Today, we're going to tell a big story with just two charts. Here's the first, which updates the chart we last featured on 15 October 2015.

In case you are wondering what we mean by "QE Promise" in the chart above, we're hearing that the European Central Bank is looking to extend its current Quantitative Easing program, where it is currently buying 60 billion Euros worth of bonds each month, by another six months. Oh, and is also considering expanding it by another 10-20 billion Euros per month.

But that's not the big question that needs to be answered, because in our second chart, in which we get under the hood of the S&P 500 with some old school analysis, spanning 2015 to date, we show why what we showed in the first chart is such a concern....

Here's the problem. The ECB launched their current 60 billion Euro per month QE program back in March 2015, having virtually no effect on U.S. stock prices, which behaved exactly as our theory says they should, with the change in the rate of growth (acceleration) of stock prices being directly proportionate to the change in the rate of growth (acceleration) of expected future trailing year dividends per share at the point of time in the future where investors have focused their forward-looking attention.

But now, in the days since the market reacted to the ECB's announcement that it is considering extending and potentially expanding its QE program, U.S. stock prices have risen well above the levels we would expect to see them at if they were purely being driven by the market's underlying fundamentals.

That suggests that speculation, more than any other factor, is what has driven stock prices to their currently elevated levels, where investors in the U.S. market are betting in favor of one or more of the following possibilities:

• The amount of dividends per share that the market will pay in the future will be much higher than currently expected levels, for which we have data looking forward through 2016-Q3 that says that we should only look for single digit growth, at best.
• The U.S. Federal Reserve will not only not hike short term interest rates, it will add Oprah Winfrey to its board, who is going to launch her own new round of quantitative easing, and it will be glorious ("And you get a billion, and you get a billion, and you get a billion!...").
• The multiplier in the fundamental relationship between stock prices and their underlying dividends per share, instead of being nearly constant as it has been over the past several years, has suddenly, unexpectedly and inexplicably changed, from +5 to something on the order of -50.

In short, we think it's a noise event. The good news it that is would appear to be one that is actually providing a positive benefit in that it has shifted the likely future trajectory of stock prices to be higher than what we were projecting a month ago.

The bad news is that it's a noise event. All noise events end - it's only ever a question of when.

We don't comment on the analysis posted at ZeroHedge very often, as many of the contributions to the site have a very high noise to signal ratio, but we have to tip our hats to the Tyler Durdens because they've helped answer a question we've had about the internal market mechanics that are needed to drive a Lévy Flight Rally.

A Lévy flight is perhaps best described as a random walk where the otherwise random path an object takes as it moves is periodically punctuated by sudden, large movements. That's very different from a typical random walk, also called Brownian Motion, where the variation in the magnitude of movements might be described by a normal distribution.

Going by that frame of reference, the large movements of a Lévy flight would therefore be highly unlikely, and therefore, unpredictable. Or as a mathematician might describe the bell curve associated with the distribution of a Lévy flight, they have much fatter tails than do typical normal distributions.

But then, the stock market is well known for its sheer number of improbably fat-tailed events. A good example is the recent rally that took place between 29 September 2015 and 5 October 2015. Here, we had observed in our model of how stock prices work as the transition from investors being focused on 2016-Q1 to instead be focused on 2016-Q2 (or Q3).

We could easily understand how stock prices could crash in a Lévy Flight event, as might happen when investors suddenly shift their focus from a future quarter with more positive prospects for their investments to a different future quarter with more negative prospects. All that takes is an increased demand to sell in a market environment with reluctant buyers considering a negative sentiments for the future prospects of their newly acquired holdings. But why would that sentiment suddenly reverse to power stock prices up at a much faster pace than markets rise during boom times? Especially in the absence of positive news for the market.

And that's where ZeroHedge's analysis by actual market traders becomes invaluable. They dug into the "savage reversal" and found a rather amazing amount of short covering, where investors who had speculated too far to the negative side of the market during the Lévy Flight crash that preceded the rally were force to cover their short investments by buying up shares - especially of the stocks they were most seeking to sell short.

We see then that a very large short squeeze played a very large role in driving stock prices back up so quickly. Better still, in the days following the rally, the Tyler Durdens also documented which stocks were the most "hated", as measured by the percentage of their floating shares being shorted, going into the rally.

And though our model of how stock prices work allows us to determine in advance where stock prices will go during a Lévy flight crash or rally, we're still learning what it takes for stock prices to actually make those quantum shifts during such "fat-tailed" events.

Welcome back to the cutting edge!

One final note - in our chart showing the alternative future trajectories of stock prices above, since our model incorporates historic stock prices, its projections of future stock prices can be affected by the volatility associated with them, which we refer to as the echo effect. To account for that factor in upcoming days, we've simply drawn a straight line (the purple shaded region) across the period where we observe that our model's projections are most affected by larger than typical volatility in those historic stock prices.

On 21 September 2015, we wrote:

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:

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

Here is what the updated version of that chart looks like now that we're past the end of the third quarter of 2015:

And here is what the succeeding chart for the fourth quarter of 2015 now looks like, as of the close of trading on 7 October 2015:

The large and pronounced changes we have been observing in the level of stock prices is the result of what we'll call our quantum random walk hypothesis, which largely resolves and reconciles the fundamental and apparently incompatible differences in the theories advanced by such economists as Eugene Fama and Robert Shiller for how stock prices behave, for which they were jointly awarded the Nobel prize in economics (or whatever it's really called) in 2013.

And since today is the official beginning of the previous quarter's earnings reporting season, where we have the very real potential to see a major shakeup in the future expectations for the S&P 500's dividends per share, we might soon see how changes in the fundamental driver of stock prices that defines the "quantum levels" of future stock prices affects their likely projected trajectories.

Welcome back to the cutting edge!

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.

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?

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.