Sticky Luck

Five:

The Effect of the Future on the Market

The nature of market-forecasting models.  Contrasting with scientific and other financial modeling.  Market as sum of all market-forecasting models.  How to suddenly halve all market wealth.  Pricing any new technology era.  The unlikeliness of continuity and what it means for our assumptions.  The fallacy of mean reversion.

Against the arguments in the last chapter, the managers and advisors would defend themselves with the capabilities of their forecasting models.  These are software programs usually of considerable sophistication, which will make future projections of one or more of individual company performances, their stock prices, relevant industries, the stock market as a whole, and the national and/or global economy.  By “model,” we mean a set of formulas into which are fed data taken from the current environment, plus a set of assumptions about the future.  Of course, the data on the current environment, both at the individual company level and the at macro-economic level, represent part of reality.  The formulas and assumptions attempt to progress today’s reality forward, showing how one set of data will eventually have an effect upon other sets of data, ultimately (for our purposes) estimating future stock prices.

Where do the formulas and assumptions come from?  The answer must be, past experience.  For example, inflation has averaged some 3% per year for most of the 20^th Century, so this is a fairly typical assumption used for future inflation.  The formulas represent the relationship between different data items.  For example, a formula might show that next year’s stock market level is a function – among other things – of next year’s inflation level, the economic growth in between, changes in consumer confidence, and the Fed’s decisions on interest rates.  These formulas are derived by looking at past relationships between the variables involved.  In other words, to project the future we use the past.  Since the past itself has been very variable, we need to decide on “trends” – whether a series of data is going up, down, in an arc, in a U, in a hockey-stick, rises to a plateau, fluctuates, etc.  The modeler can either consult the past to decide on trends, or make a new decision about them.  Unless the cause of the trend is known, the decision will need to be arbitrary.

All respected forecasters must use models.  Even the market-pattern advocate who sees a recurring wave in the data is using a model, but one that can easily be shown pictorially.  In such a model, all the weight of the prediction rests on the shape of a trend, typically of the market index or stock price itself.   Conversely, it can be seen that the modeler with the complex formulas is not really different from the market-pattern advocate.  He or she sees past shapes in data, represented in this case by formulas and assumptions, and rolls them into the future.  The fact that the projected price data is a function of other data is simply to say that the “curve” of prices follows the projected “curves” of these other data according to a certain rule from past experience.   So we are faced with the same problem we identified with explicit market patterns.  If past patterns cannot predict future patterns, how useful can our forecasting model be?

Modeling the natural world works well.  It allows us to construct new buildings, design new cars, control water supplies, preserve eco-systems and forecast the weather.  That is because the natural world usually follows mechanical patterns that can be predicted with a measurable degree of confidence.  Even though weather systems are highly complex, enough study of past weather patterns allows us to predict changes over the next week or so with fairly high probabilities.  These patterns are reliable because they either don’t change much or, if they do change, then the changes are gradual and we can map a trend line to adjust for them.  The financial future, however, follows no natural pattern.  We do not know if consumer confidence will get stronger or weaker, if inflation will go higher or lower, if the market will drive down or raise interest rates, or if sudden shocks or disasters will occur.  The interplay of factors which determine each of these financial drivers is so complex that a model cannot reproduce them with confidence, even roughly.  One major factor affecting all of them is the future state of human minds, and we cannot model free will.

Market-Forecasting Versus Financial Forecasting

I am not questioning the value of financial modeling itself - far from it.  Financial modeling is an inescapable necessity for both business and government.  It is integral to any planning.  It also has a vital role in investment planning, when used in the right way.  However, the good forecaster is always humble about the inadequacies of his or her model, and how it over-simplifies reality.  He or she knows that the final outcome may be hugely different from what is forecast.  The value of the model is to determine a path towards an outcome which, no matter how many course corrections are needed, will constantly narrow the gap between estimate and outcome as the time of the outcome approaches.  Its purpose is to avoid, if at all possible, violent course adjustments before they prove too expensive or even too difficult.  The financial forecaster uses the past to project the future simply because there is nothing better to use.  He or she makes a big distinction between trends for which there is causal evidence of continuity (population growth, pollution, etc.) and ones for which we only have the past as guidepost (inflation, improving productivity, etc.)

