The statistical forecasting model says:
October, 2019:  +2% (Outstanding, but one model now has doubts.)
Next 6 Months:  +15%  (Very high again.)
Probability of at least breaking even: 96% – 98% (Excellent)
What am I doing? Fully invested since spring 2009.

These probabilistic stock market forecasting models remain strongly positive, but for the past several months the market has significantly under-performed their expectations. 

Sadly, given stark and disparate fears among investors, I expect volatility to remain high — or increase — so I doubt that the models will be very accurate for the near future. Trump, Brexit, China trade, declining manufacturing, interest rate inversion — there are plenty of quite scary possibilities out there to worry stock holders.  No one really likes it, but volatility remains a good thing for the market.

Why do my models remain optimistic?  I use several leading indicators for recessions — in general they do not see a recession coming very soon.  I have several measures of financial market panic — they are not even twitching.  Market deviation from long term trends — nope, stock markets in the U.S. are following their normal long term paths.  Federal action to quiet the economy — with high deficit spending, increasing money supply, and declining interest rates the government at several levels is stimulating the economy.

Eventually things will turn bad. Sooner or later there will always be a re-balancing. But, my models do not think it will happen soon.

Long Term Trend Lines
Both the Value Line Arithmetic Average (smaller companies count as much as the giants) and the S&P 500 (emphasizing huge companies) are within their general long term channels.  The S&P 500 continues to be on the high side and the Value Line clings to the bottom of its normal range.  No big clues to future market performance.

The statistical forecasting model says:
September, 2019:  +3% (Outstanding.)
Next 6 Months:  +19%  (Very high!)
Probability of at least breaking even: 96% – 99% (Excellent)
What am I doing? Fully invested since spring 2009.

How low can interest rates go? And stay low for how long?  Those are the big questions for the economy and the stock market.  I wish I had an answer, but I don’t.  Further declines in interest rates could spark a spectacular stock market rise, while rate increases could bring on the next big recession.  It feels to me like we are balanced on a knife edge.

My gut emotions about the stock market have a long and solid track record of being flat out wrong. Time and time again I misjudge the situation.  For example, I have been scared stiff for well over a year about buying long term bonds. I was sure that interest rates would have to rise sooner or later and that would send the value of long term bonds crashing.  But, so far this year long term bond funds are up about 25%.  Much better than the stock market! 

My lousy gut-level forecasts are why I built my stock market forecasting models over a decade ago. The models combine the most probable impacts of about a dozen economic / business / investor-emotion variables and arrive at statistical forecasts of what is most likely to happen next.  The effects of every factor I use have proven statistical validity since at least 1984. Most of them have been tracked since at least the 1960’s. Together they form a group of similar models that forecast what the stock market is most likely to do next.

The current contrast between my gut reaction to the market and my models is black and white!  My gut worries, but the models remain wildly positive about the path of stocks for the next half year. 

One thing I use to comfort myself is my faith that volatility is actually good for the stock market. Volatility makes it unlikely that the market will settle into a complacent trend that will take it far off the track that the economy would justify.  Given the reality show President we have, high market volatility is near certain.  Unpleasant as market volatility can be, it is probably a good thing for now.

Long Term Trend

The S&P 500 trend is well within its normal trend zone.  But, the much more predictable Value Line Arithmetic Average is right at the lower boundary — 10% below its many decade trend.  Good reason to be concerned.

This blog and my forecasting models have nothing to do with high frequency trading.  This short post explains the situation.

A major theorem of the mathematical field of statistics says that high speed or high frequency trading can be profitable — at least in theory.

The Central Limit Theorem is a cornerstone of conventional statistics. If you take a sample of some sort of group, say, the height of third grade students in a particular school,  you tend to get survey results that look something like a bell curve.  The heights of the kids will vary from tall to short, but most of their heights will tend to fall somewhere near the middle.  The Central Limit Theorem doesn’t say anything about how that initial survey comes out.  (Maybe the third grade class you sampled is made up of kiddie basketball recruits mixed with tiny gymnasts.)

But, the Central Limit Theorem says if you run multiple samples of the same population, the median of those samples will form a very tight normal distribution (bell curve).  The variance, the total difference (squared) of things from the true average) should be much less for all the surveys taken together than for just a single survey.

In the context of high frequency trading this means that if you make a zillion trades, you can bet against trades that are being made by other people far from the current strike price. If someone is willing to make a statistically unusual (i.e. ‘stupid’) trade you can make money by betting against them.  Make enough of these trades and you should be able to make money.  This is what ‘algorithmic trading’ is all about.  It should work.

But.

High Frequency Trading  Only Works Until it Doesn’t
Long Term Capital Management was a firm that practiced highly leveraged,  high frequency probabilistic trading from 1993 to 1998.  It attracted roughly $120 billion in capital and was wildly successful.  In 1998 LTCM was betting in a very big way on a rebound in the falling Russian currency. But, suddenly Russia defaulted on its government debt. LTCM went bankrupt nearly instantly, and quickly the world economy was on the brink of economic collapse. Algorithmic trading works until it doesn’t work.

Low Hanging Fruit Was Eaten Years Ago
High frequency trading has been around for years. It is no big secret anymore. I attended a graduate seminar on it nearly a decade ago.

What has happened is that over time the opportunity for new players to profit has shrunk.  In the early stages ‘high frequency’ would mean trading with a gap of a few seconds.  Even a decade ago the frequency of trade response had shrunk to the range of nanoseconds.  Players fought to get their trading servers as near as possible to the stock market exchange computers.

