Sticky Luck

Eight:

The Market

Model

Our own expected return, buying and selling.  How market votes are counted, and the expected return they imply.  Buying and selling pressure.  Distributions of expectations.  The F, inverted F and E distributions.  How all security sales are linked to Treasuries.  The myth of the nervous investor.  How prices respond to market pressure, keeping expectations constant.  Anatomy of a stock responding to news.  Market movements as news.  Risk-free returns as bridges connecting expectations.  The effect of market-timers.

We are all familiar with a freely-traded security’s market value:  it is constantly posted.  Those who take time to think about it also know what that market value means – an agreed price between those who have decided to buy and those who have decided to sell.  Our “freely traded” concept assumes plenty of volume, so we can reliably get something close to the price quoted just prior to sale or purchase.  As previously mentioned, we assume that all investors want to maximize their earnings, no matter how irrationally we might think they go about it.  So, when they buy a security, they think it will have the greatest expected return of all securities at that time.  If they didn’t think that, they would buy another security.  By “expected return,” most investors would accept a vague concept of “weighted for risk” or “risk-adjusted.” 

We know that we may not get the return we hope or plan for.  For an apparently risky stock, there’s a chance of a high return but also of a low – including negative – return.  Each of us weighs the risk against the potential return, no matter how vaguely we do it in our minds.  For example, with high-tech stocks soaring, we think that there is a good chance of them continuing to soar, and also some chance of them collapsing.  We would balance the two somehow and conclude, when these chances were taken together, it was either the best bet with our money or we should keep looking. 

If we actually thought about it in words, we might say something like, “There’s a 70% chance of me making a return of 20%, and a 30% chance of me making a negative return of 10%.”  Of course, even this is a simplification, because there are plenty of other possible results besides 20% and a negative 10%.  But if we have to come up with some kind of formula, it’s both natural and rational to “group” potential return in this way.  The 20% may be some kind of mid-point between 10% and 30%, and the -10% between +10% and -30%.  Such details don’t really matter.  What is important is that we recognize there is a chance of a higher loss than from a safer security, but also a higher gain which may or may not balance the higher loss.  When these two chances are weighed together, we either end up with an expected return which is above that of a risk-free bond, or else we would prefer the risk-free bond.  The great majority of investors, after all, do not believe in efficient-market theory.  They will decide that the expected return for a chosen security is significantly above that of a risk-free bond, and maybe above that of any security at that time which offers a comparable risk profile.

The seller, on the other hand, typically expects that a better return is available through some other investment, or even through holding cash.   If the seller was also forced to think it through, he or she might choose the same ranges as the buyer, but attach opposite probabilities – 70% for the downside, 30% for the upside.  He or she may even think there remains a chance of a high return, but the probability is too low relative to the risk of the loss.  Instead of 70% and 30%, we may have a more complex range.  But these probabilities and returns can all be combined into a single, weighted expected return, as for the buyer. 

I have not defined any time period over which the return is expected – it could be days or years, a decision about which many investors would be vague, at best.  A seller may expect the price to drop in the short term, and then plan to buy the stock back later.  We are only concerned with the current decision – the sale – so for this individual, only the short-term expectations driving the sale are relevant.  I have also not specified if the returns quoted – negative 10% and 30%, and positive 10% and 30% - are annualized returns or otherwise.  Consider one investor who decides he is likely to lose 20% over the next year, and another one who decides she will lose 10% over the next week.  If these are the only driving considerations, then I define the “expected returns” to be negative 20% and 10% respectively, with an average of negative 15%.  However, longer-term investors do tend to think in terms of annual returns, so a year would seem to be the maximum period for measurement.  For shorter-term investors, we will simply take their expected gain or loss.  Though this is technically inconsistent, I think it mirrors investors’ thinking most closely, which is the critical consideration.

A Target Price – Sooner or Later

This “timeless” approach is roughly in keeping with professional advisors, whose common approach is to quote a “target price” which could be reached any time over a defined future period.  Of course, a target price, as well as carrying all the problems of ambivalence I have described earlier, also makes no attempt at probability weighting.  But just now we are dealing with the realities of the market - how people actually make their decisions to buy or sell stock, however imperfectly.  Efficient-market theory cannot depend upon investors behaving in some rational, orderly way when selecting securities, still less imagine that they go through some systematic probability analysis.  The best I can claim is that, for those professionals who use models for decision-making, this type of probability analysis is built within such models, no matter how implicitly.  I can also go as far as to suggest that much of this modeling does control a large portion of market action, through both institutional investors and professional recommendations.  That recommendation may be in the form of a target price, but it has been arrived at through some kind of probability model.

