q1, suggesting that investors gave equal weighting to the difference between these two future quarters in setting stock prices.

The positive momentum continued on 27 August 2015, with the significant upward revision of U.S. GDP recorded in the second quarter of 2015. That news strengthened the view among U.S. investors that the Fed would hold to its September rate hike plans, with the S&P 500 closing in on a level that would be more heavily weighted in favor of that hypothesis.

On Friday, 28 August 2015, there was very little movement in stock prices, but that would be expected for investors having focused once more on the likelihood that the Fed would indeed hike interest rates in September 2015, a view given great emphasis during the day by Stanley Fischer, the Number Two official at the U.S. Federal Reserve.

Random vs Quantum Walk - Source: http://rsta.royalsocietypublishing.org/content/364/1849/3407

There are four things we really need to point out about the movement of stock prices during the period from the close of trading on 21 August 2015 through 28 August 2015. First, the concept of a quantum random walk goes a very long way toward explaining why stock prices just simply don't jump straight from one quantum level to another. The uncertainty that investors have regarding the likelihood of future events can restrain the potential extent of such movements.

Second, the quantum levels themselves are not random. They're based on the real and quantifiable expectations for the change in the growth rate of dividends per share that will be paid out at specific points of time in the future, which are projected on top of where stock prices are and have been. That's important because it is the relative distance between the quantum levels that exist when investors are choosing between the hypotheses that apply at different points of time in the future that determines whether stock prices follow a true random walk-style Brownian Motion, or go into a full Lévy Flight such as we observed in the last week.

Third, as stock prices change, so does the likely trajectory of stock prices in the future. Given the math involved, we now see the echo of the China-driven stock market crash in September in our animated chart above.

However, that doesn't mean that stock prices will follow that trajectory. In general, the echoes of past volatility do not tend to affect the trajectory of current day stock prices, although in rare cases, they can. What provides the potential for determining whether they might is the amount of money that might have been tied up in investments with fixed maturity dates, such as options contracts or bonds, which would come due when such echoes appear in our model.

But whether they do have any real world impact depends on what the investment climate looks like when they do come due. It is always the prospects for the future that determine the actual trajectory of stock prices.

Fourth, the existence of the quantum random walk phenomenon helps explain why stock returns have fat tail distributions. To the extent those distributions primarily resemble bell curves is an indication of the extent to which investors collectively tend to focus on one potential future, or investment-driving hypothesis, at a time as they make investing decisions.

Welcome back to the cutting edge!

Previously on Political Calculations

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August 28, 2015

Three weeks ago, we featured the work of the young Australian behind the Primitive Technology blog, who built a stone adze from scratch in the wild, which he then proceeded to use to build a primitive, yet effective and durable shelter from his surrounding materials.

As human invention goes, the adze is a contemporary of the axe, another tool that first saw the light of day in the stone age.

Today, we're going to feature the modern reinvention of the axe, in which the millenia-old design is being revisited by Finnish inventor Heikki Kärnä to make it a more effective tool, funding for the development of which is now being sought via Kickstarter. Meet the Leveraxe:

We love the quote from Business Insider regarding the invention:

This weird, super-efficient axe solves an engineering problem most people don't even know exists.

Which explains why we're helping to spread the word. For anyone who has ever had or will have a need to split wood logs, this design looks to have an edge up over its traditional axe competition.

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August 27, 2015

Believe it or not, August is shaping up to be the second best month for dividends in 2015.

But don't take our word for it - the proof is in our near-real time measure of the level of distress in the U.S. economy, the cumulative number of U.S. firms announcing that they are cutting their cash dividend payments to their shareholder owners by day of the quarter.

Cumulative Number of U.S. Companies Announcing Dividends Cuts by Day of Quarter, 2015-Q1, Q2 and Q3, Snapshot on 26 August 2015

The best month of 2015 was June 2015, which only saw 10 firms cut their dividends according to Seeking Alpha's Market Currents and the Wall Street Journal's daily listing of dividend declarations. At 13 (and counting since the month hasn't run out of trading days yet), it is unlikely that the total for August 2015 will surpass the next-highest total of 21, which was recorded in January 2015.

Still, any figure over 10 is consistent with recessionary conditions being present in the U.S. economy, although the reduction in the number of firms announcing dividend cuts below levels that are consistent with contraction occurring in the U.S. economy is a positive development.

And since 26 August 2015 qualifies as what we would consider to be an interesting day for the stock market, here's the latest update to our alternative futures chart, where it you can predict how far ahead in time investors are focusing their attention, you can anticipate within a relatively narrow margin of where stock prices will go next.

Alternative Futures - S&P 500 - 2015Q3 - Rebaselined Model - Snapshot 26 August 2015

Even with closing up by 72.90 points, the third best trading day ever for the S&P 500 in terms of the point difference from the previous day's closing value, investors would appear to remain focused on 2016-Q1 in setting today's stock prices. Keeping in mind that we're referring to the dividend futures contract that will come into effect after the third Friday of December 2015, which means it covers dividends that will be paid out at the end of the current calendar year through the third Friday in March 2016, that very recent shift in focus is not a good one for investors looking for positive returns.

In our updated chart above, we've begun projecting the impact from the shock wave left behind by the extraordinary market activity of the past week into the future, much of which is a consequence of the event's effect upon the nation's bond markets. Speaking of which, that's a major factor in how we were able to accurately forecast the onset of the event, a good portion of which was embedded into the future of the stock market because of what happened exactly two years ago.

Meanwhile, behind the scenes, we've peered ahead in time through the end of the year, but we're going to hold off on commenting on what we've seen until this initial shock has dissippated to a greater extent and we have a better idea of what the impact crater it is leaving behind will look like.

Data Sources

Seeking Alpha Market Currents. Filtered for Dividends. [Online Database]. Accessed 26 August 2015.

Wall Street Journal. Dividend Declarations. [Online Database]. Accessed 26 August 2015.

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