集体的智慧与奇思妙想

Michael J. Mauboussin Chief Investment Strategist Legg Mason Capital Management Baltimore

The debate over whether financial markets are efficient has raged for decades.

Proponents of market efficiency point to the difficulty of outperforming markets to support their view, whereas opponents note the frequency of mispricings to support theirs. The resolution to the dilemma may lie in the dynamics of group decision making.

t is my ambitious goal to unify two seemingly and characteristics that emerge from the interaction I irreconcilable camps. The first camp consists of of investors that cannot be anticipated by looking at people who believe markets are efficient. This group the underlying investors themselves. I like to think includes many academics and investment industry about this issue on three levels, each with its own luminaries. The practical recommendation from this unit of analysis.

camp is simply to buy an index fund, which is, We must first consider psychology, in which indeed, very good advice for most people. The sec- the level is the individual and the unit of analysis ond camp includes people in the behavioral finance is the individual. Next, we must understand social group, who argue that people behave suboptimally, psychology, in which the level of analysis is the creating so-called market anomalies. I am going to group and the unit of analysis is the individual. By try to reconcile these two camps by proposing that looking at these levels, we are attempting to gain the market is a complex adaptive system. This is a an understanding of how individuals operate as compelling  First, it view forus allows a number to relaxofthe reasons:

assumption of parts of a group.

The final level is sociology, which studies groups rationality either for all investors or even a sub- and how groups behave. Here, the unit of analysis is set of arbitrageurs. the group. Notice, by the way, that these are all

• Second, it sets out conditions under which mar- distinct disciplines, and we should be very careful kets tend to be efficient and conditions under about maintaining these distinctions. My view is that which markets are inefficient. many market inefficiencies are largely sociological.

• Finally, it accommodates empirical realities, particularly fat-tailed price distributions.

I will first discuss the classic mean–variance and no-arbitrage-opportunity explanations for market Let me start with a common sense observation about efficiency. Then, I will explain the concept of markets market efficiency: It is clearly hard for active manag-as a complex adaptive system. Finally, I will wrap up ers to outperform the market, which has been true for with what I call the “whims of the collective,” which as long as anyone has tracked the results of active explains why markets periodically go to excess. managers. This may not mean that markets are effi-Some wonder whether we can understand the cient in any sort of technical sense, but it does suggest market by adding up the actions of the individual that they are practically efficient. That is, there are no agents. In other words, are markets Newtonian (or simple, systematic ways to outperform the market. reductionist) in the sense that the whole must equal In contrast, we obviously do see periodic, and the sum of the parts? The answer to that question, I sometimes dramatic, excesses. Efficient market pro-believe, is a resounding no. Markets have properties ponents would be hard pressed to argue that the dot-com era of the late 1990s was a time when the This presentation comes from the Efficient Market and Behavioral markets were efficient in the sense that asset prices Finance conference held in Boston on 5–6 June 2007. represented an unbiased estimate of asset values.

Finally, there is academic evidence that some time that this is not the case but have, to some investors do outperform the market over time. I degree, understated its significance. Panel A of Fig-personally believe these people exist, but I am not ure 1 shows actual daily changes in the S&P 500 at all persuaded that their skill sets are transferable. Index from January 1978 to March 2007. The solid There are essentially three ways to explain line in Panel A is the actual distribution of price market efficiency. The first approach stipulates the changes. The dotted line represents a fitted normal existence of rational market participants who distribution based on the standard deviation of the

understand their risk preferences and the distribu- returnsreturns.

actual Looked atnormal.

are deceptively in this manner, the actual But to emphasize tion of asset prices and who rationally trade off risk and reward. The second approach relies on the the extent to which the actual distribution is non-ability of arbitrageurs to eliminate arbitrage oppor- normal, in Panel B, we plotted the difference tunities. This is an important step in the right direc- between the normal distribution and the actual tion because now I can relax the assumption that outcomes. With this view, three observations all investors must be rational. Instead, all I really become noteworthy. First, many more small-need to achieve market efficiency is for a subset of change days occurred than expected. Second, fewer the population—arbitrageurs—to be rational. medium-sized-change days occurred than normality suggests. Third, and perhaps most importantly, Arbitrageurs will identify price discrepancies and there were many more fat-tailed days than there move to correct them by buying the undervalued should have been. As can be seen, there are 5, 6, and assets and selling the expensive assets. The third 7 sigma events represented here.

