Category Archives: chaos

What We Do, Explained by Others

One of the nicer things ever said about the kinds of analysis we do here at Political Calculations recently surfaced over at the ChicagoBoyz blog, as Grurray took on the challenge of explaining the unique brand of stock market forecasting we do.

We can look at ways of fundamentally gauging the valuation of the stock market such as price to earnings ratio or the so-called Warren Buffet Indicator of total market cap to GDP ratio. I like to look at the Q ratio which is a simple comparison of the total price of the stock market to the replacement costs of all companies listed. This is the favored metric of billionaire black swan investor Mark Spitznagel, who by the way wrote a most excellent book, The Dao of Capital, about Boydian investment strategies.

Q Ratio Since 1900, July 2015, Data through June 2015 - Source: Doug Short - ratio - Pricey but is it dicey?

By this measure, the market looks to be at a pricey level compared to other points in time. 1907, 1929, 1937, and 1968 were all years when the stock market peaked and saw a significant decline. The problem is it’s also at the same level as 1997, which had a small pause before marking the half way point in multi-year rally. We generally have seen regression to the mean in the past, but that doesn’t necessarily suggest it has to ever happen again. We could be waiting a long time for a sanity check to take hold, especially if the definition of sanity has changed.

A shorter term answer possibly comes from the world’s best econometrics blog Politcal Calculations. They believe, convincingly in my opinion, that expectations for future dividends drive stock prices in the near future, absent any surprising shocks to upset the apple cart. Those of us who used to watch Larry Kudlow on CNBC (since his show was cancelled there hasn’t been any reason to watch that silly network anymore) remember he used to say ‘earnings are the mother’s milk of stocks’. Well if that’s true than dividends are your father’s pemmican.

What they do is take values of dividend futures traded on the Chicago Board of Options Exchange and apply a multiple (and some other math) to convert them to expected stock prices. Their calculations show a possible slide in prices for the next few weeks to few months. It has worked reasonably well in the past with a few caveats.

There are different instruments traded for different times in the future. Prices can and do take leaps from one trajectory to the other. It usually happens when someone from the FED talks about raising rates, and then the financial press speculates what specific month or quarter it can happen. In this way, stock prices behave similar to quantum particles bouncing from one energy level to another. It’s not a good way to pin down exactly where stocks are going but just gives a range.

The other caveat is this measurement only works when the market is in a state of relative order, and not buoyed or rattled by some overly cheery or dreary news. While at a smaller level the market seems to obey quantum mechanics, at the macro level it acts like a natural system, following mathematical probabilities such as those observed in predators hunting or even groups of people foraging. The market moves from more easily observable and predictable periods until the forageables (earnings and dividends) run out, in which case it moves into chaos and unpredictability until new expectations are established.

What will trigger rapid moves in either direction and out of the current financial horse latitudes is anybody’s guess. There’s a big vote in Greece this weekend, but how many times has that situation reached a cliffhanger? Perhaps too many to matter anymore. As unsatisfactory as it sounds, what usually occurs is something we weren’t expecting, not an event that seems to replay itself over and over again. The best we can really predict is that we won’t be drifting forever, and the time will come when the stock market will move far away from this level. The key is to stay ready for it when it finally does.

Here's the link to our stock market forecasting math and here's our math-free description of how stock prices work.

Now, to address Grurray's "other caveat"! When you get into our model, you'll find that our math actually does continue to work when stock prices go on what's called a Lévy flight, which is the pattern that Grurray is referring to when he links to articles describing how both predators and people adapt their hunting and foraging methods when food is scarce. We know it continues to work in that situation because we invented behind our analytical methods in the latter months of 2008, when stock prices were collapsing (we publicly introduced the discovery we made that enabled us to develop our forecasting methods on 10 December 2008).

Behind the scenes, in the early months of 2009, we were finding that we could anticipate where stock prices were heading as they were crashing after they had entered into Lévy flight, because what was changing was the expectations for dividends in the future, changes in which preceded subsequent changes in stock prices, which is what allowed us to confirm the direction of causality in the relationship between the two.

Not to mention being able to quickly confirm just a week after the fact that the bottom had been set for that particular Lévy flight for U.S. stock prices. We later proved (again, behind the scenes) in late 2012 that our model is capable of handling the opposite situation. That latter episode also confirmed that the quantum nature of those expectations always applies - even during Lévy flight.

