Sticky Luck

Six:

The Source of Stickiness

Market Patterns and Memory

The confusion of rationality with efficiency.  Monday and January effects.  Behaviorists choose the wrong enemy.  FX as a market of pure sentiment.  The psychology of momentum.  How economics drives both currency and equity markets.  Prices reflect the probability of continued performance.  The let-winners-run fallacy.  Why walks are not random.  The Yen-carry trade.  The earth's tree distribution as analogy.  The fractal nature of markets - why hours and centuries look alike.

Anyone convinced of the predictive power of market patterns should spend time studying currency movements.  Though freely floating currencies are a relatively recent phenomenon, the data accumulated over the past thirty years tells a rich story.  Certainly, that same period was long enough to take the investing world from a high degree of skepticism about equities to one where they are perceived as both essential and generally (from the long-term perspective) quite safe for individual retirement accounts.  Currency markets offer us an important window for studying the two primary theoretical approaches to the stock market.  The first is efficient-market theory, and the second is the type of analysis performed by the behaviorist school, of which the leading public light is Professor Shiller.

According to behaviorist theory, the market is governed essentially by psychological factors, and frequently leads to pricings and price movements that have no good rational explanation.  Market commentators have often sought to present efficient-market theory and behaviorist theories as competitors, even opposites, where one must be right and the other wrong.  It is a thesis of this book that these two theories are entirely compatible, and both shed important and complementary truths on market behavior.  The apparent rivalry is convenient for the advisory and fund management industries, as it helps diminish the significance of any particular market theory, and encourages investors to leave such academic pursuits alone and get back to the “practical” business of investing.  As we have discussed, efficient-market theory discourages the payment of high fees to fund managers.  Behaviorist theory is a lesser threat and, in his Irrational Exuberance, Shiller defended the added value of fund management.

It is worth mentioning the argument he has made.  While acknowledging the evidence that fund managers do not in practice beat the averages, he explains that this by itself is no evidence that they are not actually making good decisions.  Since other investors can follow the commentary and portfolios of the professionals, “with a short time-lag,” the fund managers could have led the whole market in the right direction and thus, one way or another, we all benefit from their research and choices.

This argument seems unworthy of the rest of the book.  It would be a strange commercial world if people who chose their own stocks took a free ride on professional fund management, while the fund’s customers generously paid for this service.  Anyone watching the market daily knows that even short time-lags make a large difference.  Funds typically publish only their largest holdings each quarter – hardly enough information – and the phenomenon of “window-dressing” (switching to bigger names at the quarter-end date for appearances sake, then back out again) is not only well-known but another perfect example of form over substance.  If independent investors really believed the fund managers knew better and should be followed, paying 30-50 basis points for the real thing instead of a pale shadow would be a no-brainer. 

Confusion of Rationality With Efficiency

Shiller goes out onto such thin ice because he thinks he needs to attack efficient-market theory.  In fact, his real target is those who seek to misinterpret efficient-market theory by claiming that, as a consequence, “the market is therefore always right.”  Shiller repeatedly states that efficient-market theory is based on the assumption that investors generally make rational decisions.  As his books title suggests, he does not believe investors behaved rationally during the late 1990s.  Depending upon how he defines “rational,” I believe he has a good case.   I would agree strongly that many investors acted as if there was not much risk, exactly at a time when market risks became unusually intense.  This is not necessarily irrational.  The child who cuddles the growing tiger cub is not being irrational.  He or she simply does not have enough information about the tiger’s true nature, and is extrapolating from experience to reach what we happen to know is the wrong conclusion.  In the same way, most investors saw positive market during these bull years, and were similarly extrapolating.  They could easily articulate why they believed they were doing the right thing.  Many books and articles did exactly the same, in great detail.  They were exhaustively analyzing the tiger cub’s behavior since birth, including each playtime, each moment of possible aggression that turned out to be benign, etc.

Shiller also makes the argument that investors did not appreciate the degree of risk involved.   But his defense of professional investment expertise is at odds with the role he describes for fund management in what he saw as a bubble market.  Instead of repeatedly warning against high prices, the fund-management industry responded with a host of specialty technology funds and emphasized their short-term performance.  Even many funds with no technology label became seriously over-weight with NASDAQ stocks.  Though bears did exist among professionals, they exist at all times, and most of them have been “perma-bears” since the mid-Eighties through the time of writing.  In short, the professionals showed no more sensitivity to increasing risk than did the investing public.

The behaviorist school does a similar disservice to its science when it claims that certain choices that the investors routinely make create predictable patterms.   Examples of these are the “January effect” and the “Monday effect,” where past data shows patterns of stocks rising more than average in January and falling more than average on Mondays.  This would seem to open up a simple way to get rich.  Always load up as much as you can on Monday at 3.50 pm and always lighten up on Friday at 3.50 pm.  Do the same on the last trading days of December and January.  But this leads us to a paradox.  Firms like Goldman Sachs have presumably noticed this effect.  Having vast lines of credit, they could leverage this effect with a vengeance.  But then wouldn’t it push stocks higher on Monday afternoons and at year-end, and lower them on Fridays and at January’s end?  Wouldn’t they keep dipping into the free-money well until it dried up?

Not only do such “free money” plays seem to have no logical basis, but any observed pattern can be explained by happenstance.  As repeatedly stated in this book, the market has done exceptionally well over two centuries.  Therefore, statistically, any approach to “equity leverage” as I have described it, will on average have increased that performance.  I have mentioned small stocks as an example of this, but there are many less obvious examples.  On Mondays, time has moved on 65.5 hours since the last close, rather than 17.5 hours on other weekdays.  There is less data published over a weekend, yet psychological factors are still at work.  In fact, as investors have moved more heavily into equities, many of the actual decisions, conscious or unconscious, have tended to occur during the quieter hours of the weekend.  There may be a tendency for investors to reflect and decide to consolidate their gains, only to get more enthused on average during the week as new information tends more on the bullish side.  There may even be a tendency for the type of data released on Mondays – maybe world events that are sobering and expected to have a more negative effect on the market than they eventually do – to be different from the rest of the week.  Maybe most of us are just a little bit gloomier on Mondays, facing a working week.