Forecasting future stock prices is essentially different from other financial planning.  If I say that the market will be 15% higher this time next year, I am saying I know more than the millions of people holding cash and bonds, and also the millions who are currently reducing their equity stake.  Such people may have their own models, but I am saying my model is superior.  How do I know that?  I cannot excuse myself by saying, “I hope my model is better – I have done my humble best and wish to be judged by investors for the grand prize this year.”  To forecast a market return significantly different from the risk-free rate of return is to say, “The consensus of all active investors is substantially wrong.”    If I am not prepared to make such a statement, then my model has no practical predictive value.  To provide useful guidance, I must believe with good reason that my model is better than the combined judgment of the whole market itself.  So again, how do I know that?

I have a finite computer model.  It may contain millions of lines of code but, in comparison with the real world that determines the market of next year, it is but a grain of sand on a wide beach.  First, consider the volumes of data that the Fed considers when adjusting its interest rates throughout a year.  Then consider the countless elements that contribute to that data – the productivity of each business in the economy, household spending and the people who makes those decisions, price inflation and the components that make up those prices – and the decisions of people who set those prices, responding in turn to their labor costs, material costs, capital costs, growth targets and buyer demand.  And these are the trillions of data items that contribute to just one small influence on the market – the Fed’s influence on short-term interest rates.  What of all the factors affecting the entire global economy, on which all global markets are dependent and inter-related? 

The model designer will say that he or she has focused on the principal components of the economy, business and investment, simplifying the picture for ease of understanding and focus.  Again, we see the similarity with the market pattern – a focus on principal economic patterns that have occurred in the past and which are assumed to continue in the future.  But efficient-market theory tells us that, no matter how much these patterns have been identified in the past, they cannot tell us the future because only brand new information will influence market direction.  To the extent that patterns exist, they are “old information,” and thousands of the investing world’s vast array of market models will already have taken them fully into account.  The models of those quick-on-the draw, gut-feel players will have quickly squeezed a good living from each new data item that either confirms or breaks the pattern, and there is nothing left over for the rest of us.  If the patterns point up, a million models will have raced to price the market accordingly.  The same is true when the patterns point down.

The Market as the Sum of All Market Models

Though each investor’s model is a poor reflection of reality, no matter how complex it is, the sum total of all investors’ models will reflect a vast compendium of independent thought, analysis, and knowledge.  Though still relying on equations and assumptions, the sum of all the facts built into these models will greatly exceed any one forecaster’s facts.  Moreover, the level of the market next year will be a function of all these models again, some added, some removed, others modified.  Our single forecaster, selling his or her market advice, is claiming to not only understand how many trillions of data items will determine next year’s environment, but also the way in which the market’s huge collection of models will respond to what they did not expect.

All this would be true even if the market, and its underlying fundamentals, had been relatively stable over time.  However, the scary instability of the market, even when viewed from the benign outcome of the 20^th Century, makes the very idea of market prediction seem unreasonable.  The great crashes of the century – in the early 1930s and 1970s – can now be seen as the consequence of investors losing large measures of confidence in the market over limited periods of time.  The loss of confidence was the result of quite dramatic events.  However, the intensity of both the events and loss of confidence were entirely unpredictable.  Equally, the restorative events (in one case a world war) and the recovery of confidence were also unpredictable.  It follows that the absence of such events is also unpredictable.  But these were the largest crashes.  Why would smaller ones, and their recoveries, be more predictable?  In other words, all fluctuations are unpredictable because they are responses to new information. 

