Category Archives: chaos

The Dragons Beyond the Edge of the Map and the S&P 500

Last week, we considered what the potential impact of stock buybacks would be to the S&P 500 as if the venerable stock market index was the stock price of a single company. We concluded our analysis as follows:

What does that mean for the market going forward? We'll let a JPMorgan analyst's comments from May 2013 (via ZeroHedge) explain:

"The other side effect of elevated dividends and share buybacks is that these distributions to shareholders may reduce the long term potential of the company to grow relative to the alternative of capital spending."

Two years later, that dynamic would be a major reason why the upward growth of the S&P 500 has largely stalled out through the first seven months of 2015, which through Friday, 24 July 2015, is less than 1% higher than it was at the end of 2014. It likely took longer than they expected, but scenario described by JPMorgan's analyst arrived all the same.

But not for the reasons they believe.

To understand why, you have to appreciate the central fallacy we built into our "what if" analysis, which involved treating the value of the S&P 500 index as if it were the share price of a single company. To understand why that's wrong requires a brief review of S&P's U.S. Indices Methodology:

On any given day, the index value is the quotient of the total float-adjusted market capitalization of the index’s constituents and its divisor. Continuity in index values is maintained by adjusting the divisor for all changes in the constituents’ share capital after the base date. This includes additions and deletions to the index, rights issues, share buybacks and issuances, and spin-offs. The divisor’s time series is, in effect, a chronological summary of all changes affecting the base capital of the index. The divisor is adjusted such that the index value at an instant just prior to a change in base capital equals the index value at an instant immediately following that change.

Because of those adjustments, it is not correct to apply the same math as would apply to the stock price of a single company as we did in our "what if" analysis, as the value of the index is continually adjusted to account for the effect of share buybacks on each component stock's market capitalization weighting as they occur. [The math that's used is explained in this PDF Document.]

So if you're an investor looking to the S&P 500 index to capitalize on share buybacks, you're investing in the wrong place. To that end, S&P also maintains an equal-weighted share buyback index that might be more suited to you, which the Financial Lexicon has ably described.

As for the real reason the S&P 500 is stalling out, you don't need to look any further than the lack of adequate momentum for growing the index' future dividends (or rather, the sustainable portion of earnings that are likely to be realized in the future), whose upward growth has been likewise stalling out. Speaking of which, let's take a look at what our rebaselined model is projecting for the future trajectory of the S&P 500 through 2015-Q3, as our standard model reached the edge of its map of the future:

S&P 500 Alternative Futures - 2015Q3 - Rebaselined Model - Snapshot 30 July 2015

We confirm that through 30 July 2015, investors remained closely focused on the third quarter of 2015, where the expectations associated with the quarter, which ends in September, driving their investment decisions. The "2015 Greek Bailout" minor speculation bubble that had prompted the S&P 500 to run hot two weeks ago has fully dissipated.

So at least the dragons that be on this side of the map's edge are familiar ones!


Standard and Poor. S&P Dow Jones Indices: Index Methodology. [PDF Document]. March 2015. Accessed 31 July 2015.

Running Hot with the S&P 500

Last week, we indicated that stock prices in the U.S., through Tuesday, 14 July 2015, were "running hot" and were "almost 3% higher than they might otherwise be" because of positive news regarding the resolution of Greece's debt default crisis.

Through the close of trading on Friday, 17 July 2015, U.S. stock prices, as measured by the S&P 500 index, remain almost 3% higher than they might otherwise be.

How do we know that?

Fortunately for us, the last two weeks have provided nearly optimal conditions for being able to assess what's behind the movement of stock prices using our standard model. With Federal Reserve Chair Janet Yellen set to testify before the U.S. Congress on Wednesday, 15 July 2015, she and a majority of other Fed officials had been working overtime over the preceding two weeks to provide investors with forward guidance on what to expect for when the central bank would begin hiking short term interest rates. The expectation they were seeking to set is that the Fed would act by the end of the third quarter of 2015 to begin raising its effective Federal Funds Rate above the 0-0.25% range where it has been set since December 2008.

According to the WSJ's July 2015 survey of private forecasters, they've been successful in setting that expectation for the future.