An individual investor swimming in the pond of high frequency trading is like a minnow swimming with a school of sharks.

In Brief: 
This long term stock market model compares the current level of the U.S. stock market against its very long term trend.  The market has followed an exponential growth trend closely most of the time since at least 1871.  When it wandered off course in the past, things did not end well.

The model relies on 5 key elements:

• Long term exponential growth history of the S&P 500 (adjusted) going back to 1871,
• Factoring out major booms and busts when the market deviates wildly from its long term track. 
• Congressional Budget Office  (CBO) Real Potential Gross Domestic Product model using GDP data back to 1949
• 10-year Treasury bond interest rates
• Contrast the S&P 500 with a market index that is calculated on an equal-weight basis, making it less influenced by financial speculation.

The model’s aim is simply to point out if stock market indexes are grossly distorted and are ripe for a major correction. The model does not say ‘when’ a correction will occur; that’s the purpose of my 6-month stock market model. But, the long term stock market model will tend to give a solid indication of the direction of the next major market move and some guidance on the likely magnitude of a coming correction.

From the Beginning
With a bit of distortion, the stock market reflects the economy, and from the dawn of civilization the world economy has been growing — not at a steady rate, but at an increasing rate.  The chart below from Wikipedia.org shows per capita GDP growth since 1500.  Data is available elsewhere showing that growth has been increasingly-increasing for the past half million years! More people, more accumulated capital and capacity, and advancing technology (very broadly defined) are the reason for this amazing growth.  It has been far from steady (e.g. the Black Plague, World Wars) but growth has been relentless.  The rest of this blog post shows that the same basic exponenetial-exponential growth rate is still intact.

(Credit: By Qwfp – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=7122503)

Increasingly Increasing Growth Since 1871
The Standard & Poor’s 500 Index is probably the most widely recognized index for U.S. stocks. It began as the Standard & Poor’s Composite Index in 1923 and assumed its present form in 1957.  Data is available, however, going back to 1871 that is based on the principles used to calculate the index.

Running a statistical regression analysis shows that the S&P 500 Index has grown at a fairly constant rate for that century-and-a-half period — despite booms, busts, wars, countless leaps in technology, a developing world, and innumerable changes in government, from when the U.S. had 13 fewer states and the “talking telegraph” (telephone) was invented.  It was not a random process. We know that too many factors to count do, indeed, impact the stock market day by day, week by week, and even decade by decade.  None the less, a simple, fairly steady growth curve describes roughly 150 years of stock market history remarkably well.  In the long run the stock market isn’t so crazy after all. Thank the Law of Large Numbers for that.

Stock market growth has not been perfectly constant.  Instead, the rate of growth of the S&P 500 has been slowly increasing.  Growth of the Index over time has been “increasingly increasing”.

Inflation has also been a factor in the increasing level of the S&P 500.  But, it is not entirely clear exactly how inflation should be factored into the equation. The erosion of the value of the dollar has been far from constant, and there also can be fair disagreements over how inflation gets measured, (For example, a very significant aspect of our recent low inflation has been the radical continuing decline in the price of personal electronics.  Does a faster cell phone actually decrease your real cost of living? Or do you just have a faster cell phone out of the deal?)  One way or another, though, continuing inflation is part of the picture of the increasingly increasing level of the S&P 500.

The graph below shows the best fit of an exponential-exponential trend line with the S&P 500 Index.. The correlation between the S&P 500 and the simple steady growth path is 0.95 — where a correlation of 1.0 would be a perfect match and 0 would be no match at all.  At first glance it looks like the trend curve and the actual Index match incredibly well except for two glaring divergences which turn out to be the Dot Com Bubble and the Great Recession.  That is very far from the truth.  The curve fit in earlier years was not as smooth as it looks and the recent divergences were not as bad as they look in this graph. Next, let’s see why.

Percentage Growth is What Matters
The graph below also shows the path of the S&P 500 Index since 1871 with the same exponential trend. It is the same data as the previous graph, but the vertical axis plots the logarithm of the Index value.  Each vertical unit is a given percentage change in the Index, not a linear increase.  If the market grew at a constant percentage rate the resultant plot would be a straight line.  Since the actual plot curves up smoothly, it means the rate of growth has been slowly and somewhat-steadily increasing.

Focusing on percentage market shifts is essential. It becomes clear that the early years of the S&P 500 were nowhere near as smooth as they appear in the first graph.  For example, through the Dot Com crash, on a month by month basis the S&P 500 dropped roughly 650 points, a gut-wrenching collapse of over 40%.  In contrast, the Great Crash of 1929 amounted to only about a 25 point fall in the S&P 500 — but that amounted to an incredible drop of over 80%! This log-based plot shows how the Great Depression severely held back the stock market for over a decade.  Our more recent Great Recession was a minor blip in comparison. Overall, the Index recently was no more erratic than long ago.

Sometimes Things Do Go Crazy

From the graph above — and my experienced reality — I take a general view that for, say, 75% of the time the stock market behaves normally. (Literally, its relative value and frequent variations tend to follow a statistical normal distribution very closely with large deviations happening every once in a while.) Investing bubbles and market busts, bull and bear markets are extremes /aberrations from normal market growth.