Are market forecasters excused from ignoring such individual events, instead looking at a “bigger picture” which smoothes out the fluctuations and discerns an underlying trend?  This might be the case if there were some universal “norm” for the valuation of equity securities from which we have diverted only at exceptional times.  However, there has never been such a norm, and it is difficult to imagine how there could be.  To explain this view, it is worth discussing the technical basis for stock valuations.  To some readers the following explanation is well known.  To others, it is worth spending the time to understand it because, otherwise, it is not possible to grasp what “good fundamentals” really mean in the context of an investment.  Even staunch believers in intrinsic-value investing need to know the limitations of their theory.

Many investors will invest in the hope of selling a stock at a higher price.  However, unless there are solid grounds for that higher price, such hope amounts to no more than what is called the “greater fool theory” – you will make money only if you find a greater fool to pay the higher price.  The careful investor must be prepared to hold the stock indefinitely.  The value of that stock is then the value of its future earnings.  If the stock is later sold, then the sale value is the value of the then-future earnings to the buyer, and so on.  In this way, a stock’s real value can be seen as the sum of all its future earnings.  Since, unlike bonds, there is no date at which companies give back their capital to investors, those future earnings stretch out into the indefinite future.

The Present-Value Concept

How to place a value on this future money?  The essential formula is universally accepted.  It can be illustrated with a very simple example of a payment of one dollar due in twelve months’ time.  What is the value of that payment to me today?  Suppose I can invest money in a bank account earnings 4% per year.  If I invest 96c today, I know it will accumulate to $1.00 in twelve months.  So the one dollar in twelve months can be said to be equal in value to 96c today.  We say that the $1.00 is “discounted” to today at 4%, and that today’s “present value” of the $1.00 next year is 96c.  In the same way, $1.00 payable in two years time would be worth 92c today, or we say that today’s present value of $1.00 in two years’ time is 92c.  In the same way, the present value of $1.00 in three years’ time is just under 89c, if we continue to assume interest at 4%.

The value of a stock is the present value of all its future earnings.  Let’s take a share of stock for which the related share of company earnings is $1 per year.  If we keep the same bank account, I know that the first three years’ earnings have a present value of $0.96 + $0.92 + $0.89 = $2.77 to me.  But how to add up a series of these discounted dividends stretched indefinitely into the future?  Luckily, there’s a simple mathematical formula for that.  The present value of an infinite series of $1 payments each year, using a 4% discount rate is:

$1/4% = $100/4 = $25

In other words, we only have to divide the annual payment by the interest rate (or discount rate) itself.  The reader can verify this using an excel spreadsheet.  He or she can create a column starting with one, then dividing it successively by 1.04, moving down the column. The present value of the first 84 years’ earnings is $24.03.   The present value of the first 142 years’ earnings is $24.90.  The present value of the first 201 years’ earnings is $24.990.  The present value of the first 260 payments is $24.9990.  377 payments give us $24.99990.  And so on – after 671 years we have ten 9’s, and after 837 years we have thirteen 9’s.  It is clear that the sum of the present values of these annual earnings converges on $25.

It’s now very easy to value infinite series of $1 earnings at different interest rates.  At 5%, the value is $20.  At 6%, the value is $16.66.  At 7%, it is $14.29.  At 10%, it is $10.  As interest rates rise, the value of our series of earnings falls - a phenomenon we notice frequently in the stock market.  But our model is, of course, far too simple.  First, we know that a company’s future earnings will not be constant, but will change over time.  Second, how do we choose the appropriate interest rate?  After all, if the bank offered me 6% instead of 4%, would it make sense that my stock values immediately drop by a third?