Just More Sticky Luck

We don’t know which these effects really applies as they are highly subjective, and studies could reveal many conflicting theories.  The point that behaviorists miss is that it does not matter.  It is just one more sticky-luck pattern of indefinite length, to disappear or reverse as soon as it is noticed and traded against.  When it disappears, the market ceases to trade against it, opening up the possibility of it emerging again until it gets beaten down again.  It is no different from a bull sector market, where you jump on the band-wagon at your peril, perhaps just when the pattern goes into reverse with a vengeance.

January involves clearer psychology, as investors review their prior year’s performance and plan for the New Year, as if investment years were entirely distinct.  Tax laws encourage selling in December, but there is no reason why such sales should not be accompanied with equal purchases, as investors maintain their equity ratios.  It may well be the case that, were the market to steadily decline for many years and eventually destroy people’s faith in equities, we would witness negative January and positive Monday effects.

The SLMH has a more sophisticated comment around these effects.  Because of the psychology, it may well be that a market fall on Monday and rise in January is more likely.  However, as we have demonstrated earlier, this does not equate to a higher expected return.  The year that the January effect fails to appear, the market may be more likely to sink like a stone.  This negative possibility would balance the more modest, positive probability, giving the same expected return.

Other behavioral objections to efficient-market theory amount to no more than further attempts to pin the word “rational” to its definition.  For example, we are asked, isn’t it irrational or inefficient that closed-end funds should sell at a regular discount to their break-up value?  Or that spinning off a business should suddenly create greater value for the parts than the previous whole?  As we have defined “efficient,” these facts are fully compatible with efficient-market theory unless it can be shown that a special profit can be expected by buying shares in closed-end funds or any company that might be broken up.  But, if you cannot persuade the market to suddenly pay full price for your closed-end fund shares after you buy them at a discount, you will similarly sell them at a discount.  Discounts in such instances may have to do with conflicting interests of shareholders and management.  Management may choose not to spin off a business because it believes it is best capable of turning it around, whereas investors know of buyers with similar confidence and ready cash.  More cynically, management’s pay may be determined relative to peers running companies of similar size.  Closed-end funds also have management whose remuneration will not make their interests identical to those of investors.

Barking Up the Wrong Tree

It is therefore a pity that the behavioral school spends a significant amount of time attacking efficient-market theory rather than those who would misuse it.  One misuse is to claim that the market is always appropriately priced.  Such a statement is either a worthless tautology – the price is obviously appropriate from the market’s perspective at this moment – or some vague claim that people should relax about market risk, as it is more apparent than real.  Paradoxically, efficient-market theory and the behavioral school are in lock-step trying to convey to the investing public that market risks are in reality much greater than investors today can imagine.  They are simply different perspectives of the same phenomenon.  The behavioral school emphasizes the enormous difference that emotion can make to investors’ perception of the market. Efficient-market theory states that, whatever the emotions and facts that have gone into today’s prices, the new information that will change those emotions and facts is unavailable to anyone.  Moreover, as we shall see, the market is a precarious pivot of wildly different interpretations of information to date.  Even small amounts of new, unexpected information may cause huge swings around that pivot.

Given its vast liquidity, trading volume and levels of institutional investment, the currency market is every bit as efficient as the stock market, as we have defined it for efficient-market theory.  But trading currencies offers no significant “expected return.”  Though some currencies will offer a greater rate of interest than others, the earning of additional interest is not – with occasional exceptions such as the so-called “Yen carry trade” – a primary driver of currency movement.  (Also, as we will discuss later concerning this trade, the additional return is offset in an efficient market by the risk of currency-devaluation loss.) The main driver is one currency’s appreciation relative to another, and the capture of that appreciation by sale back into the trader’s “measurement currency” – the core currency in which that trader intends to make a profit. 

Yet that is not to say that currency movements are insensitive to a currency’s interest-rate changes – far from it.  An unexpected decision by the Fed or the European Central Bank to raise interest rates can sharply increase their respective currency values.  A one-percent increase in annual rate could increase the currency’s value by a similar amount, immediately offsetting a whole year’s interest advantage of switching into that currency.  Clearly, interest-rate changes perform a different function in exchange-rate movements than the actual earning of the interest itself to the currency holder.

Interest-rate movements are instead a critical market signal.  It does not take much contemplation of modern currencies to realize that their underlying value is a nebulous thing.  A central bank is typically free to continue generating as much currency as it sees fit – largely through credit terms – and may at times have an interest in weakening the currency’s value.  Speculators can have a direct financial interest in weakening a currency by selling it, and testing a bank’s ability and resolve to defend its value.  Interest-rate changes are signals of resolve, and economic-performance numbers are signals of ability.  As with the gifted stock trader, the currency trader has seconds to judge the market’s response to new information and make his or her move.  Signals can take many forms:  comments by officials, commodity prices, home-sale statistics, employment numbers, etc.  Those of us not fast or intuitive enough to respond appropriately to signals must instead ponder past patterns of currency movements.

The Natural Lure of FX

The FX industry has made an excellent living out of pattern-followers.  A legitimate form of on-line gambling today is to take temporary positions in one currency against another.  You can then immediately watch money drain out of, or accumulate into, your account until you close that position.  The industry does not present itself as a gambling concern, of course.  It provides mountains of tools to track and analyze currency patterns, from “beginners” to “advanced,” and offers newsletters, research, courses and seminars.  You, too, can be a profitable currency trader if you teach yourself to “see the pattern.”  The materials provide endless detail about past movements and associated events and data, about upcoming events and data, and about past patterns and “resistance points” – exchange rates which, when hit, are supposed to generate activity that will tend to either stop a particular currency slide or else, when breached, allow further sliding.

The industry’s marketing posture is that, with enough education about currency movement, combined with certain skills that anyone might possess, retail traders can achieve enough consistency in their calls about future movements to make regular money this way.  Efficient-market theory does not deny that such skills exist, freely acknowledging the gifted trader’s rapid, gut-response to new information.  Moreover, new information can take any form.  As with stock markets, one type of new information is the market’s own response to an earlier piece of new information.  For example, suppose the Bank of England increases interest rates unexpectedly, and the market’s immediate response is surprisingly mute.  Our gifted trader may conclude that the market has for weeks been pushing the Pound Sterling to an overpriced level, based on a sequence of positive British economic news.  Pushing it further may be more than the speculators can stomach.  Maybe on this occasion the interest-rate hike will tip the British economy into recession.  The muted response to the hike suggests the Pound can rise no further.  Our trader starts selling Pounds, hopefully before its sudden drop.