First, imagine a world of rational investors who always apply the probability weightings I have described, or who else have their money managed by those who do, or follow the recommendations of those who do.   Each investor has chosen his or her own specific time horizon for their expected return.  Based upon the level of expected return, high or low, the investors decide how much stock they wish to buy and sell.  Because the greater the amount of stock held increases the buyer’s risk exposure through concentration, the expected return must be higher to justify a greater holding.  The seller will sell more, to generate more cash for other investments, if the expected return is lower, dropping below the expected return of those other investments.  Consequently, those investors who expect the higher return will buy the more stock, and those who expect the lower return will sell the more stock. 

The time horizon of the investors’ expected returns will not be a factor affecting the amount of stock purchased because, for a freely traded security, they can realize their actual return as easily in a day as in a year.  Since we assume that the investors factor into their decision all aspects of risk for the amount they decide to invest then, at the time of the sale or purchase, the transaction is the best one available to them.  In other words, it was either the best-value purchase they could make or the best-value sale they could make.  Since we have assumed that all our investors want to earn the best return and also that this group is rational then, if there were a better value transaction available, they would make that other transaction instead.

Now we come to the theoretical slight-of-hand.  In terms of behavior, our fuzzy-thinking group of investors is indistinguishable from our probability-weighting investors.   In other words, for every fuzzy-thinking investor who buys or sells a certain amount of stock based upon pure whim, we can find a rational investor who buys or sells the same amount of stock.  Using mathematical language, we can say there is a “one to one” relationship between the fuzzy and rational investors.   In terms of market action, it doesn’t matter what investors actually think, it matters how they act.  A buy or sell decision sends to the market what I call a market “vote.”  It is an official, recordable vote, and a sincere one backed by the investor’s money.  That vote is measured by volume of money at a given time, whether a buy or a sell. That volume of money can be counted as  an implied “expected return” in a theoretical world of rational investors. 

How Market Votes Are Counted

A small investor may put all his or her money is a single stock to vote a very high expected return, but that amount may be equal to a large investor’s purchase based on a lower expected return.  Clearly, individual amounts invested do not give us enough information.  But the large investor has greater voting power to be weighed by the market.  The total amount offered to purchase a stock is the weighted votes of all buying investors, combining their voting power with their expectations.  In combination, it will give us a total, market-weighted expectation.  In this way, each voter is included in that weighting, in proportion to both the percentage of available funds voted (a measure of personal return expectation relative to alternatives) and overall voting power (total available funds).  It is not too difficult to see a single, market-weighted expected return for all buyers at a given moment, and also a single, market-weighted expected return for all sellers at the same moment.  Efficient-market theory tells us that, when buyers and sellers are balanced, even for just a moment, the average of the buyers’ and sellers’ expected returns is equal to the risk-free rate of return. 

The risk-free rate of return is somewhat different for different lengths of term (time over which the return is promised).  I have mentioned that all the investors in the weighted-average expected returns have their own concept of term, from days to years.  The risk-free return we will reference for the purpose of a security or index will therefore have a weighted-average term of the investors’ expected terms.   But we cannot know this term because we don’t know what is in investors’ minds.  We assume that any actual investor could be represented by a rational investor who has a certain investment term in mind and who decided how much to invest based upon both this term and the probability weightings of various returns. 

Traditional explanations of efficient-market theory introduce the concept of the arbitrageur to explain the existence of irrational investors in an efficient market.  The arbitrageur, it is assumed, will fleece the irrational investors by selling them dearly and buying from the cheaply, thus rebalancing the market.  Unfortunately, the dot-com bubble showed how many of the “rational” arbitrageurs got fleeced instead.  As I have stressed in this book, dear and cheap are in the eye of the beholder.  The only expected winners are the gifted, gut-feel, news-sharks.  An arbitrageur whose strategy is not measured in seconds has, in an efficient market, no better weighted expectations than the dart-throwing monkey.  

As in any scientific inquiry about human behavior, we need to focus upon what actually happens, not what we think is going on in people’s minds.  No matter what definition we choose for “rational,” we cannot measure how rational investors are being.  One who stakes all his savings on a dot-com because he just loved the look and feel if its website, is indistinguishable in market action from one who stakes all her savings on the same dot-com because of a rigorous probability analysis of its projected earnings.  Who is to say who is the more rational?  Our theory requires only that, at any point in the market cycle, there could exist a plausible analysis that could support the purchase.  Since we have already shown that discounted future cash-flows can have infinite present value, then I argue that a plausible analysis is available (and was available even at the height of the dot-com bubble) for any finite price.

Buying and Selling Pressure

Consider an investor’s weighted-average expected return after subtracting the risk-free return.  For the buyers, this “delta” is a measure of the advantage of taking the risk of purchase.  The “buying delta” can be considered a measure of “buying pressure.”  For the sellers, assuming that the delta is negative, it is a measure of the disadvantage of taking the risk of not selling.   The “selling delta” can be considered a measure of “selling pressure.”  Because the amount of stock sold is always equal to the amount of stock bought at any one time, the selling delta and buying delta should be equal, at least when a stock price is in equilibrium.