For almost all stocks, it is typical to assume earnings growth.  At the time of writing, earnings growth among the S&P 500 has been particularly strong in recent years, having been in double digits for several years and expected to be in high single digits in the year this books is written.  If we assume our stock is “average” for the S&P 500, what would be a reasonable growth assumption for the indefinite future?  Anything over 6% would be high by historical standards but, as have been discussing, is history any guide?  Why should corporate growth over the last eighty years, which started when mass production was in its infancy, be any guide to the next eighty years?  Back then, defense, aerospace, healthcare, electronics and branded goods barely existed in the form of large public companies.  Today, they dominate. 

We might assume a high rate for the next few years but pretty quickly adjust to a “long term” rate – maybe after three or four years – so the long term rate would dominate our calculation, and we can ignore the effect of the immediate bump.  In the long term, we are limited by the growth of the economy, but for S&P 500 companies this has become increasingly the global economy and not just the US.  Would 4% seem reasonable?  Are 3%, 5% and 6% any less reasonable?  Who knows what efficiencies can be continually squeezed out by technology?  But then who knows when the productivity effect of technology hits a brick wall?

But What Interest Rate?

Now we need to consider the discount rate.  Clearly it should be a long-term rate, which we could expect to earn for tying our money up for so long (or the money of those who buy from us.)  But is a long-term Treasury rate appropriate?  Conventional wisdom says not.  If we are allowing for a growth rate such as 4%, there is presumably a risk involved here – the risk we fail to keep up this pace.  But here the dilemma starts in earnest.  If we are conservative enough about growth, maybe we don’t need to factor risk into the interest rate.  But exactly how conservative do we need to be in order to feel we are “risk free”?  Maybe a corporate bond yield is more appropriate, but what quality bond?  Maybe the average S&P 500 quality bond?  One trouble here is that such bonds don’t stretch out far enough in the future, but we can wing that one by assuming a “theoretical” bond which is an extreme version of actual bonds.  But now we start to wonder if we are inserting ourselves into a trap.  As market modelers, believing in our own superior market forecasting, we obviously do not put any credence by efficient-market theory.  Yet here we are, equating the return on bonds with those of equities!  By pricing stock earnings growth using bond returns, we are defining the returns as equal.  If people are actually paying what we value the stocks to be, then we are actually helping to verify efficient-market theory.

The modeler who believes in the inevitable equity-risk premium must therefore bank on the fact that investors are buying stocks for less than their “true value” as described above.  This becomes a little worrying to his or her potential audience.  Equity-risk premium believers, after all, tend to be a fairly constant lot, seeing the bull case in both down and up markets.  But what if their model showed that people were actually paying above the “true value”?  That would mean an equity-risk deficit into the infinite future.  Might there be a temptation to tweak one of the assumptions?  Possibly, increase that 4% earnings growth to a 5% earnings growth?  After all, who is to say 5% is unreasonable?  If growth has been higher recently, then 5% appears modest.  If growth has been slower – well, probably it’s in a cyclical downturn and will rebound, to keep the long-term average at its historically improving levels.

How much difference would such seemingly innocent tweaks make to our stock market valuation?  To show this, we introduce a new mathematical “trick.”  Unlike the first one, this is an approximate formula, but it is easily close enough for our purposes.  Let’s say we are valuing earnings that are growing at 4% per year, and using a discount rate of 6% to reflect corporate bond yields. The $1 in our prior example will be $1.04 the following year, $1.08 the next year, $1.12 the next year and so on.  The present value of this infinite sequence of rising earnings can be determined using the same formula as before, but by first subtracting the growth rate from the interest rate.  In this case 6% less 4% gives 2%.  The present value of all future earnings is therefore:

$1/2% = $100/2 = $50.

Now, let’s suppose we have become suspicious that our forecaster has tweaked his assumptions to get the answer he wanted.  First, we think it would be more prudent to assume a 3% earnings growth rate.  But second, we question the 6%, which reflects high-quality corporate bond yields.  After all, in the event that a company becomes insolvent, its equity it generally worthless, but bond holders can expect some percentage recovery.  What additional yield might this imply?  There is no easy answer, and maybe we are trying to be over-precise faced with our nebulous growth assumption, but perhaps lower-grade bond yields – even junk-bond yields – are some kind of guide.  Perhaps a very rough guide indeed, given their historic volatility, but they might justify an increase to the discount rate to 7%.  So now our formula requires 7% less 3%, or 4%.  The present value of all future earnings is now:

$1/4% = $100/4 = $25.