There is good evidence that the stock and currency markets do respond to their own movements as with the input of other new information.  The most famous event for the stock market was the crash of Monday, October 19, 1987, when relatively little external news emerged, compared to the prior week.  This event is sometimes cited as evidence of market inefficiency.  But for inefficiency as we have defined it to be evident, it should have been technically clear to most good advisors and fund managers that the relatively modest fall on Friday had been insufficient to reflect the significance of then-known information.  In reality, it was not at all clear that any of the following three facts were now true:  that the market was over-valued, that investors as a whole would recognize it was over-valued, and that investors would take immediate action to try and reduce their exposure to over-valued positions.  As discussed earlier, no forecasting model can  objectively prove the market’s “true” value within a 50%-200% range, let alone confidently predict the investing universe’s changed perception of value when major new information is received.  This lack of an outside reference point means that most traders must take their cue from others’ reactions, which creates the first important source of stickiness – the tendency of the market to feed upon its own movements.

The Psychology of Momentum

Here, again, is the “momentum” tendency of the market – buying because increasing numbers of other people are buying (evidenced by price increases) and selling for the opposite reason.  Of course there are investors who do the opposite (part of the group labeled as “contrarian”) but they appear to be a minority.  What could be the logic of buying because something is more expensive, and selling because it is cheaper?  If the reader is not a contrarian, he or she should have their own rational answer, but let me offer my own rationalization:

1. Other people must know something I don’t know;
2. Since I know the market tends to move in one direction for a considerable time (i.e. it is sticky) I stand to make money, at least for a while, and can always reverse course before the market does;
3. I hate to “lose out” relative to others around me.  I want to join in their celebration, and will take the chance of sharing their pain.

From anecdotal evidence, I believe all three are strong motivators, and I will assume that they do not require further explanation.  All three explain what is unflatteringly called the “herd mentality” of the market.  “Herd mentality” is a characteristic of human behavior in many situations, and in history has no doubt been vital to our survival, helping to explain its evolutionary origins.  (Later we will talk more about the intriguing effects of our evolutionary heritage upon our investment behavior.)  For better or worse in financial markets, it does mean that buying begets more buying and selling begets more selling.  This is true of individual stocks, market sectors and broad market indices.  Such “momentum” buying is sometimes rationalized at the individual stock level by the observation that increasing stock value gives a company more access to capital, and supposedly facilitating its business goals.  Such access, however, is as likely to lead to inefficient investment, so price momentum by itself tells us nothing about future performance.

Few experienced observers of exchange rates would maintain that their levels reflect currencies’ purchasing power more than at a very crude level.  Like the “intrinsic value” approach to stock, the ratio of market rates to “purchasing power parity” (the cost of purchasing local consumer items) can be as extreme as 50%-200%.  When it comes to transportable items, price connection is maintained partly by the opportunity to move those items between countries in order to sell or buy them at the most favorable price.  For most people’s primary expenditure, which goes on homes, transportation, foods and local services, there is little mechanism for prices to reflect exchange rates.  It should therefore not be too surprising that the British Pound descended from a exchange rate of over $2.00 in 1981 to $1.05 in 1985, rose again to about $2.00 in 1991-2, fell to $1.40 in 2002 and rose again above $2.00 in 2007.  Throughout those periods, there was no major disconnect between the US and UK economies that would suggest such large changes.  Neither is this a currency aberration, as similar fluctuations occurred with the Euro-Dollar exchange rate.  I have chosen Pounds simply because the Euro has been an official currency for a much shorter period, and the other most commonly traded currency, the Yen, has been subject to the extraordinary experience of the Japanese economy over the past twenty years.  (Again, more of this later.)

If we look at a 30-year GBP/USD exchange-rate chart, we can see long, steady periods of years over which it has risen and fallen.  There is no question that good money was made over lengthy periods even by retail currency purchasers, whether on-line today or formerly through other means.   The same sense of momentum, the same lengthy underlying trend, would have been evident year after year – until, of course, it all went into reverse.  The fact that such major reversals do take place makes us able to accept more easily that we are dealing here with a chance process.  At any time, the direction of the exchange rate could have reversed itself for the long term.  Yet the stickiness of those long marches in a single general direction is undeniable.  They are so sticky that the normal rules of chance clearly do not apply here.  Maybe the herd mentality is a partial explanation, but it does not seem to be a full one.  The general trend line shows periods of rest and short-term reversal, which would seem to dampen the effects of sheer momentum.  What is the explanation for consistent, underlying trend over a period of years, which then suddenly trends the other way?  And can that explanation live alongside efficient-market theory?

A Market of Pure Sentiment

The FX market offers such a fascinating insight into market movement because it cannot depend upon “rational” investment decisions.  At the time of writing, the British Pound has exceeded its purchasing power parity (PPP) with the US dollar for almost four years.   It dipped back towards PPP around the start of 2006, but for the next fifteen months rose steadily, with the usual ups and downs we would see of a stock, to some 20% above PPP.  An Englishman could convert tens of millions of his pounds to dollars and enjoy the 20% premium purchasing goods in the United States.  Why would currency investors offer such a premium to sell their dollars for pounds?  They obviously think that there will be many more dollars for sale in the future, driving down the dollar’s price, as America tries to repay its debts.  But more dollars lead to inflation, and inflation drives the Federal Reserve to tighten the money supply.  Whenever there is an unexpected sign of such tightening, the dollar rapidly strengthens.  Though there may be a case for a “pound premium,” there is no logic that helps us choose between a 10%, 20%, 30% or 40% premium.  In summary, there is no currency “intrinsic value” concept.  