For the skeptic, I will again explain why we should measure the pressure relative to the risk-free return and not some other point. This is best explained by considering the risk-free security itself.   In the sense that I have defined pressure here, there is no such pressure for risk-free securities, as both buyer and seller are agreed on exactly the same expected return – because that return is a certainty.  Of course, there is regular buying and selling, but it is driven only by reference to other investment opportunities and not by an individual opinion of what the risk-free security might yield.  We are using the term “pressure” in a special way here, to explain price movement.  In a loose sense, it’s the “animal” pressure that drives the market, ignoring the wisdom of efficient-market theory.  It’s the pressure of greed and fear, bull and bear, risk and the rewards of risk.

Now consider a high-quality corporate bond.  Compared with the risk-free bond, the selling and buying deltas start to appear.  The buyers think that the additional yield over risk-free looks good relative to the risks of default, etc., or else they would buy Treasuries.  Though the sellers may not choose to buy Treasuries as an alternative, they have “voted” through market action against their corporate bond and have not voted against Treasuries – hence they have created selling pressure relative to Treasuries that balances the buying pressure relative to Treasuries. 

As we choose riskier and riskier securities, the deltas widen.  As we have discussed, all securities run on a continuous spectrum of risk, all being future cash-flows with varying degrees of probability and amount.  There is no real division between debt and equity as the majority of securities contain at least some elemental characteristic of each, and every point on the debt-equity spectrum can be populated.   

I have started with the weighted average of all buyers and sellers to explain how they offset each other to give a “net” expect return of a risk-free security.  To dig further into the theory, we need to break down the weighted averages into their individual investor components again.  Each of our theoretical, rational investors weighs up each probability of return and computes a weighted-average expected return on a security, and each of these investors is plotted on a line which stretches from the left side of high negative deltas to the right side of high positive deltas.  How are these likely to be spread?

The Bullish “F” Distribution

Under today’s normal market conditions, we would expect the buyers’ range to have some kind of skewed normal distribution.  In other words, there’s a high concentration around the positive 4-7% range that most equity investors believe they will earn above the risk-free return in the long term.  There will be a short tail down to zero, then a long tail above 7%.  This long tail will include, for example, those investors who believe a long-term equity return of 20% per year is possible, and those who are expecting to sell after a quick 30% bounce.

The sellers’ range is likely to look quite different.  The majority of sellers may share the belief of the buyers that equities will return substantially more than risk-free securities, and will use the proceeds of the sale to buy some other equity.  They simply view their current holding as not offering the best available return for their money.  They may expect their sold security to lose money in the short term, and they may even plan to buy it back later at a cheaper price.  Their sense of the stock’s temporary over-valuation could be anything – anywhere between 10% and perhaps 90% for a high-risk asset.  On the other hand, some investors may still expect the security to return 10% a year but believe another security will yield 20%.  The profile of sellers’ expectations therefore seems quite indeterminate. 

In a very rough picture, we might describe the distribution of buyers’ and sellers’ expectations as an “F”, with the expected returns measured along a vertical axis (the upright of the F) and the count of investor “votes” measured along the horizontal axis (the middle bar of the F).   Think of the top bar of the F as representing a relatively tight cluster of buyers’ expectations, in that 4-7% above-risk-free range mentioned above.  Think of the downward stroke below the middle bar representing a widely scattered range of below-risk-free expectations from sellers, having no particular concentration.  Of course, there are also scattering of buyers’ expectations above and below the cluster, and there are some sellers’ expectations above the middle bar.  The one purpose of the F image is to illustrate the asymmetry of the “expectation distribution.”  I believe it is asymmetrical for the typical equity stock today because of today’s widespread belief in the long-term equity risk premium by the majority of buyers, whether or not they have studied the topic.   These are “long term” buyers, intending to hold the stock for a year or more. 

Moreover, regardless of efficient-market theory, these “votes” of 4-7% above risk-free represent expected returns in the mathematical sense I have already described, i.e. adjusted for risk.  A sample individual who centers on 5% above risk-free would, if pressed, attach probabilities to a range of possible long-term annual returns, maybe from as low as 0% to as high as 20%.  But, when all these returns are duly weighed with their likelihoods, 5%-above-risk-free is the where he or she comes out.  When asked why they should expect this 5% equity premium, they would explain that it is the due reward for accepting the ups and downs of the market.  So long as we can stick it out, we can expect the premium.  Indeed, we deserve it for keeping the faith.

To repeat, the investor only demonstrates such a belief by his or her actions, not by thought or words.  The market responds only to the buy or sell order.  So every action must correspond to a certain belief in order for my model to have any value.  I believe it does, because the investor’s understanding of risk, even if it is just risk of fluctuation, balances the investor’s pursuit of the highest return.  The amount of his or her investable funds allocated to a certain stock will be directly related to the expected return from that stock, after factoring in risk of loss.  That expectation may be based on an irrational whim or fantasy, and may be ridiculously light in its risk adjustment.  It may be purely intuitive or incoherent in the investor’s mind.  But to make any investment decision to maximize returns, all investors must have an expectation, and that expectation can be plotted on the graph where I find my F shape.

