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Sticky Luck

Sticky Luck

Have you ever wondered why patterns persist in the stock market but never change our expected return? Well, the author of this article isn't monkeying around with the explanations.

By Mark O'Reilly

Efficient–market theory (or hypothesis, for purists) has a hard time these days. Fund managers have never liked the idea that dart–throwing chimpanzees can do just as well. They (the managers, not the chimps) gained an ally in behavioral finance. Books such as Robert Shiller's Irrational Exuberance and Andrei Schleifer's Inefficient Markets attack the theory, claiming that it requires the existence of too many rational investors. To the extent that irrational investors don't cancel each other out—so the theory is said to run—they need to lose to arbitrageurs who bet against irrational trades (e.g., if someone wants to buy the Brooklyn Bridge, the deeds are ready.) Events such as the October 1987 crash and the dot–com bubble have convinced many academics that irrational investors exist in large hordes, and can be sufficiently persistent to drown the activities of arbitrageurs (e.g., the Brooklyn Bridge deeds can be traded for years at increasing prices.) A Web search on the theory will soon turn up expressions like, "The now largely discredited..." Fund managers sleep a little more easily.

I liked Irrational Exuberance and thought it timely, but I was puzzled. Why does an efficient market require rational investors? In the 2007 edition of one of the most famous efficient–market treatises, A Random Walk Down Wall Street, Burton Malkiel lauds the contributions of behavioral finance. He does not claim that investors are rational. Yet he does say that, according to the theory, "... at any time, stocks sell at the best estimates of their intrinsic values." Worried at such strong tenets, he says he walks a "middle road." He counsels for and against various investment strategies, which I would not expect the chimps to know about. Checking popular investment literature, Malkiel seems a bit isolated today, even in his modified defense of efficient markets, with Eugene Fama and Jeremy Siegel off on different tracks. Has the theory lost the debate?

Fund Management and Heroic Medicine

Yet Malkiel has facts on his side when he describes how consistently large–cap equity mutual funds have underperformed their benchmarks over 20 years. I have completed my own analysis of all retail mutual funds (152, covering 4,224 years of management) available through my broker which have track records of 15 years or more and found that, on average, despite heavy survivor bias, they fail to beat their respective indices. Interestingly, their significant variance shows they were not closet index funds. They simply show the kind of performance spread you would expect from—well, chimpanzees. I concluded, using very rough assumptions, that some 40 million hours of human activity may have been wasted on the active management of these funds alone. Is this shocking? I got to thinking of the medical practice of bleeding a patient (heroic medicine) which was widespread for many hundreds of years and was even practiced during the great 1918 influenza pandemic.

In Irrational Exuberance, Shiller's response to such data is weak. He suggests that fund managers may well have added real value, but other investors piggy–backed (for free) on their strategies. Yet we know that mutual fund reports are really not that detailed or timely, even if we ignore quarterly window–dressing, incubator–funds, etc. In any event, the selfish among us still ask why should we, personally, pay for active fund management? And can we find anyone about whom we can say, with any degree of confidence, that he or she can be expected to beat the market?

This article is too short for me to discuss Warren Buffett, Peter Lynch and other "great investors." We are free to invest all our money in Berkshire Hathaway or a famous hedge fund, but most of us do not. We want diversification combined with steady, objective talent, if it exists. Accepting that investment and emotions are deeply intertwined, can professionals be expected to avoid the resulting pitfalls, and even take financial advantage of them? There seems little evidence that fund managers showed greater sagacity than the irrational hordes in October 1987 or during 1996–2002. If investors persist in their irrationality, will they ever pay us a rational price?

So What is Efficient?

An efficient market fully digests new public information within seconds. When the Fed makes an unexpected cut in interest rates, we can have some confidence that the market will rise quickly on the news. Can we predict what the market will do 15 minutes after the news? Not without knowing what it did in the prior 15 minutes, at least. But that prior movement is now the news. In other words, the Fed news is already old. The new news is the market's last reaction to its previous reaction. Hundreds of thousands of minds are reacting to the last thing they learned. For the professionals, that last thing will have occurred moments ago. For retail investors, it may have occurred hours, days or weeks ago, but such late market responses get absorbed into the vast noise of future events.

