Investement models
Physics
Equilibrium
Equilibrium is defined as a state of balance between opposing forces, powers, or influences. An equilibrium model typically identifies a system that is at rest; this is called static equilibrium. When competing forces are equally matched, a system reaches dynamic equilibrium. A scale that is equally weighted on both sides is an example of static equilibrium. Fill a bathtub full of water and then turn off the faucet and you will observe static equilibrium. But if you unplug the drain and then turn on the faucet so the level of the bathtub does not change, you are witnessing dynamic equilibrium. Another example is the human body. It remains in dynamic equilibrium so long as the heat loss from cooling remains in balance with the consumption of sugars.
Economic equilibrium: The simplest case of balance or equilibrium between desire and effort is found when a person satisfies one of his wants by his own direct work. When a boy picks blue-berries for his own eating, the action of picking is probably itself pleasurable for a while; and for sometime longer the pleasure of eating is more than enough to repay the trouble of picking. But after he has eaten a good deal, the desire for eating diminishes; while the task of picking begins to cause weakness, which may indeed be a feeling of monotony rather than fatigue.
Equilibrium is reached when at last his eagerness to play and his disinclination for the work of picking counterbalance the desire for eating.^3^
Efficient market theory: Fama's message was clear. Stock prices are unpredictable because the market is too efficient. In an efficient market, a great many smart people (Fama called them "rational profit maximizers") have simultaneous access to all the relevant information, and they aggressively apply that information in a way that causes prices to adjust instantaneously---thus restoring equilibrium---before anyone can profit. Predictions about the future therefore have no place in an efficient market, because share prices fully reflect all available information.
Sharpe: Sharpe was awarded the Nobel Prize in Economics for developing "a market equilibrium theory of asset prices under conditions of risk." His theory was originally outlined in a 1964 paper entitled "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk." Sharpe explained, "In equilibrium, there is a simple linear relationship between the expected return and standard deviation of return (defined as risk)."^11^ According to Sharpe, the only way to achieve a greater return is to incur additional risk. To increase expected returns, investors need only march further out the capital market line. Conversely, if investors wished to assume less risk, they would step down the capital line and by doing so receive less return. In either case, equilibrium is maintained.
The counterview from Santa Fe suggests the opposite: a market that is not rational, is organic rather than mechanistic, and is imperfectly efficient. It assumes the individual agents are, in fact, irrational and hence will misprice securities, creating the possibility for profitable strategies.
Biology
Evolution
Whereas in nature the process of evolution is one of natural selection, seeing the market within an evolutionary framework allows us to observe the law of economic selection.
Complex adaptive systems
El Farol, a bar in Santa Fe, New Mexico, used to feature Irish music on Thursday nights. Arthur, the Irishman, loved to go there. On most occasions, the bar patrons were well behaved, and it was enjoyable to sit and listen to the music. But on some nights, the bar was packed with so many people crammed together drinking and singing that the scene became unruly. Now Arthur was confronted with a problem: How could he decide which nights to go to El Farol and which nights to stay home? The chore of having to decide led him to formulate a mathematical theory he named the El Farol Problem. It has, he says, all the characteristics of a complex adaptive system.
Suppose, says Arthur, there are one hundred people in Santa Fe who are interested in going to El Farol to listen to Irish music, but none of them wants to go if the bar is going to be crowded. Now also suppose the bar published its weekly attendance for the past ten weeks. With this information, the music lovers will build models to predict how many people will show up next Thursday. Some may figure that it will be approximately the same number of people as last week. Others will take an average of the last few weeks. A few will attempt to correlate attendance data to the weather or to other activities for the same audience. There will be endless ways to build models to predict how many people will go to the bar.
Now let's say that every lover of Irish music decides that the comfort level in the small bar is sixty people. All one hundred people will decide, using whatever predictor has been the most accurate over the last few weeks, when the limit is going to be reached. Because each person has a different predictor, on any given Thursday some people will turn up at El Farol and others will stay home because their model has predicted more than sixty people will be attending. The following day, El Farol publishes its attendance and the hundred music lovers will update their models and get ready for next week's prediction.
The El Farol process can be termed an ecology of predictors, says Arthur. At any point, there is a group of models that are deemed "alive"---that is, they are useful predictors of how many people will attend the bar. Conversely, predictors that turn out to be inaccurate will slowly die off. Each week, new predictors, new models, new beliefs will compete for use by other music lovers.