Dow 7000 Again!!

In other words, it has fallen to exactly half of our previous valuation. To the retail investor, we have just said that Dow 14,000 should be Dow 7,000.  Our buy or hold advice has now flipped to a screaming sell.  So now we are able to put into some kind of context those advisors who tell us that the market is “about 10% overvalued.”  For example, the actual market’s average price valuation may imply a 3.9% long-term earnings growth rate, if we fix our discount rate at the lower-grade bond yield.  However, our advisors, in their wisdom, may have preferred a 3.5% or 4.3% growth rate.  They are telling us that their personal projection of past experience is somehow more reliable than the market consensus.  For those advisors who are predicting the market return over the following twelve months, as so many do, they are telling us that the market consensus will come round to their thinking within that specific period of time.  Such confidence in one’s own economic judgment, not to mention one’s mastery of mass psychology, seems breath-taking.

Could forecasting models actually be, at bottom, as crude as I have described them?  Despite their apparent sophistication, all such models are “normalized” on past market experience.  In other words, their parameters are set to reproduce the patterns of the past.  So if the past has delivered on average 4% earnings growth, and we are taking a “neutral” view of the future, then our model would be designed to give that result.  If earnings growth has been exceptional recently, either higher or lower, then a model that resulted in 4% growth might follow the “reversion to the mean” assumption (discussed below.)  If our model has built-in conservatism, it will be designed to give lower growth for the future, and vice versa with optimism.  No matter how many million refinements we claim for our models, our guesses at these primary unknowns will govern the outcome with formulas as simple as “one divided by the net discount rate.”

So it is not just the market itself, but also the models which attempt to project it, which are inherently unstable.  The stability of any forecaster’s results would follow only from his or her reluctance to change assumptions with changing reality – hardly a comfort.  If we are willing to dabble with our assumptions, then sudden bear markets can be justified with changes which the retail investor would view as inconsequential.  A 0.5% increase in long-term interest rates and a 0.5% drop in earnings growth would do the trick.  We tend to fret about a 25 basis-point increase in the Fed’s rate, yet the market boom of the late 1990s occurred with the Fed rate higher on average than at the time of writing.

If earnings growth is assumed to be a function of economic growth, then what kind of new information would cause our forecaster to change a long-term economic growth assumption from 4% to 3%?  A recession might invite fear, but what is it about a string of disappointing government numbers that much drop such an assumed long-term rate by 1%, and not 1.5% or 0.5%?  If long-bond holders sell off, raising interest rates, why does the modeler convert that automatically into a sell-off in stocks?  If equity investors have it right and bond investors have it wrong, why do the bond investors have such compelling influence?  The equity-risk premium advocate still feels that trap.  To justify the premium, he or she must design a model, and also must apply a discount to future cash-flows.  Yet to discount is to be captive to the whims of the very investors – those purchasers of bonds – over whom you are claiming to have superior knowledge about optimal strategies.  One moment the equity advocate tells bondholders that they can’t see the bull market.  The next moment, the bondholders’ trading decisions inform the equity-advocate’s model that the bull market is almost over.

The New Era Dilemma

The modeler is thrown back on one popular argument.  The market is not rational.  Frequently, we are told, it is subject to either excessive gloom or euphoria.  Only a rational model, no matter how crude, can keep us focused on some norm.  The dot-com burst is our prime example of why we need rational models.  This book will present its own model to explain such bubbles but which, paradoxically, uses efficient-market theory as its core principle.  And though bubbles must be addressed, the traditional model hardly gives us confidence.  Above, I explained how the market might be 100% undervalued or 50% overvalued, using two rational models.  The NASDAQ high was some 5000, and it stands at the time of writing around 2500.  True, the earnings of today’s leading technology companies are of an entirely different order.  But then, wasn’t such earnings growth predicted by the Y2K models which justified a 5000 index? 