Historically, those of the efficient–market persuasion looked at fund performance, studied the effectiveness of market–pattern theories, considered the sophistication of today's program–driven trades and market–modeling and concluded that all market prediction beyond minutes—at the index or stock level—was guesswork. Milton Friedman and Fama both articulated the rational investor–arbitrageur explanation, and some people concluded that the market must be appropriately priced at all times. But neither idea is required for, or is a logical consequence of, the above definition. My version of efficient–market theory has no place for either idea. To make clear the distinction, I refer to my own version as Sticky Luck Market Theory.

Sticky Luck

Sticky luck is easily illustrated. I play a game where I am required to deposit $240 with the house. The house rolls a pair of dice and pays me in dollars per spot, except on a double–six which costs me $240. As I start to accumulate winnings, I am the beneficiary of sticky luck. But, if my math is right, my expected return on this game is zero. I am not playing the odds; I am taking a pure gamble.

I was surprised that A Random Walk makes no reference to sticky luck or something comparable. Instead, Malkiel compares market movements to the tossing of a coin, claiming that cumulative coin–tossing gives rise to shapes like stock charts, once the effects of steady economic growth are removed. This argument does not pass scrutiny. You do not get meteoric rises or crashes over periods of years when tossing a coin. In his The (Mis)behavior of Markets, Benoit Mandelbrot (of fractal fame) seals the case arithmetically. If market movements were normally distributed, then the odds of the October 19, 1987 crash would be one in 10^–50. The ratio of the smallest subatomic particle to the breadth of the measurable universe is a larger number. Mandelbrot concluded that market patterns were fractal, i.e., exhibiting the same characteristics independent of time scale.

The stock market oozes with sticky luck. According to Morningstar (Ibbotson Methodology), during the period 1969–2006, U.S. small–cap value stocks outperformed small–cap growth stocks by 6.3 percent per year. So why would anyone be so foolish today to purchase small–cap growth stocks? Because if we did not do so, their prices would fall so low as to make them transparent bargains. In other words, the market responds to its cumulative experience and adjusts prices, either to be proven wrong again like the proverbial general fighting the last war, or else to lessen such anomalies. It is clear that investors do not see a 6 percent spread as inevitable. The luck of small–cap–value holders has been very sticky but, because of the free–market pricing mechanism, we have no reason to expect it will continue even for one more day. Yet how can this be? Patterns, patterns everywhere, but not a price drop to predict?

Dow 7000 Again

Lack of attention to sticky luck has made efficient–market theory vulnerable not only to behaviorists, but also chartists and intrinsic–value analysts. In my view, these last two groups are closely related. Intrinsic value requires assumptions about long–term growth and discount rates. How will earnings grow over the next 30 years? How do we choose a risk–adjusted discount rate for equities? Math graduates know that, if NASDAQ 2500 assumes a 6 percent discount rate and a 4 percent growth assumption, then a 7 percent discount rate and a 3 percent growth assumption implies NASDAQ 1200. How do we choose such assumptions which leverage our results so much? We must extrapolate the patterns of the past, no less than the chartist who extrapolates from a double bottom or a head and shoulders.

The pattern projectors have befriended behavioral finance because never–learn, investor sentiment seems a plausible reason for repetition. But investor sentiment is only one market element, to be combined with vast, soulless trading software designed to squeeze any discernible pattern until its pips squeak. Add in Churchill's observation that the future is just one damned thing after another, and the volatile response of sentiment, and you have all the natural patterns of a coastline (another fractal). Market prices are influenced most by the biggest bets, which access the deepest research. The very patterns that motivate such research then trigger trades which drive the financial gain out of the patterns. In other words, market activity is the constant pursuit of recognizable patterns, flattening their profit the moment some investment house's software unearths them.

So how does one explain raging bull markets in technology, commodities, REITs and small–cap value stocks that last for years? Here we need to make the simple distinction between likely gains and expected gains. In the $240 game described earlier, we are very likely to gain on each throw, yet our expected gain remains zero.