Where Grurray's other caveat is correct is when stock prices are driven by factors other than their basic fundamentals. The classic example here actually predates our model's development by a number of years, where we don't believe that our forecasting model could have tracked stock prices very well without considerable adjustment during the period of the Dot Com Bubble. That event was caused by a disparity in the tax rates that applied to capital gains and to dividends, which greatly changed the results of the investment rate of return math for dividend versus non-dividend paying stocks for investors so much that it continued to distort the entire U.S. stock market until the disparity between the investment tax rates was finally fixed in late May 2003.

Unfortunately, we are not able to put our model to the test of the Dot Com Bubble because we lack the historic dividend futures data during that period of time, which prevents us from being able to accurately re-create what the future looked like in those days.

Other than those significant non-fundamental stock price driving factors, the rest for us is pretty much noise - things that actually are the result of investors reacting to the relatively random onset of new information as it becomes known, the speculation associated with which accounts for much of the apparent day-to-day random walk of stock prices (you know, like the reaction in the U.S. market to what's going on in Greece). We spent several years after our original discovery of how stock prices work collecting the necessary data and documenting the ongoing context behind it to quantify that aspect of how stock prices behave, which allows our model to determine not just the general future trajectory of stock prices, but also the likely ranges we can reasonably expect stock prices will fall during periods with "typical" levels of noise in the market.

We've come a long way. We've gone from only being able to anticipate what the average prices of stocks would be during the next month to accurately anticipating the actual trajectory of stock prices within a small margin of error on each day of the next month (as we've previously demonstrated under optimal conditions). Or if you prefer longer range forecasts, we can reasonably anticipate the general trajectory of stock prices several months in advance.

But not much more than that. Although we can project the alternative trajectories that stock prices are likely to take on a daily basis as much as a year into the future, it is far more likely that the expectations we use in our forecasting model will change well before that distant forecast future arrives.

After all, a man's got to know his model's limitations!

Closing out the Second Quarter of 2015 with the S&P 500

Reuters has sounded some dire news:

Wall St. tumbles as investors flee equities on Greek debt crisis

U.S. stocks fell sharply in heavy trading on Monday and the S&P 500 and the Dow had their worst day since October after a collapse in Greek bailout talks intensified fears that the country could be the first to exit the euro zone.

The European Central Bank froze funding to Greek banks, forcing Athens to shut banks for a week to keep them from collapsing.

And Greece appeared to confirm it was heading for a default after a government official said the country would not pay a 1.6 billon euro loan installment due to the International Monetary Fund on Tuesday.

U.S. investors also worried about Puerto Rico's debt problems and a bear market in China the day before quarter-end and ahead of Thursday's U.S. jobs report and the long weekend for U.S. Independence Day.

So are U.S. investors really "fleeing" the U.S. stock market based on the situation in Greece, Puerto Rico and China?

Well, if we look at what our standard model of how stock prices behave, we find that the level of stock prices is within the range of values we would reasonably expect them, whether U.S. investors were focused on either the third quarter of 2015, the fourth quarter of 2015 or the second quarter of 2016!

S&P 500 - Alternative Futures - 2015-Q2 - Standard Model - Snapshot 2015-06-29

That's really a consequence of how tightly compressed the expectations for the change in the year-over-year growth of dividends per share in each of these future quarters is at this time - there's really not that much difference between them at this point (although watch out below if investors suddenly focus on 2016-Q1!).

But more practically, if we had to pick one future quarter where the expectations associated with are currently driving the trajectory of the S&P 500, we'd go with 2015-Q3, for reasons not having anything to do with Greece, Puerto Rico or China, so the answer to that first question is... not so much.

Which will be nice while and as long as that lasts, but perhaps a better and more relevant question to ask at this point is how close is order to breaking down in the U.S. stock market?

Keeping in mind that the answer is presently rising at a rate of just under 1 point per trading day, the answer that applies the S&P 500's closing value of 2067.54 on 29 June 2015 is about 1.3%, or 27.4 points away from the key statistics-based threshold.

S&P 500 Daily Closing Value vs Trailing Year Dividends per Share, 30 June 2011 through 29 June 2015

More interesting is that its happening at nearly the four year anniversary of the last time order broke down in the U.S. stock market, after 30 June 2011, when the Federal Reserve's QE 2.0 bubble suddenly deflated.