If we study currency movements day after day, month after month, it becomes much easier to grasp its essential random nature.  Try predicting currency movements each minute or each hour or each day.  There are plenty of websites to provide the data from which such a game can be played.  Of course, the lengthy trends in a single direction show plenty of scope for sticky luck, which explains why Internet trading is attracting so many pattern-lovers.  We see all the strange shapes that appear in stock graphs – head-and-shoulders, smiles, etc., which we will examine later – so stock-chartists should have equal scope here.  Yet most people would not feel the same enthusiasm to follow their stock-trading instincts here.  Should we “buy on the dip” in the dollar?  If we invert the graph, the dollar’s dip is the Pound’s rise.  We are not convinced even when we are told that, over the long-term past, the dollar has appreciated greatly against the Pound, having been just 25% in value until 1949.   We conclude that there must come a point when there is no longer any long-term trend.  Perhaps we reach a kind of plateau which then fluctuates back and forth.  But maybe we don’t even believe that, or else we would bet heavily against the Pound which has just sailed past its 26-year high.

Economies Drive Currencies and Equity Markets

In other words, exchange-rates seem wholly directionless, and at the same time wholly unstable, able to lurch in a single direction almost indefinitely.  We then have to explain to ourselves why this process is different from that of the stock market, once we eliminate the pedestrian return that we know we can earn from Treasuries. (For currencies we would also eliminate any difference between their overnight rates.)  The shapes of the graphs look entirely the same from day to day, suggesting that the opposing forces that move prices are working in the same way.  Of course, equities have been hugely more successful that Treasuries, compared with any pair of currencies, over the long term.  Yet investment is a highly leveraged activity, and can leverage in both directions, as the 1930s and 1970s showed.  To the benefit of its equity market, the US economy has greatly outstripped that of the UK since before 1914, when the gross domestic product of the British Empire was greater than that of the United States and the Pound was the dominant currency.  The US economy has distanced itself from Britain’s over much of that century, paralleling the success of its stock market.  Yet few would think it has more than an even chance of continuing that trend.  For a century through the 1980s, China declined even more sharply against the United States.  Obviously, even very long-term trends come to an end.

I believe that the primary forces driving exchange rates are, in fact, the very same as those driving stocks.  Despite a zero expected return, it is not irrational people who are driving a 20% premium to the British Pound above its purchasing power.  It is experienced traders who respond quickly to each piece of news that is known to affect exchange rates.  To them, the “true” value of a currency, like the “true” value of a stock, is irrelevant.  Premiums and discounts can last indefinitely, depending upon news.  Traders will buy and sell any one currency as soon as news influences them to do so.  There is no “long-term view” among such traders that provides a reliable source of revenue.   The difference between the markets for currencies and stocks is simply the length of the sequences of sticky luck.

Just as sticky luck is a counter-intuitive idea, so it is necessary to take a counter-intuitive approach to understand how it occurs. We have to start at the far end of the process – sufficiently close to the end point in the sticky progression that the remaining stages might be reached through sheer momentum alone, perhaps even resulting in a bubble.  At that point, the underlying facts that have justified the progression are as advanced as they will go.  In the case of exchange rates, it may be where the country with the rising currency has achieved its greatest advancement relative to the others.  In the case of stocks, it may be where an individual company has peaked in its performance relative to others.  In the case of a market as a whole, it may be where the economy and corporate profitability have peaked.

Looking back from this end point, it is always possible to explain how we got there.  The explanation may be highly convincing, but we will never know for sure if it is the true explanation.  A simple explanation is compelling, but often the real story is much more complex, and seen differently by many people.  But at least all these explanations have the advantage of knowing the end result.  Choosing the end result from an earlier point would involve, as we have discussed, peering into the future and the outcome of countless contingent events which we can never know beforehand.

Performance Is Not a Matter of Luck

Yet we have no problem accepting that one economy or one company will achieve superior performance over an extended period of time, and that this is rarely a matter of luck.   The economy may enjoy freer competition and a workforce may be particularly well adapted to a new industrial direction.  The company may have an incredible new invention or an especially inspired workforce.  Though luck plays a part, no doubt many such achievements are richly deserved.  When identifying sticky luck, we are not focusing on the achievers themselves but on the people who freely trade in the currency or stock of the achievers.  With every milestone of achievement, the market acknowledges it with a price increase.  The role of the price increase is to allow for all the achievements to date and their potential implications for future success. 

For example, two stocks are originally priced at $40 each, having the same expected future earnings.  After both announce their most recent results, Stock A is now seen to outperform Stock B such that it is now expected by market consensus to earn 10% more in the future.  According to efficient-market theory, the market pushes up Stock A to $44, so that the expected return of a $1 investment in either stock is still the same.  In other words, all the advantage of that better performance has gone to the holders at the time of the news.  This result makes intuitive sense, because these are the people who took the risk before the out-performance was known.

Let us now assume that, ten years later, Company A is dominant in its industry, while Company B is struggling to survive.  After adjusting for splits, Stock A is up to $400 while Stock B is now $20.  Company A’s investors have achieved an investment return about 35% per year greater than Company B’s investors.  A’s relative rise has been steady over time, but there have been a number of occasions when A has fallen sharply and B has risen sharply, these temporary reversals only to be reversed again by the general trend.  We are assuming at this point that neither stock has entered a “bubble” phase as we will explore later.  In retrospect, it is clear that the market underestimated A’s true potential for many years, even though, year after year, it increasingly recognized part of that potential with a price adjustment.   It might be possible to argue that the market “made a mistake,” in its underestimation, but this is impossible to prove convincingly.  The gathering evidence of A’s sustained performance was needed to convince the market that the ultimate valuation was really worth it.  The market may later lower the price if new evidence goes the other way.  The market was simply adjusts its probability measurements to the quantity of evidence received.

That evidence, of course, dominated in one direction for many years.  There are undoubtedly one or more causal reasons for that – superior management, superior product, superior sales force, and fortunate market timing which persisted over years.  Whatever the reasons, it is important to realize that they were very unlikely to have reversed on a regular basis.  For example, over the ten years, it is extremely unlikely that there were ten separate reasons which each dominated for an average of one year.  It would seem too much coincidence that management went from brilliant to average but was then compensated by brilliant product, which then went to average but was compensated by brilliant marketing, etc.  For the consistently successful, typically one or maybe two reasons will predominate in any single bull sequence, no matter how long it is. 