An Alien But Free Market

To a sophisticated alien species living somewhere else in the Galaxy, tree sap is a highly prized delicacy. To them, the sap of no two trees tastes the same, so the richest alien is the one who owns the largest collection of individual tree sap. After their own trees had withered, there was great excitement when they sent roving, unmanned sap collectors to Earth, each with a battery life of about a year. Unfortunately, they had no way of seeing Earth's terrain and so landed their thousands of collectors at random. Landing in water proved fatal. Many collectors, however, started to send back the bleep signal which signified that their random walk intersected with a tree. The venture capital firm that owned the collectors then offered each one on the open market, for which there was a thriving secondary market. The aliens all knew the same basic facts about Earth's forests, woods, leafy suburbs, farmlands and deserts—about as much as the average human if quizzed on the street. But they knew nothing about the collectors' locations aside from the frequency of the bleeps.

Some collectors would send back constant bleeps for days, weeks and even months. Their prices would rise higher and higher, buyers hoping they were in the middle of a vast forest. But a few minutes without a bleep and these lofty prices would fall steeply. Could it be a beach on the edge of the Amazon? Perhaps an Autobahn running through the Black Forest? Then sometimes a sudden burst of more bleeps... what to make of that? Some working collectors were quiet for days and so sold cheaply, as they were guessed to be on farmland or desert. Then a few of these cheap collectors started bleeping a bit, or maybe a lot. Suddenly their prices jumped, maybe becoming highly volatile as bleeps became irregular. Were they entering the outer edges of a deep forest, or just going through an oasis in a desert?

In this market of purely random success, the prices of the collectors nevertheless performed in exactly the same way as stocks—long periods of appreciation, steep declines, collapses, sudden jumps, plateaus, undulations. There were double–bottoms, heads and shoulders, smiles, frowns—every imaginable pattern. Some investors used elaborate formulas to decide which collector to buy, and some went with their gut. Prices of regular bleepers were much more likely to keep rising than non–bleepers, because trees are typically found in groups, and every new bleep added to the belief that there was a deeper wood. Yet the price rise per new bleep from the regular bleeper was usually small. The price rise per new bleep from the non–bleeper was usually big.

An alien mathematician thought he could profit from his race's bi–polar tendencies. When constant bleeping sent prices through the roof he sold short. But then his nerve cracked when someone came up with an idea for replenishing the batteries, and he faced the chance that a random walk in the Amazon could last forever. He realized his probability weightings to possible events involved too many strong assumptions which, if wrong, could throw his calculations out horrendously. Both the manic and the depressive view of the market were about as likely to be right as his own middle point.

He concluded that, in a market which responds quickly to every bleep with the sincerity of money at risk, every collector has the same expected return, as measured by the market consensus. Market prices constantly adjust to eliminate any differences in each collector's market–expected return. Moreover, he has no good way to tell if investors were being highly emotional, or if the other cool mathematicians driving big trades were resetting their assumptions.

The Market–Expected Return

What is the market's consensus view? It is every buyer's and seller's expected return, weighted by the size of their purchase or sale. Do all investors have an expected return? For many, it will not be explicit. But the size of my investment is equal to my total invested funds times the portion of those funds I decide to invest in a security. My funds are a measure of my market voting power in the market weighting. The portion I invest is a market vote for an expected return. That expected return is already weighted for my perceived risk. Even irrational investors want to maximize their investment returns, no matter how strangely they go about it. If they pour money into technology stock, it is because they are expecting a better return after allowing for the risk. If I just dip my toe in, it is because my sense of risk is weighing down my expected return. In other words, all investors behave as if they had an expected return in mind. For any given investment time–horizon, we can map invested amounts and expected returns with a one–to–one relationship. Our investors can follow their gut instinct if they want to. But usually when risking their money, they will at least rationalize their feelings. Ask anyone who has just bought a stock what return they are expecting. I doubt they will say they have no idea.

The reason why we all have an idea about expected return is because we all know the return we can get without risk. Therefore, if we take risk, we are usually expecting a greater return. The more exciting the opportunity seems, the greater the expected return. The seller may be working in reverse—wanting less risk—or else be moving on to different risk. But the seller is typically expecting a poor return from the sold security, which is the reason for the sale. At every moment in a bull market there are as many sellers as buyers, and as many buyers as sellers in a bear market. The market–expected return is the weighted average of all their expected returns. Buyers typically expect a healthy equity–risk premium, and sellers typically expect a price drop some time after they sell, at least in the short term. The weighted–average expected return would therefore seem to be quite close to a risk–free return.