An Inverted F

This F distribution would likely go into reverse – an inverted F is the best image I can come up with – in the case of a stock that has suffered severe and protracted declines, or in the event of a severe and protracted bear market, as in the 1930s and 1970s.  Consider the market bottom in 1974, after eight years of no progress even in nominal terms, destructive inflation, and then a market plummet.  The concentration is now likely to be among the sellers, many of whom would be expecting a long-term continuation of losses.  After a quarter-century bull market it is hard to imagine that such a trough is not seen as a buying opportunity, but it was the reality at the time.  Eight years of disappointment is a long time in investor psychology, as was proven more recently in Japan.  The sellers would often be “giving up” on the equity market, after long and painful experience, as offering an expected return at or below risk-free for as far as the eye could see.  The buyers would be more speculative, Buffett famously among them, anticipating anything between perhaps a 10% and a 900% recovery (the inverse of the 10%-90% drop described above.) 

Given this asymmetry between buyers and sellers, and the fact that in many cases none of these investors is either buying or selling a risk-free security in connection with the transaction, it may seem curious to talk about how the weighted average of all expectations could equal the risk-free return.  There are two answers to this.  The first is that we are constructing a model to illustrate the workings of the efficient market.  Its usefulness depends upon its ability to fit a set of curious and disparate facts about the behavior of the stock market.  The second answer is that all freely traded investments are linked through the process of buying and selling.  In this way, the Treasury bond is linked to the corporate bond, which is linked to the junk bond, which is linked to equities.  Convertibles, swaps and countless derivatives provide further linkages.

Such linkage is perhaps easier to see in a less freely traded market such as housing.  When we are deciding on the price at which we will place our house on the market, we have an agent or appraiser do “comps” with other similar houses in the area that have sold recently.  In turn, those houses would have been subject to comps with houses in their neighborhoods, and so on.  In this way, every house in the nation is “connected” in terms of pricing.  Of course, knowing the value of a two-acre property in suburban Orlando does not help us with the market price of a condo in San Francisco’s financial district.  But we could, if we had the time and inclination, develop an unbroken chain of comps between the two homes. 

How Each Sale Affects the Price of Everything Else

It is easy to see how a rise or fall in the sale price of a home can affect the comps in its neighborhood.  It takes greater imagination to see how the sale of the Florida house affects the price of the San Francisco condo.  But, ultimately, the continuous use of comps across the country tells us that there is linkage, even if it amounts to no more than a small fraction of a penny.  Of course, the price of Orlando homes may be rising while San Franciscan ones are falling, or vice versa, as a result of local demand and supply.  But a sharp drop or rise in the Orlando sale price, sooner or later, will have an echo on the Left Coast.  The fact that it is a tiny echo, perhaps moving in the opposite direction to the local trend, does not change this fact.

In such a way, all freely traded markets and securities are linked.  Investors, looking for the best returns, will collectively scour them all.  Each investor may only consider a few alternative investments, just as home-buyers in Miami may consider only a few neighborhoods.  But the constant overlapping of investors from one investment to the next creates the same kind of chain as we saw between the coasts of the US real estate market.   I may decide my best bet right now is a risk-free return, and sell my REITs.  The buyer of my REITs sells her gold to pay for them.  The buyer of her gold sells his hi-tech shares to pay for them.  My preference for the risk-free return has affected the prices of REITs, gold and hi-tech in turn.  This would appear to explain why, absent any other news, an increase in Treasury yields would lower these other prices – we all know that a “wave of selling” reduces prices.

But how does that work?  Just because I now find Treasuries more attractive, why should there be such a selling pressure and drop in price of hi-tech securities?  What explanation would we expect to find in the news for the drop in the NASDAQ?

We have become so used to the snappy comments of market commentators that we barely question their meaning.  Here are some examples:

“Investors were nervous today.”

“There was a sharp sell-off.”

“The market was glum today.”

“The bulls failed to show their faces.”

“The bulls retreated after a lackluster early-morning assault.”

“Bears ruled the day.”

“Investors ran for cover.”

“Billions of dollars were wiped off the value of the market today.”

If these phrases were nothing but colorful ways of saying, “The market indices were significantly down today,” then I could accept them.  But they attempt to do more than this, because the phrases typically accompany a chart or set of figures which anybody can see or read, so such words are not needed just to communicate market change.  Instead, such phrases attempt to convey a picture of what really happens behind the numbers, allowing the commentator to appear to have some knowledge of underlying events.  Typically the commentator will read post-hoc the economic data and relevant news, and try to create a causal link.  The commentator doesn’t know the link, of course – he or she just follows standard wisdom.  Interest rates rose?  That was the reason for the drop.  Interest rates fell?  Investors were not cheered by the interest rate fall, determined to sell off anyway.  Well, no doubt they were still very nervous… My favorite is when investors “shrug off” bad news and send the market higher anyway.  But then you have to be close to Wall Street to witness all that shrugging.