Through history most investors have not been able to spot the top of large developing market bubbles — they always expect “Greater Fools” to keep coming along. Most people did not see either the Great Crash of 1929 or the Dot Com Bubble coming.  The usual cry is “This time it’s different”  Probably not next time either. Probably.

So, in building a long term trend model let’s drop out what the market has been doing for the past few years. With certainty we can  identify past bubbles and busts.  So, as a definition, in my long term model, bubbles are times in the past when the market was way above the long term trend, and implosions were when the market was way below trend.  This is a major simplification of a lot of complexities in the market and the economy.  But, it turns out to be a very useful simplification.

The chart below shows the long term growth of the S&P 500 Index after elimination of the most egregious periods when the actual market value diverged from the first approximation of the long term trend. Most of the deletions were related to the Great Crash of 1929 and the Great Depression,  I could have gone a bit further in my data pruning and the Dot Com Bubble and Great Recession scars would have disappeared as well.  But, with just limited data scrubbing the correlation with smooth exponential goes up to 0.98 (again, 1.0 would be a perfect score.)

In all the analysis that follows, I’ll continue to drop out the largest market crises in order to better define the normal growth of the stock market.

 Market Growth from 1949

The Great Depression and World War II spurred incredible increases in the range and quality of economic data collected.  Later, computers made it possible to amass a tremendous volume and range of data and to develop sophisticated economic models. To get a more accurate long term model of the stock market we need to bring in additional information content that is only available from 1949 on.

I have a second motivation here beyond just increasing precision.  As shown above, we can show that with really surprising accuracy the U.S. stock market has followed an exponential-exponential growth trend. Also, because the U.S. economy is a massive behemoth, we can be pretty sure that the long term trend — even if it shifts — won’t shift all that much in the next few years.  But, several current economic factors could make the near term trend vary more than usual.  By pulling in the next data stream I can bring to bear another model of long term exponential economic growth that effectively reflects the combined efforts of some of the world’s top economists for the past few decades. By no coincidence, at its core this other model also focuses on exponential-exponential growth.

Real Potential GDP The Congressional Budget Office (CBO) is a highly respected, objective and non partisan arm of the U.S. Congress established in 1974. Both political parties and nearly every powerful vested interest group would like to bend the  CBO analysis to fit their agenda. That intense and highly bankrolled attention from all sides keeps the CBO model objective.  The stakes are very high in this game!

 Each year the office issues forecasts of government expenses and revenue along with anticipated 10-year impacts of proposed legislation — but, by its basic rules CBO does not make policy recommendations.

A central part of CBO analysis is a highly detailed  sector-by-sector computer model of the workings of the U.S. economy. The details of the CBO model are public, and are subject of extensive outside review.  The model is described  in 55 pages here.  CBO staff make minor adjustments to the model every few years.  Because of its pedigree, this model probably has more impact on the views of financial analysts than any other.  (Any Econ PhD student, professor or quant lobbyist would find fame and fortune if they could identify a flaw in the model or even just give the model a tweak.)

The CBO Real Potential GDP model closely matches the historical path of actual GDP (adjusted for inflation).  But, for the purposes of my long term stock market model, it does not matter much if the CBO model is accurate — it is a major cornerstone of what economists and financial analysts believe to be valid.  And, with the stock market “belief” trumps “accuracy” always. CBO Real Potential GDP data — projected 10 years into the future — is available from the Federal Reserve Economic Data (FRED) site here.

U.S. Gross Domestic Product data has only been available since 1949. That is the starting point for the CBO Real Potential GDP estimates as well. It is important to emphasize that the CBO model is focused on how the U.S. economy should perform at a sustainable pace at low unemployment. Also, the model addresses what economists call ” real” GDP — the confusing impacts of inflation are factored out.

There is a small difficulty here, however.  The CBO Real Potential GDP model addresses the U.S. economy, not the U.S. stock market.  They are far from being the same thing.

The S&P 500 Index grows faster than the U.S. economy. First, since 1949 the relative share of GDP attributable to major industry has increased. More and more we live in a world of gigantic corporations rather than small businesses. Second, the mega corporations that comprise the S&P 500 have become increasingly international in scope. In a continuing process of globalization, growth of S&P companies is not limited by the U.S. economy anymore. Third, over the second half of this period, to reduce shareholder tax burdens, corporations have shifting away from issuing dividends toward seeking faster growth and  using stock buybacks to increase stock prices.  Fourth, since the early ’80’s the rise of index-based funds, 401k – type retirement investment, no-load funds and ETF’s,  and online trading have drawn a disproportionate amount of investing directly to the S&P 500 and its component companies.  Fifth, the CBO model is of inflation-adjusted “real” , GDP, not actual raw GDP. To my mind, at least, there is an open question of which sorts of price inflation (commodity, food price, rents, entertainment, etc.) best relate GDP and stock market prices. Each of these 5 factors cause the S&P 500 Index, in particular, to grow at a different rate than the general economy.  For these reasons the long term model also includes an empirical exponential adjustment factor to better link the CBO Real Potential GDP and S&P 500 growth rates. (Yes, “empirical adjustment factor” is a contrivance or ‘kludge’ to force a better fit, but I think it is legitimate here.)

10-Year Treasury Bond Rates Interest rates have a profound effect on the stock market. At the most simple level, it is relatively easy to start a profitable business if  your dad gives you many millions of dollars, or even if you borrow your start up money at 2% .  But, it would be near impossible to start a business if you can only borrow money at a 40% rate!