WSJ: September's Still the One -

That's significant information where our analysis is concerned because of how we set the simple scale factor we use in our model of how stock prices work. Given its tremendous influence over the future expectations of investors in recent years, we've used the statements provided by influential Fed officials about its planned future actions for when it would begin increasing the Federal Funds Rate around the times of the Federal Reserve's Open Market Committee's meetings to first empirically determine that scale factor (it's about equal to 5 when used with the CBOE's dividend futures data) and to subsequently verify and periodically confirm the calibration of that scale factor as those meetings occur. We therefore know from the FOMC's last several meetings that our model scale factor is currently very well calibrated.

That strong calibration then means that during times when U.S. investors are closely focused on the forward guidance being provided by Federal Reserve officials, as they have been during the last two weeks, we have the ability to isolate and measure the effect of other factors upon U.S. stock prices that might otherwise be indistinguishable from the typical level of noise that exists in the U.S. stock market.

And in the last two weeks, nearly all of that extra noise has come from two places: Greece and China. Between the two, the actions that China's government took to avoid having its stock market crash turn into a cascading failure for the nation's economy would appear to have been somewhat effective in halting its decline. The impact on the U.S. stock market has been neutral however as the momentum needed to fully reverse the declines in China's stock markets has yet not developed.

Meanwhile, the capitulation of the Syriza Party-led government in Greece to that nation's international creditors, in which the divided party's leaders suddenly reversed the course of action they had been following to instead accept even more severe terms from their creditors than those they had previously rejected in order to be bailed out and by doing so, to avoid the full collapse of Greece's economy on their watch, contributed more significant positive noise to the U.S. stock market.

We describe that reaction as noise because as yet, there has not been a significant change in the cash dividends expected to be paid out by U.S. firms by the end of 2015-Q3, the point in time to which the Federal Reserve has succeeded in focusing the attention of U.S. markets, to support the current valuation of stock prices. Unless that changes so that the amount of cash dividends is increased to support stock prices at their current elevated level, we can reasonably expect that stock prices will adapt accordingly. At least, in the absence of additional noise or a shift in focus by investors to a different point of time in the future.

And though we previously said that we would be retiring our alternative futures chart based on our standard model for the year, we're bringing it back one last time because we really don't have a better one to illustrate what our model is communicating.

Alternative Futures - S&P 500 - 2015Q3 - Standard Model - Snapshot on 2015-07-17

We wonder how much of the recent extraordinary effort by Fed officials to focus U.S. markets on the third quarter of 2015 in their efforts to manage expectations was driven by the desire to insulate and provide stability to U.S. markets that might otherwise have become quite volatile in response to the financial crises in China and Greece.

Nearly Breaking the S&P 500’s 4-Year Trend

Since 4 August 2011, the U.S. stock market, as measured by the value of the S&P 500 index versus its trailing year dividends per share, has been in a stable, upward trend. On 8 July 2015 though, that trend came within 12 points coming to a sudden end after enduring for nearly four years.

S&P 500 Index Value vs Trailing Year Dividends per Share, 2011-

Some quick notes. First, this isn't technical analysis, and although it sort of looks like it, it shouldn't be confused with that nearly useless form of tasseography. It's really statistics, and more specifically, what we've presented in the chart above is really a visualization of a statistical hypothesis test.

Second, we're making a pretty important assumption that the trajectory of stock prices with respect to their underlying dividends per share follows a power law relationship during relative periods of order in the stock market, where order can be said to exist when the variation in stock prices with respect to its central trend trajectory can be described by a normal (or Gaussian) distribution.

Or more accurately, when the hypothesis that such a normal distribution might apply under a particular set of circumstances or a limited period of time cannot be rejected.

In reality, stock prices do not closely follow a true normal distribution, as they're not really random. And of course, order in the stock market can break down suddenly, as the leftmost portion of the data shown on our chart partially illustrates for the period between 30 June 2011 and 4 August 2011, as stock prices broke their previous trend and went into a Lévy flight as they dropped a couple hundred points as dividends continued to rise before stabilizing onto their current long-term trend.

At their current level, it wouldn't take much for the current period of order in the U.S. stock market to break down. All stock prices would need to do is to either dip below the lower dashed red curve shown in our chart above, or alternatively, simply continue to drift sideways to slightly higher as they have since the beginning of 2015.

Flooding the Zone

Federal Reserve - Source:

Just for the record, we think the Federal Reserve is really trying to set one particular expectation for investors.

How do we know? Let's just say that we haven't missed how the Fed's top officials have been flooding the zone during the last two weeks to direct investors to focus their attention upon the near term....