One Man’s Meat

Such commentaries ignore a very simple fact which makes nonsense of them all.  Every day, every hour and every minute, there is just as much buying as selling, no matter how far the market drops.  Equally, there is just as much selling as buying, no matter how far the market rises.  With a down-market we are show pictures of dejected traders, and with an up-market we see them cheer – but this is just a tiny fraction of investors taking one particular position.  Even at market depths, there are buyers as happily snapping up shares as when the market reaches its top.  All that has occurred is a wealth re-distribution.  No wealth is truly lost until such time as the overall standard of living declines.

Of course, this new picture is confusing – we cannot label it as either bad or good news.  We can’t run a continuous story about bulls and bears as we suddenly don’t know who is who.  Instead of the cut and thrust of some kind of sport or battle, we have people changing sides all the time.  There are no more snappy quotes from those seasoned professionals that seem to sum it all up.  And we cannot fuel surging emotions about the market – a rush to jump on the train as it leaves the station, or to grab a life-vest as the boat takes on water.  As we will discuss in detail later, such journalism – often paraded as quasi-advice – is not just fantasy, but it also does a great disservice to the investing public.  But now, having taken a brief break from the technicalities of this chapter, we need to finish it off with understanding how our market model works in motion.

We start with the source of any price movement – a news item of some kind.   A simple example is an earnings announcement which is less favorable that expected.  Just prior to announcement we had a set of buyers and sellers, who were distributed in the F shape described earlier, and whose expectations averaged out to the risk-free return.  Just after the announcement, most of the buyers and sellers would have been a completely different set of investors.  The expectations of the new investors will also average out to the risk-free return which we will assume has not changed since before the announcement.  We will also assume that the announcement was not so devastating as to change the fundamental F shape of the distribution.  So what actually changes?

Though the transacting investors are an entirely different group than the previous one, they are likely to be similar in nature for our purposes.  Assuming no dramatic news or price movement, the issues and decisions facing them are similar to the prior group, and they are attracted to the sell/buy decision for this security under similar circumstances, which makes their profile surely similar.  In many ways they could be regarded as much the same group as the prior group, so close are the selection criteria.  Yet one thing has changed – the existence of this disappointing news.  Compared with the previous buyers and sellers, on average all potential buyers and sellers now lower their expected returns, based on the known stock price.   But this group of potential transaction-makers will not actually trade at that price, or else the average expected return would fall below the risk-free return – something we say cannot happen. 

Prices Move to Keep Expectations Constant

The situation is rescued by whatever mechanism is used to ensure a free market.    For example, the market-maker will anticipate the price change, so buyers and sellers are already faced with a different picture.  The potential sellers now realize they will get a lower price so, if they choose not to sell, their expected future return from the security is increased by the new, lower price that has already occurred.  The potential buyers now realize they pay a lower price, so their expected future return is also increased.   The lower price eventually agreed upon by the actual buyers and sellers now resets the average expected return back to the risk-free rate. 

A similar process would happen with any computerized system that oils a free market.  An imbalance of stocks being offered for sale and to be purchased – from potential transacting individuals – will reset the price until balance is achieved.  So the actual buyers and sellers, once they know the new price, have to re-measure their expectations.  I have described this process in the theoretical world of investors who measure their expected returns.  Yet, in practice, all investors act as if they were constantly calibrating their expected returns, simply by deciding upon the size of their new investment.  The fact that stocks quite consistently go down when there is unexpected, bad news about them, and go up when there is unexpected, good news about them, shows that investors are quite rational enough for the purposes of my theory.  As we know, the total process is so efficient that the investor pretty much knows the news-adjusted price – and so can make a precise judgment – before clicking the trading button.

So here is the essential mechanism of the market.  Following news that changes investors’ expectations, prices must move so that those expectations – measured  as the individual’s concept of a return on investment – remain unchanged in aggregate.  Yet the market is in constantly flux, each stock dropping or rising ceaselessly while the market is open.  If we had a twenty-four hour market, the movement would never cease.  So does it make any sense to talk about the market ever being at a point where the aggregate, even in theory, could be calculated?  Surely buyers and sellers are always mismatched as soon as any matching is done, so we would never actually come to rest at the risk-free rate of return? 

Rest may be instantaneous, but it is real.  It occurs when a stock stops moving in one direction.  As freely-traded (as we define them) stocks seldom remain flat, stopping a course in one direction will mean moving in the other direction.  So the moment of rest is simply the inflection point.  At this moment, the buyers’ demand catches up with the sellers’ demand, or vice versa.  While the stock price was moving, the excess of demand by buyers or sellers was getting sorted out in the price movement.  For a moment the problem is solved, only to be replayed in the other direction. 