approach relies on the wisdom of crowds. After all, To give a sense of just how important the fat-it is really the aggregation of individuals who may tailed events are, I did a “knockout” study. There or may not be rational that allows us to get to the are roughly 7,300 observations in Figure 1. The right price. The wisdom-of-crowds approach does return in the market during this period was about not exclude the notion of arbitrage, but it does not 9.5 percent (excluding dividends). In the actual dis-require it either.

tribution, if I knock out the 50 worst days (less than The next question is whether the assumptions 7/10ths of 1 percent of the sample), the return goes supporting each of these approaches are reason-from 9.5 percent to 18.2 percent. These few bad days able and empirically valid. In my opinion, the can have an enormous impact. In contrast, if I knock assumptions underlying the mean–variance out the 50 best days, the return is 1 percent. Just to approach are neither. In contrast, there seems to be give some standard of reference, by simulating a at least mixed support for the no-arbitrage oppor-normal distribution based on these data, if I knock tunity assumption. Finally, I would suggest that out the 50 worst days from my simulation, the the wisdom-of-crowds approach is both a reason-return is 15.2 percent—up from 9.5 percent but able assumption and empirically valid.

much less dramatic than the change to 18.2 percent.

Alternatively, if I knock out the 50 best days, return Tests of Mean–Variance/Market Efficiency is 3.5 percent. The point that I want to emphasize is Assumptions. Just how closely does the traditional that fat-tailed events have a material impact on model of how markets work conform to empirical returns over time. The inescapable conclusion is that reality? The answer is, unfortunately, not as close as the assumption of normality inherent in the mean– we would like. Consider the capital asset pricing variance framework represents a misleading model model (CAPM), which is an elegant theory that has of how markets actually work.

been taught to MBA students for the past 30 years.

But in a paper from the early 1990s, Eugene Fama and The Role of “Sharks.” Most financial econo-Kenneth French support the (1992)

central concluded prediction thatSLB of the “tests do not [Sharpe– mists do not really believe the assumption that all market agents are rational. But at the same time, Lintner–Black] model, that average stock returns are they do not think that needs to be the case to achieve positively related to market β” (p. 449). More recently, market efficiency. For the most part, they agree that Fama and French (2004) added that “the empirical we need only a handful of these agents to be smart, record of the [SLB] model is poor—poor enough to which is obviously much more possible and plausi-invalidate the way it is used in applications” (p. 25). ble. The core idea here is that the act of arbitrage Importantly, one of the simplifying assump- eliminates the very opportunities it seeks to exploit. tions underlying the efficient market hypothesis is Essentially, if two assets are obviously inappropri-that stock price changes are normally distributed. ately priced relative to each other, a well-heeled Academics and practitioners have known for a long arbitrageur will buy one and sell the other, thus

Figure 1. Frequency Distribution, January 1978–March 2007

A. Frequency Distribution of S&P 500 Daily Returns Frequency 300

250

200 Actual

B. Frequency Difference: Normal vs. Actual Daily Returns

Source: FactSet.

eliminating the arbitrage opportunity. In an address It is also worth noting the mean–variance to the European Mortgage Finance Agency, Stephen framework and the elimination of arbitrage oppor-Ross expressed this concept well: tunities are fundamentally different approaches to Neoclassical finance is a theory of sharks and market efficiency. The rational model relies on not a theory of rational homo economicus. In notions of general equilibrium and is an absolute-liquid securities markets, though, profit oppor- pricing model. It will allow one to achieve alloca-tunities bring about infinite discrepancies tive efficiency in markets. In contrast, arbitrage is a between demand and supply. Well financed relative-pricing model. It does not ask where prices arbitrageurs spot these opportunities [and] pile on, and by their actions they close aberrant price come from. It only seeks to exploit relative price differentials. Rational finance . . . has worked differentials. The notion that one is absolute and the very hard to rid the field of its sensitivity to the other is relative is a very important distinction to psychological vagaries of investors. (Ross 2001) keep in mind.