S&P 500 Daily Closing Value vs Trailing Year Dividends per Share, December 1991 through June 2015

So will the period of order that began on 4 August 2011 finally break down after holding for four years? Well, if we consider each of the alternative trajectories for which we have sufficient data to project into the future using our standard forecasting model is any indication, the answer is... almost certainly yes.

S&P 500 - Alternative Futures - 2015 - Standard Model - Snapshot 2015-06-29

We've got about a month where we can continue to use our standard forecasting model for the S&P 500 in 2015, before we'll need to switch to our rebaselined model to work around the effects of the echoes resulting from last year's stock price volatility upon our standard model.

But this will likely be the last time we share what the alternative futures for the S&P 500 look like this year, as we'll have other things going on that will demand our attention.

The S&P 500 Finds Its Ceiling

We now have a handle on what the expected future for the S&P 500's dividends per share is through 2016-Q2. Our first chart shows the recent past history of how Standard and Poor has recorded each quarters dividends from 2013-Q1 through 2015-Q1, with the expected future dividends as recorded by the CBOE's dividend futures contracts as of 19 June 2015, the expiration date for the 2015-Q2 dividend futures contract:

Past and Expected Future Dividends per Share for the S&P 500, 2013-Q1 through 2016-Q2

Standard and Poor will report its dividends per share figure for 2015-Q2 after the end of the month.

The most important thing to take away from the dividend futures data presented in the chart above is that the rate at which dividends are expected to increase is decelerating. Which is the biggest factor behind why stock prices have mainly moved sideways to slightly higher in 2015 to date.

More interesting though is how quickly investors have shifted their forward looking focus since last week, when they were tightly focused on 2015-Q3 as they went about setting stock prices. In the last two days, they've moved their focus in stages to the more distant futures of 2015-Q4 and then 2016-Q2.

Alternative Futures for the S&P 500 - 2015Q2 - Standard Model - Snapshot 2015-06-19

And in making that last move, they've pretty much found the fundamental ceiling for the S&P 500, as the potential for continued upward movement through the end of June 2015 is limited to what we consider to be our typical margin of error.

That's not to say that stock prices couldn't move higher, but that would be consistent with what we would describe as a noise event, which would likely not be sustained in the absence of a significant improvement in the expectations for future dividends.

All noise events end. It's only ever a question of when.

Decoherent Expectations and the S&P 500

A week ago, we went to the very specific trouble of spelling out three very specific "what-if" scenarios for the trajectory that U.S. stock prices, as measured by the closing value of the S&P 500, would take during the week to be. Thanks to optimal forecasting conditions, one of those scenarios was almost perfectly dead on target.

Alternative Futures for S&P 500, 2015-Q2, Standard Model, Snapshot on 2015-06-19

The what-if scenario in question is the one where we projected what the S&P 500 would be if investors were to shift their forward-looking focus to 2015-Q3 in making their current day investment decisions. As for what made our forecasting conditions optimal, we have to thank the relative absence of noise in the market, where the Federal Reserve's Open Market Committee meeting provided the primary market news for the week.

That news was that economic conditions had improved since the first quarter of 2015, which investors interpreted as indicating that the Fed would be likely to act sooner rather than later to start hiking short term interest rates, which had become the dominant expectation on Monday, 15 June 2015. Although the Fed did not commit to a specific timetable or other details for its interest rate hiking plans, our standard model suggests that the stock market behaved in a way that is fully consistent with investors shifting their focus from 2015-Q4 in the previous week to instead fix their focus on 2015-Q3 and then holding it there through the end of the week.

So how come we couldn't have specifically forecast that specific trajectory? Why would we go to the very specific trouble of forecasting three separate likely trajectories for stock prices that differed only by how far in the future investors might focus their attention?

Well, as we keep saying, it is because stock prices obey the rules of quantum physics, where stock prices actually exist in a state of superposition, much like atoms and subatomic particles.

One mind-boggling consequence of quantum physics is that atoms and subatomic particles can actually exist in states known as "superpositions," meaning they could literally be located in two or more places at once, for instance, until "observed" — that is, until they interact with surrounding particles in some way. This concept is often illustrated using an analogy called Schrödinger's cat, in which a cat is both dead and alive until beheld.