When you are selling brands over the Internet, surely a growth rate of 6% is quite feasible?  The problem is that, if such growing earnings are projected over the long term at a discount rate of 6%, we conclude that the stock has infinite value – cheap at any price, according to the model!  This may seem an extraordinary result but, if our assumptions are correct, the result is true.  An infinite series of payment that increase at X% per year, and which are then discounted back to today using an interest rate of X% per year or more, does indeed have an infinite present value.  Maybe we should not assume an infinite series.  But if we don’t, when should we assume it ends?  Assuming an end is to assume that somehow the capital invested evaporates.  Maybe we should assume the growth rate decreases after twenty years.  But then we are faced with a rather silly degree of precision – what possible information would lead us to believe that a brand new concept like Google, for which there is no historic precedent even if it were reasonable to assume an economy like the past, would step down from a 6% rate to a 5% rate around 2027?  All such decisions are arbitrary and, at worst, simply chosen to get an answer that we “feel” is reasonable.  So much for fundamentals…

It is not difficult to see now that a discount rate of X% per year, combined with a long-term assumed growth rate of (X-1)% per year, can justify a P/E ratio of 100.  And if we increase that growth rate just fractionally, to (X-0.5)%, we can justify a P/E ratio of 200, and so on.  We begin to get a small insight into the problem of bubbles.  It is not so much that we have lost our rationality when we do such calculations.  After all, who can say that a long-term average growth rate of 5.5% is irrational – say, compared with 4% per year – when we are talking about a technology that is going to take over all aspects of our lives, and brand names that can anchor themselves in this fabulous new market?   We fall back on the argument that a P/E ratio of 200 looks so high, and 50 looks “reasonable.”  The lower one is reasonable as it reminds us more of traditional industries and their history.  Again, we are comforted by the patterns of the past, despite the fact that business and the economy has changed radically over the years.

So in fact, it would appear that the “intrinsic value” approach is vetted by the assumption of some fuzzy yet eternal P/E constant, or constant range.  We could take Buffett’s point of view and say that we don’t feel comfortable with the new-economy valuations, but such an approach ignores an increasingly important part of the stock market.   Moreover, if we cannot appreciate the value of fast and sustained growth, it also underestimates the true value of a Krispy Kreme, especially in its earlier years.  Do we assume 10% growth for ten years then 5% thereafter, or 7% growth for twenty years and 4% thereafter, or what?  Each choice in the thick fog of the future gives a very different answer.  If our essential sanity check on that answer is current price divided by current earnings, our faith in intrinsic value must be weak.  So our faith in our financial models for market forecasting is in reality weak, as we fear a departure from the core assumption that important things don’t change very much.

Yet Change Is a Constant

Yet even history tells us that things do change, and radically.  The average large-cap P/E has dropped below ten and risen above forty.  So we must choose to believe that such “extreme” ratios cannot last for long, and that there is always eventually a reversion to the historical mean.  Is there evidence of reversion in the stock market?  Hardly.  For most of history, dividend yields exceeded bond yields, yet now that would be unimaginable.  For more than two-thirds of the market’s history, there was virtually no net inflation.  Now 3% per year is considered low, and below 2% raises fear of deflation.  Recessions have gotten progressively shorter and booms longer.  All the time, the amount of disposable wealth has been growing exponentially.  It seems our faith in mean reversion is an effort to believe in constancy in an ever-changing world.  Professor Schiller refers to the importance to investors of such “psychological anchors” and I cannot disagree.  But their importance in sanitizing financial models undermines any claim to the models’ useful sophistication.  Why bother with some technical adjustment  for today’s consumer confidence index when a small shave off the earnings growth after 2025 will get us in the same ballpark?