In fact, the loss of a primary “bull factor” is likely to be followed by a journey through a bear cycle until another factor can assert itself.  The gradual revelation of the primary factor over time, steadily convincing investors of its strength, durability, effect upon success and ongoing market advantage, will be the source of the stock-price stickiness.  It is not even necessary that the investors understand what the factor is – they simply need to see it in operation and appreciate – always in retrospect – the pattern of performance it delivers.

All Expected Returns Are Already Priced In

Now, here is where the conceptual leap to sticky luck is more difficult.  Even though the ultimate success had a cause, and even though investors could see the pattern of the business performance, at no point would this pattern and causality justify any expected superior return in the stock price.  Each piece of evidence of business performance suggests a certain level of future success that is full reflected in the performance in the stock price.  The next piece of evidence, as viewed from the time just before its release, has a potential downside to match the potential upside.  This fact will hold true for every trading moment of every traded stock, even if it turns out to have block-busting appreciation for many years.

To illustrate, suppose that, after five of its ten years’ bull market, Company A had revealed enough evidence of performance to justify 60% of its ultimate price increase.   By definition, the market could not know at that time that the performance would ever justify 61% of some unknown result in the future.  Consistently disappointing performance from that time onwards would have started to send the stock price downward.   We are therefore faced with the paradox of a very long sequence of stock price changes in a single direction which are all unknown just before they occur but, in retrospect, it is possible to see the same underlying cause for all of them.

Let me try an analogy.  Suppose we are holding a competition between a group of runners, asking them to perform a long series of races.  After each race, the winner will have his or her distance lengthened the next time by the distance that he or she won the prior time – a simple form of handicapping.  You are asked to bet on the runners before each race, but all you know about is their ranking in prior races.  You know nothing about age or fitness.

It is perfectly possible that one runner will win every race held for a very long time.  At an extreme, we may have one adult athlete, the rest of the field being small children.  As punters, we would see one runner winning consistently, but realize that he or she was having to run further and further relative to the others.  There would be no good reason for continuing to bet on this individual rather than the others, and good reason to imagine exhaustion setting in.

The capabilities of the runners is analogous to the inner workings of the competing companies – the sort of day-to-day interactions that will never be evident to even the most persistent of visiting analysts.  The race results are the relative performances of the companies, for which stock prices are evaluated.  The distance handicapping is the awarding of a stock price increase to the winning runner.  In other words, the runner has to consistently exceed expectations and to repeatedly win despite the distance increase.  So, while the underlying cause of performance may have no randomness associated with it, the fact that the market handicaps each contestant based on any new public information (i.e. each win) can make each further gain in price a random, or “lucky” event. 

The Let-Winners-Run Fallacy

There is a common wisdom, found in advice to retail currency traders and other novice speculators, that experienced investors learn to “run longer” with their winners and “cut their losses” with their losers.  What is the justification for such asymmetrical advice?  It may be based on the assumption that experienced players somehow have a better feel for the ultimate length of any sequence.  Efficient-market theory tells us that we cannot expect to out-guess the market.  The advice is based on the fallacy that, even in random sequence, we can choose just to stay on the positive side of a fluctuating graph line.  If I always let my winners run and cut short my losses, I might make a fortune and it never costs me very much to play.  This is the seductive logic that draws people to the lottery – low price, high possible gain.  Yet we know that, even if all the lottery money were plowed back into winnings instead of being used as tax dollars, our expected return on such gambling is zero.  Equally, in currency speculation, our small losses are in fact always expected in total to equal our “long running” winners because, under such a strategy, they can be expected to be much more frequent.  As always, we can only end up winning through luck.

A consistent winner over a month, six months, a year or five years can suddenly turn into a consistent loser, and vice versa.  I mentioned earlier in the case of Company A that, after five years, the market saw enough evidence to convince it that 60% of the ultimate performance was there.  Let’s say the ultimate performance was $10 per share in profit, and $6 had been reached.  As investors, we would not know the difference between this company and another one of the same price, identical in all other ways and whose profit had run the same course but, as yet unknown to the market, has actually peaked at $6.  As soon as the market became aware that this other company’s profit had peaked, following quarterly earnings or some form of warning, its stock price would head downwards.  The probability of it ever reaching $10 is suddenly diminished, while that of Company A continues to increase.  No length of performance to date implies an expected gain from its continuation. 

The same type of random process can be illustrated with the whole market.  On each day of a working week we receive an independent data item suggesting economic weakness, and the market declines on every day by 1% as a result.  By Friday, we might berate ourselves for not selling off on Monday, given the clear warning sign on that day of an event that would ultimately take 5% off the market’s value.  However, the 1% drop Monday balanced the chances of a real slowdown against a false signal.  Though, looking back on Friday, we were able to see that the market movements all week were linked by the same underlying cause, which may have been a real slowdown or something which looked very much like it, we could not expect to take advantage of that fact on Monday, other than by guesswork and luck.

The Random-Walk Misnomer

We need always remind ourselves that we are not, in any of this discussion, claiming that there is a equal likelihood of a stock moving down or up, regardless of prior movements.  This is the trap that much discussion about “random walks” has fallen into.  Any casual observer can see that the movement of stocks is not a random walk – this is such an obvious fact that it hardly bears discussion.  The main purpose of this book, after all, was to explain how efficient-market theory transcends the existence of such clear patterns in market history.  As Professor Mandelbrot has emphasized in The (Mis)Behavior of Markets, stock and currency patterns show clear evidence of “memory.”  In other words, there is a tendency for the current movements to echo the last series, or earlier series.  This is an intriguing way to express the phenomenon of patterns, but I think it confuses rather than enlightens.  It might be more apt to say that the market has no memory, and is therefore destined to repeat itself.  If we do not understand the source of pattern, we will not be able to draw the right conclusions from it.

Mandelbrot offered no strong ideas for the existence of patterns, and was mainly focused on trying to build a fractal simulation of market movement.  His primary target was the mathematics that underlies most of the derivative pricing that floods today’s market.  This gargantuan derivative edifice is built on a worrying fallacy – that price movements are normally distributed.  As Mandelbrot points out with little effort, this cannot be the case.  Were it so, the probability of the October 1987 one-day crash would be so small that, expressed as a fraction, it would be smaller than the ratio of a proton’s length to the width of the known universe.  Does that fallacy matter?  It all depends whether or not, when seismic changes in the market do occur, derivative pricing increases or decreases volatility.  We cannot know the answer to that question, because no one can see the whole derivative picture.