Another take on interest rates comes from seeing that owning stocks is an alternative to owning commercial or government bonds, or holding property such as real estate.  Changing interest rates makes some investments more attractive than others — spurring massive capital flows from one kind of investment to another.  Capital can flow fast, but the relative prices of alternative investments will shift even faster.

Additionally, changing interest rates also have a huge direct effect on business profitability, the business cycle, and recessions. More expensive borrowing directly reduces profits for most businesses. Large increases to interest rates can suddenly shut down the financial system and make previously successful businesses go bankrupt.

Take a bit of time to enlarge the graph of long term interest rates below. Notice that before most periods of recession interest rates rose sharply and significantly — that is the Federal Reserve “taking away the punch bowl just as the party is getting started”. Large and fast increases in long term interest rates bring on recessions.  And stock markets tend to crash well before a recession actually begins and often more than a year before a recession is officially announced..

Also, in the period from 1949 to the present there has been a major secular (long term) pattern to interest rates.  Over the course of decades long term interest rates increased, culminating in explosive rate increases from roughly 1970 to 1981.  The trend then reversed with a continuing decline in interest rates until recently.  This prolonged change has had a huge effect on the stock market.  Steadily rising interest rates put a damper on the stock market for decades. Market pundits called this slow growth period “stagflation” — stagnant economic growth coupled with high inflation.  Then Federal Reserve policy reversed. Interest rates fairly consistently fell and the stock market reaped wonderful gains that were well above the long term average.

That three decade run of good luck caused by declining long term interest rates is over.

Long term interest rate shifts are especially relevant now — in future years interest rates have little room to drop — they can only stay roughly level or go up. The past decade or so of historically low interest rates, besides making businesses more profitable, also led businesses to borrow huge amounts of capital in order to buy back shares of their own stock thereby directly increasing their per-share market price.   Further, the residential housing market — a major factor in the economy and family wealth –became based on very low long term interest rates.  For homeowners an increase of just a couple percent could lead to a mortgage payment increase of easily 20% to 60%.  That would shut down the housing and construction markets and cripple all the businesses that flourish when people move and change houses. When interest rates go up in the next round of increases the negative economic tidal waves may be huge..

The wonderful tail wind of gradually reducing interest rates benefited both the stock market and long term bond investors since 1981.  But, that tail wind is gone. The outlook for the next decade of stock ownership is much less rosy than the last few decades. Interest rates are a major key to what happens.

The next graph shows the S&P 500 since 1949 along with a modified trend line.  The modified line factors in long term exponential growth, CBO Real Potential GDP, smoothed 10-year Treasury rates, and a factor to reconcile the difference between GDP and stock market growth rates.

With the addition of Real Potential GDP and interest rates elements, trend correlation goes up to 0.995 if we ignore the excesses of the Dot Com Bubble and the Great Recession. But, if we include all data points, the correlation is still 0.98.

Consider a Different Kind of Stock Market Index
Look at this next part as a way to gauge market speculation levels.

Though the S&P 500 Index is the most widely followed stock market average, it is not the only game in town.

As discussed earlier, the very popularity of the S&P 500 makes it subject to stock market speculation. Vast quantities of index funds and exchange traded funds based on the index mean that incredible trading volumes and dramatic price swings can occur in a flash.

The basic approach by which the value of the S&P 500 is calculated further makes it prone to speculative bubbles and sudden crashes.  The Index is based on 500 of the nation’s largest corporations that collectively amount for roughly 80% of total market capitalization. That’s good. But…

The Index is calculated based on the total capitalization of each company (number of shares times the current share price).  Those huge corporations are not weighted equally.  As this is written, Microsoft Corporation has a weight of 4.11 and Mattel Inc. has a weight of slightly under 0.016.  So, Microsoft is over 250 times more important than Mattel.

A net result is that a relatively small number of truly gigantic companies, generally with astronomical Price/Earnings ratios, dominate the S&P 500 calculation.  They don’t have to be profitable, just highly capitalized. During a market bubble a small number of companies can become the subject of massive speculation and rapidly rise within the Index, pushing down companies that are less in favor.  Once it was the Dot Com companies.  Now it is the FAANG companies like Facebook, Amazon, and Apple. Speculative greed can turn in a heartbeat to a panicked stock market crash.

I prefer to follow a major market index, the Value Line Arithmetic Average (VALUA) that includes roughly three times as many companies as the S&P 500, but weighs each of them equally. In VALUA both Microsoft and Mattel count the same — as do many companies you may never have even heard of.  VALUA is not currently available as an exchange traded fund.  An equal weight fund based on the S&P 500 companies is available with the ticker symbol RSP.

The plot below shows both VALUA and the S&P 500 Index from 1984 to the present. VALUA has performed significantly better than the S&P 500.  But, they both experience major market disruptions at about the same time.

Bringing It All Together
Finally, the two graphs below show the long term trends of VALUA and the S&P 500 since 1984.  Both are based on long term exponential-exponential growth, CBO Real Potential GDP and 10-year Treasury bond interest rates.  Both show bands that indicate 10% above and 10% below the respective trend lines.  I will be showing these graphs in most of my future blog posts. The relative strength of each compared to their long term trend lines should prove to be interesting.

(Graphs shown here are as of May, 2019)

And what, after all of this explanation do these charts say? First, both indexes are fairly close their very long term trend lines. That is comforting. Second, both indexes are somewhat above their long term trend lines.

So?