Behavioral finance has been correct to point out Figure 2. Common Features of Complex that there are limits to arbitrage, such as the inability Adaptive Systems to short, lack of appropriate substitutes, the fact that Global System (market)

arbitrage is not always riskless, and implementation costs. We also know that arbitrageurs are not always there when we need them. One of the best examples in recent memory is what happened to Long-Term y ti Capital Management (LTCM) in the late 1990s. One iv t of the more thoughtful accounts of the LTCM events id d Emergence through Interaction comes from economic sociologist Donald MacKen- A o zie in his book An Engine Not a Camera (which I N would highly recommend if you are interested in these topics). Here is what he writes in a paper included in the book:

As “spreads” widened [between off-the-run Investors with Heterogeneous and on-the-run bonds], and thus arbitrage Perspectives and Heuristics opportunities grew more attractive, arbitrageurs did not move into the market, narrow-ing spreads and restoring “normality.” The Wisdom of Crowds Instead, potential arbitrageurs continued to Let me give some examples of the wisdom of flee, widening the spreads and intensifying the crowds. In the class I teach at Columbia Business problems of those who remained, such as School, I pass around a jar of jellybeans, and there is LTCM. (MacKenzie 2004, p. 30) a $20 reward for the student who comes closest to Mean–variance and arbitrage represent reason- guessing the actual number of jellybeans. In the able approximations of reality, but only partly. most recent class, the jellybean jar had 1,116 beans Both of these models rest on implausible assump- and the consensus was 1,151—off by only about 3 tions, and both models fail at critical junctures or in percent. But significantly, only 2 of the 73 students critical ways. I would like to develop an under- did better than the consensus.

standing of markets that addresses these shortcom- Here is another example I do with my class. ings and introduce the concept of markets as a About three weeks before the Academy Awards, I complex adaptive system. hand the students a form. On the front of the form are six major categories, such as best actress, best Complex Adaptive System actor, and so on. On the back are six much more “Complex” simply means there is a lot of interac- remote categories, such as best cinematography, best music—things that few people pay much attention. “Adaptive” means that the agents change and tion to. Again, in my most recent class, the consen-evolve. “System” means that the whole is greater sus correctly named 11 out of 12 winners, although than the sum of the parts. the best student named only 9 out of 12. More Figure 2 shows a picture of how this might work. interesting, though, the average student guessed Investors interact with one another. As a result of only 5 out of 12 winners. So, the consensus was this interaction, an emergent phenomenon develops vastly better than the average, but more impor-that has properties and characteristics distinct from tantly, it was better than even the best individual. the underlying investors. Complex adaptive sys- It is worth noting that financial markets are very tems are ubiquitous in nature and society. Examples different in at least two ways from these examples. In include ant colonies, consciousness through neuron markets, there is no right answer. No one stops trad-activity, and the City of Boston. ing at the NYSE and says, “By the way, IBM is truly One point I would like to stress is that there is worth $120 a share; thank you very much for showing no additivity in these systems. That is, the system is up today.” There is also no time horizon. The perpe-not the simple sum of the individual participants. tuity dimension is very important. That said, I hope Rather, the macro system has properties and char- these examples give some sense of how the wisdom acteristics distinct from the underlying participants. of crowds can work in market-related settings.

Just as you cannot understand how an ant colony An interesting new book that addresses the works by interviewing ants, you cannot understand “why” of the wisdom of crowds is Scott Page’s The the workings of markets by observing individuals Difference (2007). One of Page’s core ideas is the within a market. Note that a complex adaptive sys- “diversity prediction theorem,” which says the Col-tem allows for arbitrageurs, but at the same time, it lective error = Individual error (the ability of the indi-does not require them. vidual) – Prediction diversity (cognitive diversity).

The diversity prediction theorem has some The third condition is the presence of important implications that can be applied to the incentives—rewards for being right and penalties previous examples. (1) The collective is smarter than for being wrong. In our society, monetary incen-the average person within the collective. Not some- tives are the most common. But incentives can also times, but always. This means that as an investor, be other things, such as reputational.

you have to recognize that if you are buying or selling Understanding Diversity Breakdowns. In at the market price, unless you are above average, the my opinion, the key to resolving the market effi-market will be smarter error is determined than in part byyou are.and ability (2) Collective in part by ciency debate relies on recognizing that inefficiency prevails when one or more of these conditions are diversity. Diversity, therefore, plays a very impor- violated. Moreover, the most likely condition to be tant role in collective accuracy. (3) The collective is violated is diversity, which occurs when we start to usually better than even the best of the individuals. act in a coordinated fashion.