An important thesis of this book is that patterns emerge because of the impact of news upon the market’s assessment of probabilities.  If an underlying and critical fact happens to be true, and the evidence of its truth emerges gradually over a long period, then it will create a long sequence of upward price movements.  Once we can say there is “probable evidence” of both the underlying fact and its eventual full proof, then we can say that upward price movements are likely, without even the need for invoking the concepts of momentum and bubbles.  Yet, at any specific date, the expected return for the future does not change.  The likelihood of the next steady increase is fully offset by the possibility of a much sharper drop, as measured by market forces.  In a sense, purchasing such a high-flying stock is the opposite of buying lottery tickets.  The stock offers a probably steady gain and a possible big loss.  Lottery tickets are a probable steady loss (cost without winning) and a possible big win. 

The Yen-Carry Trade

There is no better illustration of this investment phenomenon that the so-called Yen carry trade.  Though there are many sophisticated twists to this business, the concept is very simple and the reader can participate very easily at the retail level.   Anyone can open an account with an online currency-trading firm using $2,000 as stake money.  Such trading firms are regulated, and do not themselves carry significant currency risk – their role is to match buyers and sellers and take a commission on each transaction.  There would therefore be no reason to imagine the terms of the deal would not be honored, just as it would in a large and reputable gaming establishment in Las Vegas.  At the time of writing, you are able to borrow some $242,000 worth of Japanese Yen and invest the proceeds in British Pounds.  You are credited with about 4% more interest on the purchased Pounds than you are paying to borrow the Yen.  Annually, your net interest earnings are almost $10,000.

So, for stake money of $2,000, you can earn $10,000 per year, assuming the Pound does not fall against the Yen.  Should the Pound appreciate against the Yen, you would earn even more.  Does this sound too good to be true?  If exchange rates took random walks, it certainly would be.  If the market thought the Pound was as likely to appreciate as to depreciate, then our expected return would be 500% per year.  Yet such returns pale beside those returns achieved in the last year.  At the time of writing, the Pound has appreciated some 15%, giving a total annual return on the stake money of 2,000%.

The gambling nature of the investment becomes clearer.  A small wobble in the Pound will wipe out our stake money and require further cash infusion to keep our trade open.  Just as the Pound has risen greatly against the Yen, so it can fall such that the additional interest will be poor compensation.  The market consensus – which is, remember, a collection of widely differing opinions – has placed the exchange rate exactly where it expects the future loss of Pound value to the Yen balances the expected additional interest income.

A Market in Tree Discovery

Let me further illustrate such market forces with a novel betting game.  Suppose we place a thousand individuals in random locations on the world’s land surface.  The individuals are referenced by number only, and pundits never know where they are.  The individuals are blind-folded and walk around in random fashion for a period of six days, all at the same pace and for the same number of hours per day.  If they touch at least one tree within fifty places, they score one “dollar point”.  The pundits, all experts in measuring gambling odds, watch the accumulating dollar-points for each individual, a nil or a $1 for each fifty paces, and can buy and sell ownership in the individual’s expected final total score.  Let’s say the maximum score for anyone would be $3,000.  After Day One, individuals have accumulated anything between zero and $500.  Assuming the pundits can create an efficient market, as I’ve defined it, how do they determine the price they are willing to pay for each individual?

The “top performer” on Day One may have landed in the middle of the Amazon jungle and is destined for $3,000.  Or else he may have landed in a leafy suburb and is about to wander into some open farmland or a more urban, less arborous setting.  He may be about to exit a wood or a forest.  Likewise, the zero performer may have landed in the Sahara, or else be about to enter a wood or suburb from some open farmland.  Of course, if all individuals were offered at a price equal to Day One’s score, we would buy the ones with the highest count, as it is reasonable to expect higher scores to continue higher.  But since we have a free market to price the individuals, the higher scorers will be appropriately bid up.  If they then turn out to be leaving their wooded areas, we will lose more money than if we bought a zero that continued to be a zero.  We can say that the high scorers for Day One had sticky luck, and that the buyers of those individuals who happened to be six days’ walk from a forest clearing, and who were bought for substantially less than $3,000, were also beneficiaries of sticky luck.  But no matter how delightful to them it would be to watch the maximum score accumulate for six straight days, minute by minute, they could not claim to have done anything clever. 

The analogy with the stock market can be taken further.  By plotting the patterns of many of the individuals – scoring high, then low, then evenly, then gaining sudden “momentum,” – and then showing the progress of their changing price, we would have charts indistinguishable from company performance and stock prices, and no doubt a feast for the market chartists.  An individual with a full score for days, when suddenly registering several nils, would see their price plummet, as pundits fear they have left a forest and may not get back.  Similarly, a zero that starts getting a fairly regular sequence of $1s would see a sharp price increase, as hope rose that the individual had entered new territory.  We would even tend to see the “saw tooth” pattern of the market, where downward price movements for high-flyers are much sharper than their ascent.  Reverse saw-teeth would occur for zeroes who started hitting trees but which then trailed off.

Looking backwards on the final results, it is possible to find the cause of the high and low scores, just as we look back to explain a bull or bear market.  The maximum scores were indeed in a forest large enough for you to wander around at random for six days without exiting.  Until the end of the six days, no one would have bid a full $3,000 because of the chance of exiting the forest, so the forest would always have been underestimated on an “expected” basis, even though the expected size increased with every extra dollar score.  The instant the extra dollar score is posted, the price of the individual adjusts accordingly.  The potential for future price gain (i.e. expected return) will then be the same as for any other individual, or else another pundit would bid a higher price rather than accept a lower expected return with another individual.

Our betting game therefore gives us prices for individuals that move in a very similar way to stock prices, based upon punters’ assessments of relative “performance.”  But no matter how consistent any individual’s performance, the effect upon that individual’s price of the next piece of news does not make it a better “bet” than any other individual.  Of course, if the individual is consistently scoring points, we know that score is more likely to increase than that of some other individual who is not scoring.  But, because of our efficient market, each additional point for our high scorer will have a lower price-increase effect than for our non-scorer, and each nil score will have a greater price-decrease effect than for our non-scorer.   You might say that the high-flyer has a high chance of a small price increase and a low chance of a big price drop. 