The stock market is a little high, but does not appear to be going really crazy now.  The long term odds, of course, favor “regression to the mean” — a small correction.

The statistical forecasting model says:
August, 2019:  +2.6% (Outstanding.)
Next 6 Months:  +14%  (Very high!)
Probability of at least breaking even: 96% – 98% (Excellent)
What am I doing? Fully invested since spring 2009.

My rosy forecasts are getting horribly boring, but this is what my econometric forecasting models are spitting out.

These stock market prediction models remain highly positive.  As long as the Federal Reserve continues to keep filling up the punch bowl of intoxicating low interest rates the story probably will not change.  The U.S. economy is an incredibly large and powerful juggernaut that just keeps chugging along — despite the current irresponsible administration. 

Hey, no one really wants to be the grownup in the place who will advocate fiscal responsibility.

When the stock market and the U.S. economy eventually crash down, hopefully these models will give us some warning. But, for right now the models — several of them in fact — see the party continuing.

The statistical forecasting model says:
July, 2019:  +2.8% (Outstanding.)
Next 6 Months:  +15%  (Very high!)
Probability of at least breaking even: 97% – 98% (Excellent)
What am I doing? Fully invested since spring 2009.

Last month the model was extremely positive, but I was dubious.  Once again, the model was more nearly right than I.  No surprise there. The model expected a one month gain of 3.5%, but the S&P 500 actually rose over 6%!  Best June in decades.

The model (actually, several flavors that each view data a bit differently) remains highly positive, seeing little chance that the stock market will fall during the second half of the year. That, of course, doesn’t mean that the market cannot possibly crash.  It just means that if the market does what it typically does in response to a number of economic variables, then it will do just fine. Fortunately, the market usually does what it usually does.

Long Term Trend Lines
Not much news here.  Both the S&P 500 and the Value Line Arithmetic Average are within their normal envelopes. As a minor corroboration, the Morningstar Fair Value Graph , a favorite of mine, says the overall market is about 3% undervalued.

These are quite boring graphs, but hopefully they illustrate that the stock market is not in the middle of any wild and crazy bubble. It is just following the same basic trend it has followed for decade after decade.  The one worry is that these trend lines take account of prevailing interest rates. If interest rates shoot up, stocks will certainly tumble down. That does not appear likely for months at least.

The statistical forecasting model says:
June, 2019:  +3.5% (Outstanding.)
Next 6 Months:  +15%  (Very high!)
Probability of at least breaking even: (Excellent . 97% – 98%)
What am I doing? Fully invested since spring 2009.

I guess it’s put up or shut up time for my forecasting models.  There is not much I can write to hedge or try to obscure what their calculations conclude.

Lots of scary financial / economic /political news. Not much positive sounding news. The models don’t seem to care. They look at other stuff, and still can’t read internet news stories.

There was a big stock market drop last month.  Interest rates have inverted (short term interest rates are lower than long term rates).  Usually that means a recession is in the cards sooner or later. The federal deficit (remember when that used to be big news?), well, it is growing faster than when the Obama stimulus plan kicked in to provide emergency economic relief. I can’t keep track of all the trade wars the President has started, or seems to want to start. Brexit seems more certain, whatever that means. Home sales are down — always a bad sign. The President seems to be sinking deeper and deeper into his swamp. The list of bad omens seems pretty long at the moment.

But, my forecasting models — all my current flavors — are incredibly optimistic. They appear to be shouting: Yippee! The one month predictive model points to a 3.5% gain, which for that model is very high.  The models dealing with probability of at least breaking even see winning over the next 6 months as a near-sure thing (around 97%) The 6 month models are uniformly expecting gains of around 15% — again, that is very high for them.

So, the models aren’t hedging their forecasts.

All I know for sure is that for the past 11 years the models have a much better track record than my gut feelings. I am just staying fully invested to see how this plays out.

Time will tell.

Spoiler Alert: I plan to turn this post into a semi-permanent tab at the top of this blog page.  Most of the discussion I already covered in previous posts as I developed this long term model.

However wonderful this long term market model may be, it tells you very little about what the market is most likely to do in the next few months.


In Brief: 
This long term stock market model compares the current level of the U.S. stock market against its very long term trend.  The market has followed an exponential growth trend closely most of the time since at least 1871.  When it wandered off course in the past, things became.disturbingly interesting.

The model relies on 5 key elements:

• Long term exponential growth history of the S&P 500 (adjusted) going back to 1871,
• Factoring out major booms and busts when the market deviates wildly from its long term track. 
• Congressional Budget Office  (CBO) Real Potential Gross Domestic Product model using GDP data back to 1949
• 10-year Treasury bond interest rates
• Contrast the S&P 500 with a market index that is calculated on an equal-weight basis, making it less influenced by financial speculation.

The model’s aim is simply to point out if stock market indexes are grossly distorted and are ripe for a major correction. The model does not say ‘when’ a correction will occur; that’s the purpose of my 6-month stock market model. But, the long term stock market model will tend to give a solid indication of the direction of the next major market move and some guidance on the likely magnitude of a coming correction. 

Increasingly Increasing Growth Since 1871
The Standard & Poor’s 500 Index is probably the most widely recognized index for U.S. stocks. It began as the Standard & Poor’s Composite Index in 1923 and assumed its present form in 1957.  Data is available, however, going back to 1871 that is based on the principles used to calculate the index.