It is important to consider the conditions the There are two broad types of diversity break-wisdom of crowds requires in order to work. When downs. The first is what I call “dramatic”’ diversity one of these conditions is violated, that is where we breakdowns, usually accompanied by abrupt price will find breakdowns in market efficiency. movements. The most famous examples of this type of breakdown are the South Sea bubble, tulip Conditions Needed. The first condition is mania, and most recently, the internet bubble.

diversity of the underlying agents. Many firms have These breakdowns tend to occur when positive diversity initiatives that focus on social identity diversity—race, ethnicity, age, and so on. These feedback produces mistic sentiment extremely about a stockoptimistic or an assetor pessi-class.

could be considered proxies for this condition, but Ultimately, the fundamental view is clearly over-they do not reflect it directly. In a market context, we stretched, and it creates a set of expectations that are looking for cognitive diversity. The dimensions are out of sync with the fundamentals.

that really matter are things like perspectives on a The second type of diversity breakdown, time problem, rules of thumb, and interpretation. arbitrage, is much more subtle. It occurs when short-The second condition is an aggregation mecha- term prices reflect more noise than signal.

nism that brings information together. The financial To illustrate a dramatic diversity breakdown, markets are the aggregation mechanism we are consider Figure 3 as it relates to two Wall Street Journal most familiar with. articles about a barber in Cape Cod, Massachusetts.

Figure 3. NASDAQ Performance, 1995–2005 NASDAQ 6,000

5,000 13 March 2000

4,000

3,000

2,000

1,000 8 July 2002

0 1995 2005

On 13 March 2000, the Wall Street Journal published countless times, you would expect to see 50:50 as a the article “Stock Chit-Chat Enriches Many Cape signal. But if you flipped it only 10 times on three Cod Locals” about how the barber had become a occasions, you would see vastly different results. I local celebrity because he had put many of his believe that at times, the market extrapolates the clients into NASDAQ stocks that had done spectac- noise as if it were the real signal, which creates a time ularly well. He had made hundreds of thousands of arbitrage opportunity. Consider the following sim-dollars in the market. CNBC was on television ple illustration, shown in Figure 4. Panel A shows whenever ing an early he was cutting hair, retirement. Here’sandahe was anticipat-quote from the the plot of 20 trials of a coin toss, and the percentage of heads is only about 35 percent. Panel B is the same article, “. . . I don’t think anything could shake my trial extended to 100 tosses, and it settled not too far confidence in this market . . . even if we go down 30 from 50:50. In a market context, if investors are being percent, we’ll just come right back.” Unfortunately, this extreme confidence came right as the NASDAQ short-term oriented and see the first 20 tosses, they was peaking and could only lead to a bad outcome. may conclude that it is a tails-biased coin and price When the NASDAQ was near its ultimate low, the the asset accordingly. But if investors understand Wall Street Journal went back to the same barber- what the true signal is, then it would represent a shop. On 8 July 2002, the story “Cape Cod Barber Shop, Slumping Stocks Clip Buzz” told about how Figure 4. Illustrating Noise vs. Signal the barber was doing. Needless to say, he was despondent, as were his clients. He would have to A. 20 Trials cut hair for a lot longer because he could not retire Heads (%)

early. CNBC had been turned off, and he summed 100 up the complete change in his attitude by saying, 90 “All they ever say is buy, buy, buy, all the way down 80 from $100 a share to bankruptcy.” When they then asked if he was in the market anymore, he said he 70 had given up on the market altogether and was now 60 going to the casino for his investments. 50 A similar, albeit less dramatic, example of the 40 same phenomenon can be found in the March/ 30 April 2007 issue of the Financial Analysts Journal, 20 which featured an article on the predictive value of magazine covers (Arnold, Earl, and North 2007). 10 The authors reviewed cover stories in BusinessWeek, 0 Forbes, and Fortune from the last 20 years and cate- 0 2 4 6 8 10 12 14 16 18 20 gorized the covers from the most bullish (optimistic Number of Trials spin) to the most bearish (pessimistic spin). They found that if they looked back two years prior to the B. 100 Trials date of covers in the first category (the bullish out- Heads (%)

look), stocks had outperformed their peers by 42 100 percentage points (pps). In contrast, years prior to 90 covers in the bearish category showed that stocks 80 had underperformed their peers by 35 pps. So, there 70 was massive overperformance and massive under- 60 performance leading up to the featured magazine 50 articles. But over the next two years, the stocks of the companies in the bearish articles outperformed 40 those in the bullish articles by a 3-to-1 margin. 30 Turning our attention to the other type of 20 diversity breakdown, time arbitrage is an impor- 10 tant concept in the context of financial markets.