Earlier, we described above the unimaginable complexity of today’s markets.  Though mapping such complexity would make mapping the world’s weather systems appear simplicity itself, weather forecasters are particularly reticent about one-year projections.  Yet even this analogy is not sufficient to describe the claims of market forecasters.  Weather patterns are relatively deterministic, as we know about flows of air, changing temperatures, ocean currents, etc.  We do not know the future decisions, and future physical and psychological health of the world’s leaders.  Or the determination of angry mobs, testing their governments’ resolve.  Or the future strategy of OPEC, or the latest reports on its members’ proven and probable reserves.  Or, as FDR might have put it, Americans’ future fear of fear itself.  The forecaster may caveat his or her results with the words, “barring major unforeseen events.”  Yet unforeseen events occur each day, and their cumulative effect is always major.  Which is unforeseen – success in Iraq, or failure?

It is not difficult to understand why, despite the confidence of market forecasters, their predictions always range across a wide spectrum, from wild optimism to Armageddon.  And, like the proverbial stopped clock – or, more aptly, the coin-tossing game – most have usually been right at least once, and probably occasionally.  The fact that forecasters always fill the complete spectrum of possibilities will, of course, ensure that one of them can always claim the right prediction.  Unfortunately, there is no way to choose between the predictions before the outcome, other than through the degree of personal persuasiveness of the accompanying argument.  That argument, like the model itself, cannot reflect any conclusion that an efficient market itself has not already considered and built into the current price.

The Fallacy of Mean-Reversion

Before completing this chapter, I want to return to the seductive notion of reversion to the mean.  Though it undermines the logic of a projection of future events by constraining its results to conform to the past, in a sense the mean-reversion theory can be viewed as a forecasting model in its own right, unapologetically convinced that certain things just don’t change that much, regardless of what else changes. 

Under mean-reversion theory, there must exist some underlying force which always tends to pull the examined data sequence back towards its long-term trend.   Analysts draw charts that remove the “white noise” of market fluctuations and also the temporary surges either up or down, seeing these as random events around an underlying path.  A simple way of determining trend is to plot the path of the “rolling average price.”  For example, a 90-day average will turn the jagged progress of a stock or index into a smooth wave; taking away undue attention to any recent, probably short-lived influences.  Such rolling averages are widely used in stock analysis, and are available in many charting programs on financial websites.  As with all models, the trends of the averages are used to make judgments about future price directions and market-timing decisions.  If the mean trend is up, then sudden price drops represent a buying opportunity for the likely continued rise.  If the mean trend is down, sudden price increases represent a chance to unload our unwanted holdings before the expected continued fall.

There are two immediate problems with this approach.  The first is that we have no idea which rolling-average to use – 30-day, 90-day, 180-day or something else?  By averaging too little we get caught up in temporary phenomenon.  But by averaging too much, we would be in danger or missing the critical turning point.  After all, the purpose of such trend prediction is to catch as much of the bull-market upswing as possible and avoid the downswing.  Too much averaging, and the smooth line will still be ascending as the actual market line is well into its final descent. 

One version of “momentum” theory is to consider a stock or index on its way up when it rises above a certain rolling-average and on its way down when it falls below.  The theory is a way of making money from the diversions from the mean trend.  In effect, it is another pattern theory. It assumes that there are buy and sell points that will enhance the yield compared with continuous holding of the stock.  But this theory suffers from the same problem of choosing the right averaging period.  It also begs the question as to why such a theory would work.  Momentum advocates have advanced explanations, but these are just more hypotheses which may or may not be true.  Their main argument centers around historic bull markets which have shown such patterns. 