Running a statistical regression analysis shows that the S&P 500 Index has grown at a fairly constant rate for that century-and-a-half period — despite booms, busts, wars, countless leaps in technology, a developing world, and innumerable changes in government, from when the U.S. had 13 fewer states and the “talking telegraph” (telephone) was invented.  It was not a random process. We know that too many factors to count do, indeed, impact the stock market day by day, week by week, and even decade by decade.  None the less, a simple, fairly steady growth curve describes roughly 150 years of stock market history remarkably well.  In the long run the stock market isn’t so crazy after all. Thank the Law of Large Numbers for that.

Stock market growth has not been perfectly constant.  Instead, the rate of growth of the S&P 500 has been slowly increasing.  Growth of the Index over time has been “increasingly increasing”.

The graph below shows the best fit of an exponential-exponential trend line with the S&P 500 Index.. The correlation between the S&P 500 and the simple steady growth path is 0.95 — where a correlation of 1.0 would be a perfect match and 0 would be no match at all.  At first glance it looks like the trend curve and the actual Index match incredibly well except for two glaring divergences which turn out to be the Dot Com Bubble and the Great Recession.  That is very far from the truth.  The curve fit in earlier years was not as smooth as it looks and the recent divergences were not as bad as they look in this graph. Next, let’s see why.

Percentage Growth is What Matters
The graph below also shows the path of the S&P 500 Index since 1871 with the same exponential trend. It is the same data as the previous graph, but the vertical axis plots the logarithm of the Index value.  Each vertical unit is a given percentage change in the Index, not a linear increase.  If the market grew at a constant percentage rate the resultant plot would be a straight line.  Since the actual plot curves up smoothly, it means the rate of growth has been slowly and somewhat-steadily increasing.

Focusing on percentage market shifts is essential. It becomes clear that the early years of the S&P 500 were nowhere near as smooth as they appear in the first graph.  For example, through the Dot Com crash, on a month by month basis the S&P 500 dropped roughly 650 points, a gut-wrenching collapse of over 40%.  In contrast, the Great Crash of 1929 amounted to only about a 25 point fall in the S&P 500 — but that amounted to an incredible drop of over 80%! This log-based plot shows how the Great Depression severely held back the stock market for over a decade.  Our more recent Great Recession was a minor blip in comparison. Overall, the Index recently was no more erratic than long ago.

Sometimes Things Do Go Crazy

From the graph above — and my experienced reality — I take a general view that for, say, 75% of the time the stock market behaves normally. (Literally, its relative value and frequent variations tend to follow a statistical normal distribution very closely with large deviations happening every once in a while.) Investing bubbles and market busts, bull and bear markets are extremes /aberrations from normal market growth.

Through history most investors have not been able to spot the top of large developing market bubbles — they always expect “Greater Fools” to keep coming along. Most people did not see either the Great Crash of 1929 or the Dot Com Bubble coming.  The usual cry is “This time it’s different”  Probably not next time either. Probably.

So, in building a long term trend model let’s drop out what the market has been doing for the past few years. With certainty we can  identify past bubbles and busts.  So, as a definition, in my long term model, bubbles are times in the past when the market was way above the long term trend, and implosions were when the market was way below trend.  This is a major simplification of a lot of complexities in the market and the economy.  But, it turns out to be a very useful simplification.

The chart below shows the long term growth of the S&P 500 Index after elimination of the most egregious periods when the actual market value diverged from the first approximation of the long term trend. Most of the deletions were related to the Great Crash of 1929 and the Great Depression,  I could have gone a bit further in my data pruning and the Dot Com Bubble and Great Recession scars would have disappeared as well.  But, with just limited data scrubbing the correlation with smooth exponential goes up to 0.98 (again, 1.0 would be a perfect score.)

In all the analysis that follows, I’ll continue to drop out the largest market crises in order to better define the normal growth of the stock market.

 Market Growth from 1949

The Great Depression and World War II spurred incredible increases in the range and quality of economic data collected.  Later, computers made it possible to amass a tremendous volume and range of data and to develop sophisticated economic models. To get a more accurate long term model of the stock market we need to bring in additional information content that is only available from 1949 on.

I have a second motivation here beyond just increasing precision.  As shown above, we can show that with really surprising accuracy the U.S. stock market has followed an exponential-exponential growth trend. Also, because the U.S. economy is a massive behemoth, we can be pretty sure that the long term trend — even if it shifts — won’t shift all that much in the next few years.  But, several current economic factors could make the near term trend vary more than usual.  By pulling in the next data stream I can bring to bear another model of long term exponential economic growth that effectively reflects the combined efforts of some of the world’s top economists for the past few decades. By no coincidence, at its core this other model also focuses on exponential-exponential growth.

Real Potential GDP The Congressional Budget Office (CBO) is a highly respected, objective and non partisan arm of the U.S. Congress established in 1974. Both political parties and nearly every powerfful vested interest group would like to bend CBO analyses to fit their agenda. That intense and highly bankrolled attention from all sides keeps the CBO model objective.  The stakes are very high in this game!

 Each year the office issues forecasts of government expenses and revenue along with anticipated 10-year impacts of proposed legislation — but, by its basic rules CBO does not make policy recommendations.

A central part of CBO analysis is a highly detailed  sector-by-sector computer model of the workings of the U.S. economy. The details of the CBO model are public, and are subject of extensive outside review.  The model is described  in 55 pages here.  CBO staff make minor adjustments to the model every few years.  Because of its pedigree, this model probably has more impact on the views of financial analysts than any other.  (Any Econ Phd student, professor or quant lobbyist would find fame and fortune if they could identify a flaw in the model or even just give the model a tweak.)