A Unified Theory of Security Exchanges

Could it be exactly the risk–free return? This is a highly intriguing thought, and it is not hard to see how it works with all kinds of bonds. Buyers of corporate bonds think they have a higher yield than Treasuries; sellers act as if they think that market moves or defaults will give a lower yield. Though they may go on to buy equities instead, because of the finite number of securities at any one moment, there's an equal number of investors selling the equities—because they think the price has peaked—and buying bonds or making deposits. For the instant that prices are in equilibrium, the market consensus of each security's risks and rewards is also in balance. Put another way, if the market consensus of the risk–adjusted, expected return of one security were higher than any other security, the market would increase its price to eliminate the difference. And the risk–adjusted return on Treasuries is the risk–free return.

We now come to the great unanswered question in efficient market theory. If we cannot expect any one equity to beat another, why doesn't the same rule apply to all freely traded securities? Securities are not like folks at a barn dance, with all bonds on one side and equities on the other. Junk bonds carry equity risk; REITs and utilities have bond–income features—the income/equity spectrum is full. Moreover, greater equity focus has not led to greater returns. Value stocks typically produce more income than growth stocks and so should be closer to the bond end of the spectrum, but the 6 percent differential described earlier is as large as the equity risk premiums itself. Is 38 years too short to measure the value–growth spread? Research suggests it goes back much further. As recently as 1981, many believed the equity premium was finally dead. Twenty–six years later, popular psychology has changed mainly through the impact of media attention to over 6,000 market–closings. It also marked an unusual period of unexpected increases in perceived global political stability and unexpected advancement in electronic tools. Are those trends continuing?

Progress, Like Forests, Has Edges

The 200–year history of the stock market coincided with the electronic age, from acid batteries to online commerce. During that time we have regularly exceeded our expectations in security, health and consumption, just like the alien collector that continues to bleep continuously for months. The collector's price partly reflects the probability that it is deep in the Amazon and, with every day of continuous bleeping, our consensus expectation is exceeded. We know this process can go on indefinitely, and we also know it can halt abruptly. And I am suggesting that efficient–market pricing makes the purchase of this collector—versus a non–bleeper—no more of a good deal as measured by the market consensus than the $240 dice game. By definition, investors cannot expect to exceed their expectations. An equity risk premium may be very likely, given 200 years of mainly bleeps, but investors price away a premium from their collective expectations every few seconds. The paradox is that they might all believe in a long–term equity risk premium but the expectations—probably over some shorter period—implied by their actions speak otherwise.

So the efficient market may give us a market–expected return that can never be different from the risk–free return, which is every buyer's and seller's bogey. But the market gives us no clue to its consensus time horizon, or to its level of rationality. After all, if two rational sets of assumptions can give us both NASDAQ 5000 and 2500, were we unreasonably predicting today's technology earnings back in March 2000? What we can say is that, at any point in time, the market is the money–at–risk–weighted consensus of everyone's market model and personal rationalization. For any one person to claim it to be under or overvalued, based on their personal model of the world's future, starts to sound like Canute without the sense of humor. Yet we now call NASDAQ 5000 a bubble. How, in an efficient market, do we get bubbles?

Unsuitable for Long–Term Investors

I believe that, even at the height of a market bubble, the market–expected return remains the risk–free return, as a matter of math. However, investors' time horizons have shrunk to an all–time low. Symptoms of this phenomenon are day trading and condo flipping. The consensus average hides extreme variance of buyers expecting big gains quickly and sellers expecting an imminent crash. The market–weight of the long–term investors has been overwhelmed. Though it is not a Ponzi scheme, as Shiller suggests, investors behave as if they were in a Ponzi scheme. The market never has to crash, but the instability of extremely disbursed expectations over very short time–horizons means it usually does. Yet still, you might get lucky.

Mark O'Reilly, FIA, ASA, MAAA, is a principal at Deloitte Consulting LLP in Detroit. He can be reached at moreilly@deloitte.com. More thoughts on the topics in this article can be found at the author's Web site, StickyLuck.com.