Efficient-market theory says that all such models are based on a fallacy.  Their necessary premise is that there is some driving longer-term trend behind the market movements which exerts a steady draw in a given direction, despite short-term movements to the contrary.  As one such theorist once described a bear market, it is like a falling leaf which may rise from time to time as it gets caught up in wind gust temporarily, but which eventually must make its way to earth.  It is a compelling idea, not least because it is observable in nature.  Unfortunately, it entirely confuses cause with effect.  This is easily illustrated by taking a wide sheet of paper and drawing a fluctuating line from left to right, randomly varying your hand movement up and down the page as you do so.  Repeat several times.  Likely there will be flat lines, shallow rises and falls, steep rises and falls, and you may end up higher or lower than the point at which you started.  Now take a different colored pen and follow the general direction of the first line, but consciously dampening the swings up and down.  This approximates to a running average.  Now take another colored pen and dampen the swings of the second line.  Note how the original line oscillates around the next two, straying for a while but then coming back to pass through it and doing the same thing on the other side.

Obviously, the original line is driving the other two, and not vice versa.  The essential nature of a mean or rolling average is to keep within range of its original.  But our example shows that it reveals nothing about the original line’s direction until after that line has already been to that point.  The mean or rolling average is a blind follower.  Given that fact, it is not possible to see how a stock’s price path, passing up and down through any rolling-average of the price, provides any meaningful insight.  Naturally, such patterns can be spotted historically.   It is the very nature of rolling averages to find a mid-course, and have the actual data sequence pass through it from above and below.  What we cannot predict is whether the stock price line will turn towards its average, or the average will turn towards the price line.

The core thesis of this book is that seductive patterns abound, but serve only to fool us into thinking we know something about the future that we do not.  Draw any curve to represent the trajectory of a bull and bear cycle.  The rolling averages will always be curves launched at a lower level, but sustained beyond them in a wider arc.  Therefore, by definition, the bear cycle will drop back through the rolling-average curves on its way back down.  Successively, these curves will be the 15-day, the 30-day, the 60-day, the 90-day, and so on.  None of them are warning signals?  They are arithmetic relationships of past data, and no more.

Ever-Changing Predictive Rules

As we will discuss in more detail later, the only common features shared by all bull-bear market cycles (for both stocks and indices) is that they have successive tops and bottoms.  This is a feature shared by all lines which move randomly up and down as they progress in one lateral direction.  For sticky-luck lines, of the type we see in the market, the tops and bottoms tend to be well-pronounced.  The actual shape of the rise and fall follows no rules, with plateaus and shorter-term spikes and rounded shapes mixed in.  Some moving averages will be breached during the course of a cycle, others will not.  It depends entirely on the length and shape of the cycle.  These factors themselves depend upon how we choose to define a bull market.  Since 1981, have we had a single bull market, or two, or three?  To the SLMH, it doesn’t matter.  To the rolling-averagers, the last experience will be used to define the predictive rule until it is shown not to hold up by future experience.

I recently read of a forecaster who believes in the mean-reversion theory who added that the mean was rising.  Certainly, any rolling-average through the 20^th Century to date for  whole-market returns would show such a curve.  With enough averaging, we could wipe out the effect of the dot-com bust and see an increasingly upward sloping curve.  Yet, this delivers no useful message about the future.  The rising mean, used to explain progress so far, may at any moment become a falling mean.  After all, if we believe in mean reversion, then why shouldn’t a mean line also being reverting to its own mean?  From today, the market could start its downward journey, with any number of scary drops and sucker’s rallies, and falsely reassuring plateaus at any level.  With every disappointing year the market would drop through another rolling-average.  Some would declare Armageddon at each such point, others would predict resistance – or, more safely for their reputation, “critical decision points” – at some lower average.  Were the market to continue its downward path for another twenty or more years, devastating people’s retirement plans, we would find our original, long-term averaging curve, so significantly rising from the early 1900s through 2007, now making a gentle and smooth arch downwards.  And at no point would we have been any the wiser for it.