The CBO Real Potential GDP model closely matches the historical path of actual GDP (adjusted for inflation).  But, for the purposes of my long term stock market model, it does not matter much if the CBO model is accurate — it is a major cornerstone of what economists and financial analysts believe to be valid.  And, with the stock market “belief” trumps “accuracy” always. CBO Real Potential GDP data — projected 10 years into the future — is available from the Federal Reserve Economic Data (FRED) site here.

U.S. Gross Domestic Product data has only been available since 1949. That is the starting point for the CBO Real Potential GDP estimates as well. It is important to emphasize that the CBO model is focused on how the U.S. economy should perform at a sustainable pace at low unemployment. Also, the model addresses what economists call ” real” GDP — the confusing impacts of inflation are factored out.

There is a small difficulty here, however.  The CBO Real Potential GDP model addresses the U.S. economy, not the U.S. stock market.  They are far from being the same thing.

The S&P 500 Index grows faster than the U.S. economy. First, since 1949 the relative share of GDP attributable to major industry has increased. More and more we live in a world of gigantic corporations rather than small businesses. Second, the mega corporations that comprise the S&P 500 have become increasingly international in scope. In a continuing process of globalization, growth of S&P companies is not limited by the U.S. economy anymore. Third, over the second half of this period, to reduce shareholder tax burdens, corporations have shifting away from issuing dividends toward seeking faster growth and  using stock buybacks to increase stock prices.  Fourth, since the early ’80’s the rise of index-based funds, 401k – type retirement investment, no-load funds and ETF’s,  and online trading have drawn a disproportionate amount of investing directly to the S&P 500 and its component companies. Each of these 4 factors cause the S&P 500 Index, in particular, to rise faster than the general economy.  For these reasons the long term model also includes an empirical exponential adjustment factor to better link the CBO Real Potential GDP and S&P 500 growth rates.

10-Year Treasury Bond Rates Interest rates have a profound effect on the stock market. At the most simple level, it is relatively easy to start a profitable business if  your dad gives you many millions of dollars, or even if you borrow your start up money at 2% .  But, it would be near impossible to start a business if you can only borrow money at a 40% rate!

Another take on interest rates comes fron seeing that owning stocks is an alternative to owning commercial or government bonds, or holding property such as real estate.  Changing interest rates makes some investments more attractive than others — spurring massive capital flows from one kind of investment to another.  Capital can flow fast, but the relative prices of alternative investments will shift even faster.

Additionally, changing interest rates also have a huge direct effect on business profitability, the business cycle, and recessions. More expensive borrowing directly reduces profits for most businesses. Large increases to interest rates can suddenly shut down the financial system and make previously successful businesses go bankrupt.

Take a bit of time to enlarge the graph of long term interest rates below. Notice that before most periods of recession interest rates rose sharply and significantly — that is the Federal Reserve “taking away the punch bowl just as the party is getting started”. Large and fast increases in long term interest rates bring on recessions.  And stock markets tend to crash well before a recession actually begins and often more than a year before a recession is officially announced..

Also, in the period from 1949 to the present there has been a major secular (long term) pattern to interest rates.  Over the course of decades long term interest rates increased, culminating in explosive rate increases from roughly 1970 to 1981.  The trend then reversed with a continuing decline in interest rates until recently.  This prolonged change has had a huge effect on the stock market.  Steadily rising interest rates put a damper on the stock market for decades. Market pundits called this slow growth period “stagflation” — stagnant economic growth coupled with high inflation.  Then Federal Reserve policy reversed. Interest rates fairly consistently fell and the stock market reaped wonderful gains that were well above the long term average. 

That three decade run of good luck caused by declining long term interest rates is over.

Long term interest rate shifts are especially relevant now — in future years interest rates have little room to drop — they can only stay roughly level or go up. The past decade or so of historically low interest rates, besides making businesses more profitable, also led businesses to borrow huge amounts of capital in order to buy back shares of their own stock thereby directly increasing their per-share market price.   Further, the residential housing market — a major factor in the economy and family wealth –became based on very low long term interest rates.  For homeowners an increase of just a couple percent could lead to a mortgage payment increase of easily 20% to 60%.  That would shut down the housing and construction markets and cripple all the businesses that flourish when people move and change houses. When interest rates go up in the next round of increases the negative economic tidal waves may be huge..

The wonderful tail wind of gradually reducing interest rates benefited both the stock market and long term bond investors since 1981.  But, that tail wind is gone. The outlook for the next decade of stock ownership is much less rosy than the last few decades. Interest rates are a major key to what happens.

The next graph shows the S&P 500 since 1949 along with a modified trend line.  The modified line factors in long term exponential growth, CBO Real Potential GDP, smoothed 10-year Treasury rates, and a factor to reconcile the difference between GDP and stock market growth rates.

With the addition of Real Potential GDP and interest rates elements, trend correlation goes up to 0.995 if we ignore the excesses of the Dot Com Bubble and the Great Recession. But, if we include all data points, the correlation is still 0.98.

Consider a Different Kind of Stock Market Index
Look at this next part as a way to gauge market speculation levels.

Though the S&P 500 Index is the most widely followed stock market average, it is not the only game in town.