Understanding time arbitrage requires recognizing 0 0 10 20 30 40 50 60 70 80 90 100 that any probabilistic system has a random compo-nent (noise) and a signal. One of the easiest illustra- Number of Trials tions of this is a coin toss. If you flip a fair coin Source: Mauboussin (2005).

time arbitrage opportunity and they should buy the advantage of it to try to outperform the market? asset. Although this sounds simple enough, be Following are some thoughts:

aware that two significant things have to happen for • Look for flags or signatures of diversity break-it to work. First, you must recognize the true long- downs, such as extreme bullishness or extreme term return signal for the business, and second, the bearishness. Also, look for simple indicators signal must reveal itself. Provided these two things that stocks are trading on the cheap or expen-happen, time arbitrage represents an important sive side. If a stock or an asset class is trading way out of its historical range, that might be an source of potential diversity breakdown. interesting indicator.

Now that we have taken this journey, I come

• Further analyze these diversity breakdown can-back to my original goal of reconciling efficient mar-didates by considering what expectations the kets with behavioral finance. I think both of these stocks or financial assets reflect. Recognize that theories can sit very comfortably inside the tent of there is an important distinction between fun-complex adaptive systems. Briefly, markets are effi- damentals, which is the value of that asset cient until diversity breaks down. But taking advan- (present value of future cash flows), and expec-tage of diversity breakdowns can be extremely tations, which is the price. Try to keep those difficult for two reasons. First, we must be prepared things separate in your own mind, and try to to run counter to the group, which is very difficult think probabilistically.

psychologically. Being part of the group has clear • Try to create a proper context for decision mak-and profound evolutionary foundations. The second ing within your organization. The hardest part reason is agency problems. It is far safer for us to run is avoiding the psychological traps that organi-our money management firms as businesses gather- zations often compound rather than alleviate. ing assets and collecting fees than necessarily trying • Finally, be receptive to novel approaches using to deliver excess returns for our clients. multidisciplinary techniques to help determine where excesses might exist or where diversity Taking Advantage of Diversity Breakdowns. breakdowns may occur.

Assuming that this is the right way of thinking about the world, how does an active manager take This article qualifies for 0.5 CE credits.

R EFERENCES Arnold, Tom, John H. Earl, Jr., and David S. North. 2007. “Are MacKenzie, Donald. 2004. “Models of Markets: Finance Theory Cover Stories Effective Contrarian Indicators?” Financial Analysts and the Historical Sociology of Arbitrage.” Working paper Journal, vol. 63, no. 2 (March/April):70–75. (January).

Mauboussin, Michael J. 2005. “Capital Ideas Revisited—Part 2.”

Fama, Eugene F., and Kenneth R. French. 1992. “The Cross-Section Mauboussin on Strategy (20 May): www.leggmasoncapmgmt.

of Expected Stock Returns.” Journal of Finance, vol. 47, no. 2 com/pdf/CIR2.pdf.

(June):427–465.

Page, Scott. 2007. The Difference. Princeton, NJ: Princeton Uni- ———. 2004. “The Capital Asset Pricing Model: Theory and versity Press.

Evidence.” Journal of Economic Perspectives, vol. 18, no. 3 Ross, Stephen. 2001. “Neoclassical and Alternative Finance.” (Summer):25–46. European Finance Agency Meetings, keynote address.

Question and Answer Session Michael J. Mauboussin Question: How can organiza- faucet, are best taken care of by own sense as an investor is that tion leaders create smart collec- relying on experts. In contrast, diversity prevails.

tives in the form of work groups collectives work best on unstruc-and teams within an organization? tured, complicated problems. Question: Is regression to the mean a precept we can rely on to Mauboussin: There are a cou- Question: Will the increased produce alpha?

ple of things leaders can do. First, connectivity caused by technolog-they should collect a group that is ical advances, such as the Black- Mauboussin: It depends. I diverse, recognizing that diverse berry, lead to more frequent would say that microeconomics does not mean that they look dif- diversity breakdowns? works, which means that, over ferent but that they think differ- time, competitive forces drive ently or have different Mauboussin: It creates a tug-ofreturns down to the cost of capi-perspectives. Second, leaders war. On the one hand, more peo-

tal. I have not seen an instance must effectively solicit the opin- ple have more access to capital where that has not happened ions and views of everybody. markets than ever before, and all things being equal, that should sooner or later for every corpora-