Why do these points of time matter?  First, because they are very frequent.  Even for a stock that is declining or rising with what may seem like relentless constancy, a direction reversal – no matter how short – happens so often that even minute-to-minute graphs look jagged.  Second, these constant reversals mean that we are never very far from equilibrium and therefore the risk-free-return average.  But we now need to fit this apparent near-balance into the paradox of market history:  despite all market-expected returns being the same, how does out model help explain the constant climbing and sliding of a stock or index over an extended period of time?

The Sellers Who Balance the Equity-Premium Crowd

I talked about the F shape distribution of a typical stock, characterizing a generally bullish market view.  Most of the buyers are looking for and expect a solid equity premium, while the sellers have a variety of positions on the extent of coming sub-par performance.  By the nature of a weighted average, those sellers expecting a sharp correction – maybe 20% or more – would have twice or greater impact upon the weighted average than those buyers expecting a positive 10% return, even if this return were annual and long term.   As long as the stock continues to perform in line with expectations, there is a tendency for it to attract more of the “steady equity premium” type of investors.  As we discussed earlier, the tendency for ultimate success to steadily reveal itself means that expectations may be regularly exceeded, time and time again, so that these types of buyer steadily increase their expected annual returns.  But it is typically a measured increase, reflecting just the accumulated news to date, and the inevitable uncertainty that implies.

For every buyer, there is a seller who thinks the stock has topped out.  Each piece of good news allows him or her to walk away with a higher price.  No one can predict the top, but the seller expects an eventual decline that will make the sale timely.  As the buyers get more optimistic with passing news, the sellers get more convinced that the rising price is too much.  The buy-sell deltas widen, and the F becomes even more pronounced.  If we look at the top of the F, we see a high probability of a good return.  If we look at the bottom of the vertical, we see smaller probabilities of larger losses.  This is the same probability distribution of the weighted games described earlier.  

Sooner or later, some news will disappoint.  It is probably not so disappointing as to wipe out all exceptional gains, but it will call into question the solidity of maybe the last few months’, or even last year’s, progress.  The seller backing the long odds of a 30% price decline, evidenced perhaps by significant short-selling, may now be proven right.  Perhaps the initial decline is only 10%, but it’s enough of a drop to be “new-news” in itself. 

How did the sharp drop happen, when none of the recent rises were more than 2% in a day?  According to our model, there was a more significant difference between the before-news buy/sell crowd than the after-news buy/sell crowd than at other times.  First, the number of buyers around the “positive 10%” mark was a bit thinner.  This has happened on plenty of earlier occasions without big changes, because they were partially balanced by fewer sellers around the negative-5% area.  The difference on this occasion was that a bunch of these “milder” sellers were replaced by heavier sellers around perhaps negative 20-30%.  There may be a number of short-sellers in this group, just waiting for some disappointing news to unnerve some of the other potential sellers who never quite got around to selling.  These would be the so-called “panickers” though, who knows, they may turn out to look clever in hindsight.  In an efficient market, it is not more or less rational to sell as stock after a 10% drop than before a 10% drop. Though the seller gets 10% less, he or she didn’t know the disappointing news previously.  Any future event that is not factored into the price is, by definition, unpredictable.

So now we have a larger group of perhaps 10-20%-drop expecters to add to the selling mix.  As the stock drops 10% it draws in an extra crowd of the 10%-return buyers who feel they’ve just gotten a 10% discount.  Of course, it takes more of these people, because they are essentially just adding one more element to their broad equity portfolios.  The “panickers” are selling more per head, perhaps unwinding positions (either in the stock or the industry) which became rather too heavy during the exciting run-up.  In terms of numbers of investors, the deep spread of the sellers is now pushing down on the price, their deep negative expectations having greater leverage than the portfolio assemblers. 

There will generally be a steady supply of the portfolio assemblers at any price.  The question is whether or not they can steady existing shareholders’ panicking impulses.  (Note my use of these terms such as “steadying” and “panicking” which conform to the regular bullish vocabulary.  But it would be just as appropriate to use the language of the bear, talking about the nimble sellers and gullible buyers – perhaps suckers – that we might think more appropriate with hindsight about NASDAQ action when it dropped to 4000.)   On seeing the sudden 10% drop, for many overweight holders this will now look like “get out” time.  They may well be programmed automatically for just such a strategy - as far as possible from a panic, these investors may have deeply analyzed patterns over recent years and concluded that the 10% drop is itself a sufficient sell signal.  Of course, many of these sellers may plan to buy again quite soon – they simply expect a deeper fall.