As discussed earlier, the very popularity of the S&P 500 makes it subject to stock market speculation. Vast quantities of index funds and exchange traded funds based on the index mean that incredible trading volumes and dramatic price swings can occur in a flash.

The basic approach by which the value of the S&P 500 is calculated further makes it prone to speculative bubbles and sudden crashes.  The Index is based on 500 of the nation’s largest corporations that collectively amount for roughly 80% of total market capitalization. That’s good. But…

The Index is calculated based on the total capitalization of each company (number of shares times the current share price).  Those huge corporations are not weighted equally.  As this is written, Microsoft Corporation has a weight of 4.11 and Mattel Inc. has a weight of slightly under 0.016.  So, Microsoft is over 250 times more important than Mattel.

A net result is that a relatively small number of truly gigantic companies, generally with astronomical Price/Earnings ratios, dominate the S&P 500 calculation.  They don’t have to be profitable, just highly capitalized. During a market bubble a small number of companies can become the subject of massive speculation and rapidly rise within the Index, pushing down companies that are less in favor.  Once it was the Dot Com companies.  Now it is the FAANG companies like Facebook, Amazon, and Apple. Speculative greed can turn in a heartbeat to a panicked stock market crash.

I prefer to follow a major market index, the Value Line Arithmetic Average (VALUA) that includes roughly three times as many companies as the S&P 500, but weighs each of them equally. In VALUA both Microsoft and Mattel count the same — as do many companies you may never have even heard of.  VALUA is not currently available as an exchange traded fund.  An equal weight fund based on the S&P 500 companies is available with the ticker symbol RSP.

The plot below shows both VALUA and the S&P 500 Index from 1984 to the present. VALUA has performed significantly better than the S&P 500.  But, they both experience major market disruptions at about the same time.

Bringing It All Together
Finally, the two graphs below show the long term trends of VALUA and the S&P 500 since 1984.  Both are based on long term exponential-exponential growth, CBO Real Potential GDP and 10-year Treasury bond interest rates.  Both show bands that indicate 10% above and 10% below the respective trend lines.  I will be showing these graphs in most of my future blog posts. The relative strength of each compared to their long term trend lines should prove to be interesting.

(Graphs shown here are as of May, 2019)

And what, after all of this explanation do these charts say? First, both indexes are fairly close their very long term trend lines. That is coforting. Second, both indexes are somewhat above their long term trend lines.

So?

The stock market is a little high, but does not appear to be going really crazy now.  The long term odds, of course, favor “regression to the mean” — a small correction. My 6-month market model may beg to differ or not.

The statistical forecasting model says:
May, 2019:  +0.7%  (Models not very certain about May)
Next 6 Months:  +6 to +8% 
Probability of at least breaking even: Good to Very Good.
What am I doing? Fully invested.

The models’ forecasts for the coming half year are somewhere good but not great.  The models that I have been reporting on for the last decade are mainly in the “good performance” camp.  I am in the process of transitioning to updated versions of the models.  These newer models have about the same view of the market.  

I have no idea what is likely in the coming month, however. The several models’ forecasts for just the month of May are split.  But the only time these one-month models deserve any attention anyway is when their forecasts are either very high or very low. So, ignore them. :o)

Overall, it looks like there is a good chance the stock market is heading into a “blow off top”. My personal expectation is for some volatility. Seems like time for a bit of fear to creep back in.

The trend lines for the S&P 500 and the Value Line Arithmetic Index together say that the stock market overall is following its very long term track based on Real Potential GDP and long term shifts in interest rates. That’s good.

But, there is a somewhat interesting nuance — the S&P 500 is near to the top of the channel while the Value Line Arithmetic is not.  No big deal, but normally that means that stocks may be moving into a minor bubble.

(Click on image to enlarge.)

The statistical forecasting model says:
March, 2019:  +0.5%  (Average)
Next 6 Months: +9% (Above average)
Probability of at least breaking even: Good.
What am I doing? Fully invested.

The interest rates for 10-year Treasury Notes and 3-month Treasury Bills were the same this past week.  That is usually a very bad sign of low confidence in economic growth and typically points to economic recession. But, it doesn’t mean that the stock market is going to crash right away. 

If the spread between long and short term rates gets worse over the next couple of months, it will be time to worry.  Current statements from the Federal Reserve are dove-ish. The Fed is not intentionally trying to slow the economy. They are willing to be very very patient in maneuvering the economy out of the historically low rates needed to end the Great Recession. (Don’t hold your breath — it could take another decade to complete the process.)

My forecasting model has become more optimistic, expecting the next 6 months to be bullish for the stock market.  Me? I’m not so sure. I expect more volatility as we go through the process of treating government and the economy as some sort of reality TV show that is mainly interested in high ratings.

Long Term Trends
I have included graphs of long term trends for the Value Line Arithmetic Average and the S&P 500.  In both cases the trend lines are based on the Congressional Budget Office Real Potential Gross Domestic Product model and smoothed data on 10-year U.S. Treasury notes. You will need to click on the images to enlarge them enough to really see much. At the moment, VALUA is slightly below trend and S&P 500 is a bit above trend.  I wouldn’t read too much into these differences.  The whole purpose of these long term trend lines is to see if the market is grossly above or below their long term trends. Right now, both appear to be fairly close.  No big bubble.

Well, actually that isn’t quite true. Over the long haul the broad-based VALUA has performed distinctly better than the S&P 500. But, when investors are enthusiastic the S&P will shoot up faster.  We are seeing a bit of that now.