We can quickly see how the El Farol process echoes the Darwinian idea of survival through natural selection and how logically it extends to economies and markets. In the markets, each agent's predictive models compete for survival against the models of all other agents, and the feedback that is generated causes some models to be changed
| Biological | Financial |
|---|---|
| Species | Trading Strategy |
| Individual organism | Trader |
| Genotype (genetic const.) | Functional representation of strategy |
| Phenotype (appearance) | Actions of the strategy (buying, selling) |
| Population | Capital |
| External environment | Price and other informational input |
| Selection | Capital allocation |
| Mutation and recombination | Creation of new strategies |
If we go back through the history of the stock market and seek to identify the trading strategies that dominated the landscape, I believe there have been five major strategies,
1. In the 1930s and 1940s, the discount-to-hard-book value strategy, first proposed by Benjamin Graham.
2. After World War II the second major strategy that dominated finance was the dividend model. As the memories of the 1929 market crash faded and prosperity returned, investors were increasingly attracted to stocks that paid high dividends, and lower-paying bonds lost favor. So popular was the dividend strategy that by the 1950s, the yield on dividend-paying stocks dropped below the yield of bonds---a historical first.
3. By the 1960s, a third strategy appeared. Investors exchanged stocks paying high dividends for companies that were expected to grow their earnings at a high rate.
4. By the 1980s, a fourth strategy took over. Warren Buffett stressed the need to focus on companies with high "owner-earnings" or cash flows.
5. Today we can see that cash return on invested capital is emerging as the fifth new strategy.
Sociology
Diversity and independence
Johnson's research suggests that the stock market, theoretically, is more robust when it is composed of a diverse group of agents---some of average intelligence, some of below-average intelligence, and some very smart---than a market singularly composed of smart agents. At first, this discovery appears counterintuitive. Today, we are quick to blame the amateur behavior of uninformed individual investors and day traders for the volatile nature of the market. But if Johnson is correct, the diverse participation of all investors, traders and speculators---smart and dumb alike---should make the markets stronger, not weaker.
The two critical variables necessary for a collective to make superior decisions are diversity and independence. If a collective is able to tabulate decisions from a diverse group of individuals who have different ideas or opinions on how to solve a problem, the results will be superior to a decision made by a group of like-minded thinkers.
We know the stock market is an incentive-based system that can aggregate investor decisions. What we need to understand is the market's level of diversity and the independence of its participants. If the stock market is adequately diversified and, most importantly, if the decisions of its participants have been reached independently, then it is likely the market is efficient. Surowiecki reminds us that just because we can observe some irrational investors, that does not necessarily mean the market is inefficient. Indeed, proponents of the efficient market hypothesis have latched onto the "wisdom of the crowds" as a plausible explanation for market efficiency.
But what if independence is lost? What if the decisions of the market's participants are not independent but are now coalesced into one opinion? When this occurs, the system has effectively lost its diversity and along with it any chance of generating an optimal solution. If diversity is the key to how collectives can best reach solutions, then diversity breakdowns are the cause of suboptimal outcomes---or in the case of the stock market, diversity breakdowns cause the market to become inefficient.
"information cascades (which can lead to diversity breakdowns) occur when people make decisions based on the actions of others rather than on their own private information. These cascades help explain booms, fads, fashions, and crashes."^12^ Social network theorists, who view social relationships in terms of nodes and ties, whereby nodes are the individual actors and ties are the relationships between the actors
Self-organizing criticality
Most of the time, the interplay between trend followers and fundamentalists is somewhat balanced. Buying and selling continue with no discernible change in the overall behavior of the market. We might say the sand pile is growing without any corresponding avalanche effects. Put differently, diversification is present in the market.
But when stock prices climb, the ratio of trend followers to fundamentalists begins to grow. This makes sense. As prices increase, a larger number of fundamentalists decide to sell and leave the market and are replaced by a growing number of trend followers who are attracted to rising prices. When the relative number of fundamentalists is small, stock market bubbles occur, explained Bak, because prices have moved far above the fair price a fundamentalist would pay. Extending the sand pile metaphor further, as the number of fundamentalists in the market declines, and the relative number of trend followers increases, the slope of the sand pile becomes ever steeper, increasing the possibility of an avalanche. Once again, we can put this differently by saying that when the mix of fundamentalists and trend followers becomes unbalanced, we are heading toward a diversity breakdown.
It is important for us to remember at this point that while Per Bak's self-organizing criticality explains the overall behavior of avalanches, it does nothing to explain any one particular avalanche.
An obvious question at this point is how people select from a collection of choices. According to Richards, if there is no clear favorite, the tendency of the system is to continually cycle over the possibilities. You might think this cyclical outcome would lead to instability, but according to Richards, it need not if the agents share similar mental concepts (that is, mutual knowledge) about the various choices. It is when the agents in the system do not have similar concepts about the possible choices that the system is in danger of becoming unstable. And that is clearly the case in the stock market.