The Invisibility of Any Skills

Can a gifted investor somehow spot the cause of the success or failure that is more than likely to lead to a consistent sequence of market movements?  Efficient-market theory does not deny the possibility, only our ability to know that they do, or for them to communicate the successful approach to us.  Sticky luck masks any true skill over any individual’s lifetime, and any communicable skills would be programmed into a million market models, wiping out any stock-selection advantage.  The market searches ceaselessly for clues as to the roots of stock performance and, as soon as it finds them, awards the relevant company a price increase reflecting the probability it will turn those roots into future high performance.  Again, the market is the balance of all investors’ estimated probabilities, weighted by the amount of money with which they are prepared to back their estimates.  Any advisor whose view is different is in practice unable to prove it superior.

I had started this chapter with currency exchange rates, explaining how they are equally subject to sticky luck and that it is somewhat easier to accept the existence of such luck, given the overall zero-sum game of currency speculation.  The historic charts themselves testify to the stickiness.  Instead of corporate performance, currencies follow countries’ economic performance, plus a host of other factors such as central bank interest rates, trade surpluses and deficits, etc., all of which are partly related and partly subject to unique factors.  There is no fundamental, underlying trend in exchange rates which currencies always return to after shorter-term effects.  I mentioned that the British Pound has ranged between $1 and $2 in the last quarter-century, without any specific trend, and there is no reason why it should not remain predominantly in the $1.50-$2.50 range forever in the future, quite possibly more often towards the higher end.  Though consumer prices suggest “parity” at around $1.65, there is no reason why Britain should not remain a more expensive country that the US, as has Switzerland for most of modern times.  Fundamental shifts in economic performance, reversing a previous long-term trend and related to the shift in importance of different industry sectors, are a likely cause but, again, only in retrospect.

When considering equity market sectors, we are typically faced with a single primary driver of a sticky series – product demand.  Even if the actual demand has not yet materialized, the market will anticipate it with stock price rises as soon as evidence emerges that makes the demand appear more likely.  Demand often drives further industry investment, which can help the sector expand further.  But expansion does not necessarily create more demand.  Sometimes it does, but sometimes it can produce a glut which can shrink the industry again.  There have been some phenomenal sector expansions which have lasted over many years – a couple of which led to my friend Eric’s fortune – but many have been short-lived.  Unless there is new information regularly adding certainty and strength to the sector boom, its potential will have already been priced in with the older news and the sector stocks will cease to grow in value.

Efficient Markets Always Make Mistakes

Do efficient markets make mistakes?  Of course - all the time.  The fluctuations of the market are the result of it realizing it over-reacted or under-reacted to prior information and, of course, this is not just a daily but an hourly occurrence.  Because every individual response to a news item is deeply subjective, so must be the whole market’s response.  Facts about today’s earnings, management changes, economic indicators and political and military events do not readily translate into stock prices, which represent the capital value of the company’s entire future earnings.  It is reasonable to say that much of the reaction has become almost convention – a particular piece of bad or goods news is considered to be worth about 1% of the market, because that is the way the market has responded in the past.  Traders are trying to guess how others will react, and get in ahead of them.  When the bad news is confirmed or countered, how much should that 1% be increased or decreased?  It’s easy to see how the market can lose track over time of fundamental measures.  Series of good news can increase average P/E ratios from 18 to 27, making stocks 50% more expensive by this measure.  Bulls will then explain that this 50% is the value of increased future earnings.  As we have described earlier, there is no way that a sequence of good news can be valued this way by anything but pure sentiment.

To complete the market picture in this chapter, I want to raise an intriguing observation made by Benoit Mandelbrot in The (Mis)Behavior of Markets.  He pointed out that market patterns were fractals.  Fractals are a special type of mathematical pattern, developed by Mandelbrot himself, where magnification, at any level and to an infinite degree, reveals identical properties.  Fractals have become famous not only in the world of math but also design.  Many artists have created fractal patterns and I have little doubt that the reader will have seen one, if only on a tee-shirt.

One way to understand the fractal nature of market data is go through the following procedure.  Go to a website that shows exchange-rate movements in chart form over different periods.  Print out hourly, daily, three-monthly, yearly, five-yearly, twenty-yearly, and any other available charts for a range of different currencies – ideally, try as many cross-rates as available such as GBP/EUR, EUR/CHF, AUD/GBP as well as each currency against the US dollar.  Then trace the patterns, roughly, on separate pieces of paper without reference to the particular stock or the time period for measurement.  Discard the printed charts, and shuffle the papers on which you traced the lines.  Look at the different patterns.  When studying the pattern shapes, you should not be able to tell the daily from the five-yearly, or from any of the other charts.  In other words, the shapes of the lines have the same spikes, troughs and plateaus, typically mixed in the same proportions and sizes, regardless of the time period over which the underlying observations were measured. 

I choose currencies for this analysis, but in principle it would work with all freely traded financial markets.  The limitation is the fact that, with stocks, we have happened to have experienced a spectacular bull market over some twenty-five years, making the trend of that period, and even the last five-year period, fairly uniformly upwards.  As discussed earlier, this is one tiny window on all possible alternatives the market could have experienced, but we do not have thousands of years of data to demonstrate the fractal nature of the stock market.  Our limited time horizon, compared with the vastness of the fractal pattern in question, obscures our perspective.  Hence the importance of exchange rates in this chapter to give us the bigger picture.   Whereas investors and the global economy can show unexpected growth and optimism lasting a quarter-century, demonstrating the stickiness of its luck, the relative competitiveness of currencies appears less sticky, at least in recent years.  You might say that, though the developed countries’ “economic armies” have been advancing steadily, their order on the field has changed constantly during that time.