Superpositions are very fragile. Once disturbed in some way, they collapse or "decohere" to just a single outcome.

For stock prices, the things that exist in superpositions are the expectations for the amount of cash dividends that will be paid out by specific points of time in the future, so we automatically have the situation where multiple expectations exist simultaneouly in the market. When investors observe, or in our terminology, "focus" upon a specific point of time in the future in response to new information as it becomes known, stock prices will collapse or decohere to a single outcome that is consistent with the expectations for dividends at the point of time they've focused upon within a relatively small margin of error - at least, given the amount of noise that typically exists in the market.

That situation applies when nearly all investors shift their attention to a single point of time in the future. There have been times when we've observed investors splitting their forward-looking attention between two separate points of time in the future, with stock prices falling between the "100% focused" trajectories our model forecasts, with stock prices being weighted accordingly with respect to the percentage split in investor focus.

As you might imagine, depending upon how different the expectations are for different points of time in the future, changes in stock prices that result from shifts in how far ahead in time that investors are focusing their attention can be very pronounced. Those shifts are a major contributor to volatility in the stock market when they occur and account for much of the apparently chaotic behavior of stock prices.

Knowing all that then, projecting the future trajectories of stock prices with some degree of accuracy is a complex proposition, but not a difficult one once you have the data that applies for each future point of time whose expectations for dividends are known. Anybody who can solve a simple quantum kinematics problem can do it.

The Economy Is Better, So Why Is the S&P 500 Slipping?

The single best measure of the relative state of the U.S. economy when it is experiencing some degree distress is perhaps the number of publicly-traded U.S. companies that announce they are cutting their dividends each month. Through 12 June 2015, that indicator suggests that the U.S. economy has taken a positive turn beginning in May 2015, which we can confirm because the cumulative number of dividend-cutting firms in the U.S. in the second quarter of 2015 is now coming in quite a bit lower than the pace that was established in the first quarter, which experienced negative GDP growth:

Cumulative Announced Dividend Cuts in U.S. Stock Market by Day of Quarter, 2015, Snapshot on 12 June 2015

But you wouldn't know that's the case from the U.S. stock market, which has basically been slipping sideways or only slightly moving higher throughout the whole second quarter of 2015:

Alternative Futures for the S&P 500 - 2015-Q2 - Standard Model - Snapshot on 12 June 2015

The reason why the market has been moving sideways has to do with the complex nature of how stock prices work (described in math here), but in a nutshell, the explanation is this - while the U.S. economy is indeed performing better than in the first quarter of 2015, it hasn't translated into a robust improvement in the outlook for cash dividends expected to be paid out in future quarters.

Instead, the change in the year-over-year growth rates for each of the future quarters for which we currently have data (2015-Q3, 2015-Q4 and 2016-Q1) is such that stock prices are such that when we translate those expectations into the likely trajectories that stock prices are likely to follow, we find that they are much more likely to either continue moving sideways or to fall than rise, with the actual trajectory dependent upon the future point in time to which investors fix their attention.

That forward-looking focus appears to have become highly correlated with the U.S. Federal Reserve's plans for hiking short-term interest rates in the U.S. Here, the timing of when that might begin to happen has become a key driver for U.S. stock prices.

At present, the dynamics of that factor are as follows:

  • For a hike in 2015-Q3, stock prices would initially dip a bit, before resuming a largely sideways trajectory in the short term (through the end of June). This scenario would correspond to the Federal Reserve coming to the conclusion that the U.S. economy is performing so strongly that it must act to begin cooling it off.
  • For a hike in 2015-Q4, stock prices would move sideways to slightly higher in the short term. This scenario would correspond to the Fed seeing a slower rate of improvement in the U.S. economy.
  • For a hike in 2016-Q1, stock prices would fall sharply before stabilizing at a level about 5% lower than the current level. This scenario would likely play out if the Federal Reserve comes to the conclusion that the outlook for the U.S. economy is likely to slow down from how it began performing in May 2015, and might also be influenced by external factors, such as Greece's looming debt default in Europe and its effect upon global markets.

The wild card in this is that we do not yet know what the expectations are for dividends in 2016-Q2. We'll know more about what the stock market future associated with that quarter sometime next week.