The Price Change is the News

So, for a time, the market drop feeds on itself.  Perhaps there are occasional small rallies, as a steady stream of “buy it on the dip” investors start jumping in.  But for now let’s assume they are not enough to staunch the growing crowd of owners who feel the bad news signals the end.  The news didn’t sound so bad at first but – see that market reaction! – “the Street” must know more and maybe the smart money really is bailing.   A week or so later, during which the guts of the constant owners have been tested and the 10%-discounters have been frustrated, the stock has lost 40% of its peak value.  Maybe some additional news has added to this debacle, such as an interview with the CEO which wasn’t quite upbeat enough to reassure the worriers.  At 40% off, the stock treads water for a while.  Some chartists see a second shoulder and collapse; some see a first shoulder and even greater glory (and both could be right, at least in terms of seeing shoulders.)  What next?

At every inflexion point during these turbulent days, the market-expected rate of return was the risk-free return.  This may still seem a huge paradox, given the manic action, but hopefully it is no longer an apparent contradiction.  We can never have consensus on anything but the risk-free security and, in this case, individuals’ views have been actually getting further apart.  Yet in an efficient market, despite all the intense passion, worry, teeth-grinding and program-trading, at every rest point the stock has found a market value that makes it, on average, just as good or just as bad a buy as any other security.  It may well carry more or less risk than other securities, and its risk profile may also have changed even during the drop.  But risk doesn’t change expected return, it simply widens the possible range of perceived returns.  At $60, the stock has the same expected return as it had at $100.  The difference is the news. 

The Bulls’ and Bears’ Perceptions

A natural argument against this view is that, surely, the news didn’t explain the full drop – the market ran with it too far?  But that is just the bulls’ view.  The bears’ view is that the market finally got the message.  In bear-speak, the stock was headed for a fall and finally got what it deserved.  Before the fall, the bulls were about right and the bears were negative.  After the fall, the bears were about right and the bulls were raging positive.  The market-average of both is the risk-free return.

So, as we tread water down 40%, we don’t know what is next.  But probably, the F shape has inverted or at least changed to an E shape.  Fewer people expect any more sharp drops, but there is an increasing number of bears gathering round the “slow decline” marker.  After all, the stock was $10 three years ago, so there’s still plenty of room to fall.  An E shape suggests that these moderate bears are balanced by the moderate bulls, who now see a 40% discount and are willing to accept what now appears to be greater risk.  So maybe it wasn’t worth $100 after all but, at $60, this stock looks pretty good value.  An E shape suggests no more big movements either way, as the modest bears steadily sell to the modest bulls.

An inverted F, in contrast, allows for greater play.  Some raging bulls have a target price of $180 and now view the stock as 67% undervalued.  Other bulls span the rest of the scale down to the modest bull group.  They are aware of the risks of a stock like this and are not going to jump in hugely just yet – after all, the bad news might just be a harbinger of something totally unexpected – but, if there is good news coming next, they will do their best to fuel a rally to match the bears’ mauling.  They take a decent sized position at $60 then, at the right news signal, go out on a limb all the way up to some new high.  At $120, they feel things have gone a little too quickly too soon and they take some well-deserved profits, thereby becoming short-term bears.  The profit-taking goes a little too far for comfort.  There are renewed cries of “second shoulder.”

Or maybe the next piece of news is bad.  Maybe it is not as bad as the first piece of bad news, or maybe it is much worse.  We have no way of knowing.  The best industry experts have been dredging for more information throughout this time, and feeding it back to investment houses who have been selling it to fund managers.  All that information creates an expectation around earnings.  But the critical issue is, will the earnings turn out to be better or worse than the consensus estimate?  Will guidance for the future be better or worse than expected?  By definition, the whole market doesn’t know.  Many parts of the market think they knows, because they think they are smarter than the whole market, but all these smarter people (and all their followers) add up to being, paradoxically, the whole market. 

We have considered Fs, inverted Fs, and Es.  Could there be an “I” shape?  In other words, no concentration along any part of the expectation axis?   I will save that discussion to the topic of bubbles.  But it is not too difficult to see how the dot-com phenomenon fell into such a category.

The Risk-Free Bridge

But we should return to the title subject of this work, and recap all this with greater focus on the SLMH.  We have a plausible model of market behavior, seeing how the risk-free return acts as the bridge between all the conflicting expectations.  It is not just a theoretical convenience, but a logical consequence of the market’s cumulative ability to weight all existing facts according to its cumulative opinion, and to know nothing about information that has not already been made public (if we ignore illegal activity).  If the weighted average of all expectations, as implied by market actions, were NOT the risk-free return, then the prices of all risk-bearing securities would rise/fall, because the market judgment would be that they are better/worse value than risk-free securities, after adjusting for risk.