At this point, we have a fixed compass on how to analyze social systems. Whether they are economic, political, or social, we can say these systems are complex (they have a large number of individual units), and they are adaptive (the individual units adapt their behavior on the basis of interactions with other units as well as with the overall system). We also recognize that these systems have self-organizing properties and that, once organized, they generate emergent behavior. Finally, we realize that complex adaptive systems are constantly unstable and periodically reach a state of self-organized criticality.
Psychology
Loss aversion
Equity risk premium is a term many investors have heard but few actually understand. It refers to the potential for higher returns represented by the inherently risky stock market compared to the risk-free rate, defined as the rate of a ten-year U.S. Treasury bond in effect at whatever point you're considering. (It is called the risk-free rate because up until now the government has never defaulted on its loans.) Whatever return an individual stock or the overall stock market earns beyond that rate is the investor's compensation for taking on the higher risk of the stock market---the equity risk. For example, if the return on a stock is 10 percent and the risk-free rate is 5 percent over the same period, the equity risk premium would be 5 percent. The size of the risk premium will vary based on the perceived riskiness of a particular stock or the stock market as a whole. According to Aswath Damodaran, professor of finance at the Stern School of Business at New York University, the implied equity risk premium has vacillated between less than 3 percent in 1961 and 6.5 percent in the early 1980s.
Thaler and Benartzi were puzzled by two questions. One, why is the equity risk premium so high; and two, why is anyone willing to hold bonds when we know that over the years, stocks have consistently outperformed? The answer, they believed, rested upon two central concepts from Kahneman and Tversky. The first was loss aversion. The second was a behavioral concept called mental accounting.
T haler and Benartzi reasoned the longer the investor holds an asset, the more attractive the asset becomes but only if the investment is not evaluated frequently. If you don't check your portfolio every day, you will be spared the angst of watching daily price gyrations; the longer you hold off, the less you will be confronted with volatility and therefore the more attractive your choices seem. Put differently, the two factors that contribute to an investor's unwillingness to bear the risks of holding stocks are loss aversion and a frequent evaluation period.
Using the medical word for shortsightedness, Thaler and Benartzi coined the term myopic loss aversion to reflect a combination of loss aversion and the frequency with which an investment is measured.
Thaler and Benartzi next considered whether myopic loss aversion could help explain the equity risk premium. They wondered what combination of loss aversion and evaluation frequency would explain the historical pattern of stock returns. How often, they asked, would an investor need to evaluate a stock portfolio to be indifferent to the historical distribution of returns on stocks and bonds? The answer: one year.
Thaler and Benartzi argue that any discussion of loss aversion must be accompanied by a specification of the frequency by which returns are calculated. Clearly, investors are less attracted to high-risk investments like stocks when they evaluate their portfolio over shorter time horizons. "Loss aversion is a fact of life," explain Thaler and Benartzi. "In contrast, the frequency of evaluations is a policy choice that presumably could be altered, at least in principle."
Noise and signal
We are, through a long process of evolution, acutely uncomfortable and anxious in the face of uncertainty, so much so that we are willing to listen to those who promise to alleviate that anxiety. Even though we know in the rational part of our minds that market forecasters cannot predict what will happen tomorrow or next week, we want to believe they can, because the alternative (not knowing) is too uncomfortable.
To overcome noise in a communication system, Shannon recommended that what he called a "correction device" be placed between the receiver and the destination. This correcting device would take the information from the receiving terminal, separate out the noise, and then reconstruct the messages so the information arrived correctly at its final destination.
Shannon's correction system is a perfect metaphor for how investors should process information. We must mentally place a correcting device in our information channel. The first task for this correcting device is to maintain integrity of the information coming from the source. The device must filter out incorrect source information and reconfigure the signal if it has become garbled. The process for doing this is within our control. To do so means improving our ability to gather and analyze information and use it to further our understanding.
The other side of our correcting device, the side that faces the receiving terminal, is responsible for verifying that the information is properly passed through and accurately received, without interference of psychological biases. The process for doing this is also within our control, but it is challenging. We must make ourselves aware of all the ways that emotion-based errors and errors of thinking can interfere with good investing decisions, as described in this chapter, and we must constantly be on guard against our own psychological missteps.
Philosophy
If things remain a mystery, our job then is to shuffle our descriptions and offer redescriptions. Think of it this way: redescriptions are very powerful tools capable of breaking gridlock that sometimes occurs in the pursuit of understanding. I firmly believe, for instance, that one reason we have such difficulty understanding markets is that we have been locked into an equilibrium description of how they should behave. To reach a higher level of understanding, we must remain open-minded to accepting new descriptions of systems that appear complex, whether they are financial markets, social and political systems, or the physical world.