And also for the record, what they have succeeded in doing is focusing investors on 2015-Q3. And while the news from Greece has added positive noise to U.S. stock prices since 10 July 2015, boosting the value of the S&P 500 almost exactly 3% higher than they might otherwise be, that figure is still within the typical range we would expect if investors were tightly focusing their attention on the expectations they have that are associated with 2015-Q3.

Which is to say that the stock market is running somewhat on the hot side of things. Plan accordingly.

China’s Import Recession Continues and Weighs on Stocks

After April 2015's data anomaly, the year-over-year growth rate of the value of all the goods exported from the U.S. to China once fell back to levels that suggest that China's economy is experiencing recessionary conditions for the just-reported month of May 2015.

At the same time, the value of goods being imported by the U.S. from China rose back to positive territory, indicating that the U.S. economy experience positive but slow growth conditions in May 2015.

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

Through May 2015, the economic situation in China is clearly not improving, as a nation experiencing robust economic growth would need to import a growing level of goods to sustain its growth. Instead, the decline in the year-over-year growth rate in the value of goods imported by China from the U.S. suggests that a considerable amount of slack has developed within China's economy, which the U.S. Census Bureau's international trade data indicates has not yet really begun to close.

That continuing weakness has persisted despite the Chinese government's interventions. The following chart from the World Bank's June 2015 China Economic Update illustrates the actions that China's government has taken as

World Bank - China Economic Update - June 2015 - Updated 3 July 2015 - Figure 1.4 - p. 5 -

These are not actions that are taken by the government of a nation whose economy is really growing at a rate of 7% per year, which suggests that once again, China's own reported economic data is highly suspect. Or as Christopher Balding memorably described the mismatch between China's promised GDP figures and the reported profitability of Chinese businesses on Twitter:

1. GDP growth of 7% w/profit growth of 0.6%=really bad managers or 2. GDP growth not really 7%. Choose 1 or 2 #China

We should acknowledge that the Chinese government's new efforts to prop up share prices on the nation's stock exchanges are also not those of a nation whose economy is really growing at a rate of 7% per year. Bloomberg provides a chart giving additional context to the relevant time series here:

Bloomberg: China's Market and Policy Timeline - November 2014 through 5 July 2015 -

In addition, the Financial Times reports that China's government has taken the unusual step of informally banning the phrases "equity disaster" and "rescue the market" from Chinese publications, even as it has acted to halt trading in the stocks of 940 over 1,300 firms. In addition, Bloomberg declares in a headline that "China Tells Investors: Go Ahead, Bet the House" in a report on how China's government is allowing Chinese investors' houses to be put up as collateral for margin loans if they borrow money to buy Chinese stocks, which is also an effort to try to get more Chinese investors to plow more money into the nation's stock markets. As is restricting major stockholders from selling any of their shares.

Here's where China's reported 0.6% profit growth for its businesses is a problem. Back in 2013, China's top companies were encouraged by their government to pay at least 30% of their annual profits to shareholders to lure more investors into the nation's stock markets.

From our perspective, that policy clearly worked. However as Chinese investors are now learning, having directly linked dividends to be a set percentage of earnings provides very little insulation from having stock prices suddenly crash when investors shift their attention to a more distant future and realize that the earnings growth needed to support the cash dividend payments they may previously have been expecting won't be there. That's simply part of the math of how stock prices work and is the cause for the "panic sentiment" that has come to grip the nation's stock markets over the past three weeks.

At this point, what needs to happen for Chinese stock prices to stabilize and reverse their negative trend is for the acceleration of the growth rate of expected future dividends per share to shift from negative to positive (or rather, the rate at which expectations for future dividends are worsening needs to slow down). To enhance stock price stability and reduce volatility in the longer term, Chinese firms would then need to decouple the direct linkage between their dividends per share and their earnings per share, setting their dividend policies to be on a more stable and sustainable growth trajectory as their prices recover.

At least that would be a far more useful path for China's political and business leaders to follow going forward. Take it from us - if we can train the Fed's minions to avoid downturns and stabilize U.S. stock prices by managing expectations, we can certainly do the same for their Chinese counterparts.


Board of Governors of the Federal Reserve System. China / U.S. Foreign Exchange Rate. G.5 Foreign Exchange Rates. Accessed 7 July 2015.

U.S. Census Bureau. Trade in Goods with China. Accessed 7 July 2015.