We have explained how, in a bullish market, the weighting of distributions around their averages is not even, but is “F” shaped.  Given the “culture of equity” that has existed during most of the 20^th Century (1930-45 and 1973-82 excepted) a high proportion of buyers have clustered around the 4-7% risk premium, or 9-12% return region.  Since 1982 the number of retail investors has exploded, but I believe these proportions have remained similarly focused no matter the size of the investor pool.  The pool of sellers at any one time are, by contrast, spread thinly along a wide range of negative positions, largely (but not exclusively) below the risk-free return.  Many of these seller’s negative expectations are quite short-term.  After all, these sellers are themselves equity investors and many of them are just switching stocks.  They may be switching out of stocks temporarily, ready to buy back at a lower level.  But they distinguish themselves from the buyers by containing a higher percentage which is expecting a large market change – much larger than the size of the expected risk premium.  This group of grizzly bears makes up for its smaller number by the weight of its depressing expectation, signaled by its execution of big sales. 

To the confusion of market commentators, these grizzly bears may be the same raging bulls for other stocks, or ready to become a raging bull for all equities after a correction.  Who they are is irrelevant.  What is important is how they behave towards a particular stock, or to the equity market as a whole.  All potential grizzly bears are waiting for the bad news – in my earlier analogy, the sudden thinning of the forest.  Should such a signal occur, they believe, the game is up – at least temporarily.  But really bad news for a successful company during normal times is not so common.  Management does its best to manage expectations and smooth out any apparent wrinkles.   During reasonably good times, steady additions to the risk-premium crowd keep dragging the price up at a steady, though rarely dramatic, pace.  Though it is no longer a surprise that the trees continue to show up time and time again, people’s impression of the potential size of the forest gets gradually larger.  Now we see sticky luck taking hold.  The more good things don’t change, the better the potential future.  Belief in the historic risk-premium is reinforced, and more people buy the idea and dip their toes in the water.  When the climate is good, then no news is good news.

When the tree count drops to zero for any extended period, all this reinforcement unravels.  One bad quarter’s results means our unbroken chain is broken.  No smoke without fire.  Momentum has clearly faltered and maybe stopped.   Though we did not expect growth to continue forever, we were not prepared to see it stop just yet…   Now we find a fresh number of potential grizzlies prepared to join the usual grizzlies.  They never wanted to miss the upside, no matter how unreasonable they think the price to which the stock or market has risen.  These are the market-timers and they’ve just received their signal to sell.  They add greatly to the precipitation of the downside, trying to lock in as much of the long, sticky luck as possible. 

Of course, the new-born bears don’t see it as luck – they believe they have “outsmarted” the market.  Because of the durable sticky luck of bull markets and sectors, they may even have made a handsome living this way for many years.  Like the dice game described earlier, they have rolled plenty of times without hitting the double six.  They have found nothing but forests since they began.

Market-Timers Exaggerate the Effect

The market-timers help make the end of a run of sticky luck look brutal, creating the classic saw-tooth pattern of the market and encouraging a new generation of market timers as they wonder at such revealed patterns.  In the continuing but choppy bull-market scenario, the saw-tooth is followed by yet another, each drop taking a bite out of the prior advance but followed by a still greater advance.  The final tooth to the bull saw, whenever that may be, leads to the true bear market.

During a bear market we replay the logic above but we would expect a tendency for the process to work in reverse.  Once a substantial decline has already set in and there seems little prospect of recovery any time soon to former levels, we start to switch to the inverted F.   A limited number of waiting bulls are ready to drive the price quickly and much higher upon unexpectedly good news.  A larger number of disillusioned owners, anticipating more steady declines, are gradually selling off.  When the first good news arrives they sell off more rapidly into the quick wave of buying and price-rise, having seen too many false dawns in the past.  In the continued bear scenario, they keep selling past the bulls’ surge and the price starts working its way down again once the bulls retreat.  Our saw-tooth now leans to the left, rather than to the right as it did during the bull phase.  But do not be fooled that this is any kind of market signal.  As always, we can only chart the depth of a bear market in retrospect.  Depending upon the nature of new information received, a bear tooth can be followed by a bull tooth at any time.  The shape of the teeth describes market sentiment at the time.  They predict nothing.

It is not easy for the investor to see such patterns and accept their intrinsic randomness, in terms of providing no information about expected returns.  A world of investment advice discourages the random view, anyway.  Paradoxically, the collective belief in the superiority of equity returns and the merits of active portfolio management are critical ingredients for sticky luck.  They are even probably necessary to ensure an efficient market, because people pay more for analysis in the hope of earning more.   The second paradox is that the efficient market we have purchased with our fees leaves our fund managers with nothing but the pursuit of sticky luck.  Luckily for them, the stickiness is such a convincing mask that we see little difference between their competition and that of modern humanity’s other great passion, its sports teams. 

A final note on how stocks respond to a change in the risk-free rate of return.  The typical market response to a rise in interest rates is an equity-market fall, and the response to a fall in interest rates is an equity-market rise.  These responses clearly make sense under the theory.   Price must be lower in order for the market-expected return to rise, even assuming a steady outlook; the reverse is also true.  If the market does not fall on a rate increase, it is clearly a sign of confidence, such that the market would otherwise have risen if rates had not increased.  If the market does not rise on a rate reduction, it is clearly a sign of weakness, such that the market would have otherwise fallen.