For investors it is important to realize the slippery slope of narratives. Storytelling inadvertently increases our confidence in propositions as the story itself becomes its own proof. "The focus of stories is on the individual rather than the averages, on motives rather than movements, on context rather than raw data," explains Paulos.^15^ Because investors primarily use storytelling to explain markets and economies, the absence of statistical evidence weakens the description. Quoting James Boswell, best known as the biographer of Samuel Johnson: "A thousand stories which the ignorant tell, and believe, die away at once when the computist takes them in his gripe [sic]."^16^
The lessons we have learned thus far from Benoit Mandelbrot, Ludwig Wittgenstein, C. P. Snow, and John Allen Paulos are all connected. The right description is critical for providing the right explanation. However, there is often more than one obvious description. Even so, we go to great lengths to defend our chosen description, constructing elaborate and entertaining stories in order to make our point despite the risk of statistical inconsistencies.
The only way to do better than someone else, or more importantly, to outperform the stock market, is to have a way of interpreting the data that is different from other people's interpretations. To that I would add the need to have sources of information and experiences that are different.^26^ In studying the great minds in investing, the one trait that stands out is the broad reach of their interests. Once your field of vision is widened, you are able to understand more fully what you observe, and then you use those insights for greater investment success.
We live and work in a world in which the pace of change is staggering; just when you think things can't possibly move any faster, the pace once again accelerates. In such a world, successful performance demands flexible thinking. In an environment of rapid change, the flexible mind will always prevail over the rigid and absolute.
Mathematics
Variation within and variation of the system
The most important lesson investors can learn from Gould's experience is to appreciate the differences between the trend of the system and trends in the system. Put differently, investors need to understand the difference between the average return of the stock market and the performance variation of individual stocks. One of the easiest ways for investors to appreciate the differences is to study sideways markets.
Putting it in Gould's terms, investors who observed the stock market between 1975 and 1982 and focused on the market average came to the wrong conclusion. They wrongly assumed that the direction of the market was sideways, when in fact the variation within the market was dramatic and led to plenty of opportunities to earn high excess returns.
Regression to the mean
J. P. Morgan was once asked what the stock market would do next. His response: "It will fluctuate." No one at the time thought this was a backhanded way of describing regression to the mean. But this now-famous reply has become the credo for contrarian investors. They would tell you greed forces stock prices to move higher and higher from intrinsic value, just as fear forces prices lower and lower from intrinsic value, until regression to the mean takes over. Eventually, variance will be corrected in the system.
The frustration comes from three sources. First, reversion to the mean is not always instantaneous. Overvaluation and undervaluation can persist for a period longer---much longer---than patient rationality might dictate. Second, volatility is so high, with deviations so irregular, that stock prices don't correct neatly or come to rest easily on top of the mean. Last, and most important, in fluid environments (like markets) the mean itself may be unstable. Yesterday's normal is not tomorrow's. The mean may have shifted to a new location.
Fifty years ago, the S&P 500 Index was dominated by manufacturing, energy, and utility companies. Today it is dominated by technology, health care, and financial companies. Because the return on equity for the latter three is higher than the first group of three, the average return on equity of the index is now higher today than it was thirty years ago. The mean has shifted. In the words of Thomas Kuhn, there has been a paradigm shift.
Overemphasizing the present without understanding the subtle shifts in composition can lead to perilous and faulty decisions. Although regression to the mean remains an important strategy, it is imperative that investors remember it is not inviolable. Stocks that are thought to be high in price can still move higher; stocks that are low in price can continue to decline. It is important to remain flexible in your thinking. Although reversion to the mean is the most likely outcome in markets, its presence is not sacrosanct.
Decision Making
As investors, we too must strike a balance between exploiting what is most obvious while allocating some mental energy to exploring new possibilities.
By recombining our existing building blocks, we are in fact learning and adapting to a changing environment. Think back for a moment to the description of neural networks and the theory of connectionism in Chapter 1. It will be immediately obvious to you that by choosing and then recombining building blocks, what we are doing is creating our own neural network, our connectionist model.
It's important to understand that you have the opportunity to discover many new things and add new building blocks to your mental models without ever taking undue risk. You can throw a lot of theories and ideas into your thinking mix, assemble them into a model, and, like a pilot in a flight simulator, try them out in the marketplace. If the new building blocks prove useful, then keep them and give them the appropriate weight. But if they appear to add no value, you simply store them away and draw them up again some day in the future.
But remember, none of this will happen if you conclude that you already know enough. Never stop discovering new building blocks. When a corporation cuts its research and development budget to focus on the here and now, that may produce greater profits in the short term, but more likely it places the company in competitive jeopardy at some point in the future. Likewise, if we stop exploring for new ideas, we may still be able to navigate the stock market for a while, but most likely we are putting ourselves at a disadvantage for tomorrow's changing environment.