A Fractal Joke

The best way I can think to illustrate why stocks can appear to diverge from the fractal rule for so long is by way of a schoolboy joke.  One example of a fractal in nature is a coastline.  When viewed from space, the pattern of a coastline is indistinguishable from the pattern taken from a helicopter.  We have the same craggy shapes, inlets, protrusions and offshore islands at any scale.  By showing someone an outline of a coast, they would be unable to say at what height the outline was taken, and to what scale it was drawn.  But our schoolboy imagines two ants discussing Mandelbrot’s fractals as they cross a large, smooth boulder lying on the shore, and conclude that they have disproved the theory.  I tend to see some of the criticism of efficient-market theory of the same myopic quality.  At least the ants lived to reconsider when they dropped onto a slate outcrop.

Why should a coastline be fractal?  It would seem that the interaction between water and rock is essentially the same at any scale.  The time period over which it works may differ, but the end result is the same.  Moreover, if we are exploring a coastline on some distant planet for the first time, again at any height, the emerging shape is random to us.  A long, flat stretch could be broken at any time by a long jagged sequence, or a short one, or a wavy sequence of any length.  These sticky-luck properties are determined by the underlying rock strata, but we know nothing about them.  An inlet may be a small pool, or the size of the San Francisco Bay, or the Gulf of Mexico. 

Now compare fractals with our conventional thinking about randomness.  As people leave Las Vegas, we poll them at random about how much they won or lost.  We keep a running total of the cumulative win or loss.  We draw a chart with the cumulative win or loss marked on the Y axis, and the people count on the X axis.  The individual amounts vary greatly, from a few dollars either way to hundreds of thousands, and so the running total fluctuates greatly.  We first interview a thousand, then 100,000.  We put the results of each of these groups on a single page, without any indication of the dollar cumulative amounts, so we just see the relative values.  To make sure the “texture” of the graphs doesn’t give the game away, we make sure that any one line is of a minimum thickness.  Yet it is still very easy to tell the two graphs apart.  For its scale, the larger (100,000) number polled will appear to have fewer extreme values – despite the fact that in dollar terms it will likely have many greater individual values than the thousand.  Despite the unlimited randomness of the data, the greater number will make for more relative predictability.

Predictability Through Large Numbers

There is a simple reason for this pattern.  The further away from the “expected value” a result happens to be (in this case, the expected value would be a moderate loss) the rarer it will tend to be.  Very large values are very rare.  The increasing poll numbers exercise an increasingly dampening effect upon the impact of the largest win-or-loss numbers.  So when our chart allows for the greater number of events stacked along the same-length X axis, the fluctuations along the Y-axis will look smaller.  This “averaging” effect applies to all the games of chance that we have used, even the ones which were used to “mimic” the market to measure the probability of being a successful investor.  In effect, there is a certain quantity of risk associated with each event.  The more you accumulate events, the more you can average out that risk.  You can illustrate this by telling the 100,000 polled gamblers that, instead of their one winnings, next time they go to Vegas they will get the average of the entire group’s winnings.  It’s intuitively obvious that we are then exposed to less risk, and opportunity, than being part of the same plan with the thousand gamblers.

If we accept the stock market pattern as a fractal, we are struck immediately by a scary thought.  We know that a single hour’s or a single day’s trading can be wild.  Could such violent patterns also be likely over many years?  This is, of course, what we have seen, though generally on the upside.  If we back out of the market’s long-term progress the risk-free rate of return, which obviously trends upwards when compounded, the fluctuations are even sharper, with much deeper dives in the 1930s and 1970s than the typical index would suggest.  In 1981, few people could have imagined the surging prices that would then follow.  Equally today, few people can imagine an equivalent collapse occurring, as if such sudden fluctuations can only occur upwards.  Could it be that the 20^th Century’s equivalent of a single day on Wall Street, where we see a big surge in the last few hours?  If so, what does tomorrow hold?  Certainly, this concept would throw serious doubt on the wisdom of “stocks for the long run.”  We may have been comforted too long with the idea that, just so long as we sit tight, the market will eventually get us to where we want to go. 

I mentioned that, for coastal patterns, it seemed that the effect of water on rock depends little upon scale.  The fractal nature of market patterns suggests that what moves prices by the hour has some critical relationship with what moves them by the decade.  We watch the market rally, minute by minute for a couple of hours at the end of the day, maybe with a few momentary “corrections” before it regains the same path.  Those two hours are actually very long sequences: for perhaps 6900 of 7200 seconds we say an up-tick instead of a down-tick.  After digesting the Fed’s encouraging words, some investors noticed interesting activity in a certain sector and read it as another bullish sign.  They began buying heavily and the rest of the market responded, feeding on a combination of benign news and investor confidence.  Stocks have been down and marking time for quite a while, and a lot of liquidity was ready for this moment…

Hours and Centuries Look the Same

There is nothing conceptually different between this description and the quarter-century bull market.  Of course, the longer stretches had to be sustained by actual performance, but such performance had been improving long before, and price rises raced ahead of company’s actual achievements.  A huge impetus had come from the Fed’s success in fighting inflation, creating much greater investor confidence.  The rewards of a responsive stock market were undoubtedly major drivers to the innovation during that period, making the process self-reinforcing, just like the two-hour buying spree.  In both cases, there was a point up ahead that investors considered “fair value” provided conditions were right.  The market worked its way to that point with every data signal that continued to reinforce its likelihood.  Once reached, the bubble phenomenon took over, first moderately, then excessively.  A little bit of actual performance data went a long way, then perhaps went to far.  This parallel with the afternoon rally suggests that the bubble phenomenon should exist at any scale. In other words, if market patterns are truly fractals and bubbles exist, it would seem to make sense that bubbles can exist even for minutes.

Our more general point for this chapter is that, just as the extent of the afternoon rally was unpredictable at any stage, so the quarter-century bull market was unpredictable at any stage.  Both are long sequences of movements predominantly in the same direction, driven my elements of good news and so-called “animal spirits.”  As with natural phenomenon such as coastlines and the branching of a tree, the smaller-scale activities do not “average out” when taken as a whole.  Instead, the randomness of the smaller activities seems to coagulate into the same degree of randomness whatever scale we rise to.  We can imagine a timeless God, seeing the performance of the US stock market over the next million years, compared to which the 20^th Century is roughly on the same scale as one day’s trading is for us.  “Stocks for the long term” would mean something quite different to St. Peter.