Then I asked the CEO a question. If these projects were “independent”—that is, the success of one was unrelated to the success of another—how many of the projects would you want to undertake? His answer: all of them! By taking on the twenty-three projects, the firm expects to make $11.5 million (since each one is worth an expected half million), and a bit of mathematics reveals that the chance of losing any money overall is less than 5%. He considered undertaking a collection of projects like this a no-brainer.
“Well, that means you have a problem,” I responded to the CEO. “Because you are not going to get twenty-three of these projects—you are only getting three. You must be doing something wrong, either by hiring wimpy managers who are unwilling to bear risks, or, more likely, by creating an incentive system in which taking this sort of a risk is not rewarded.” The CEO smiled knowingly but stayed silent, waiting to see what the other participants would say. I turned to one of the managers who had said he would not undertake the project and asked him why not. He said that if the project was a success, he would probably get a pat on the back and possibly a bonus, say three months’ income. But if the project failed, he thought there would be a decent chance he would be fired. He liked his job and didn’t want to risk it on a coin flip in which he only stood to gain three months’ income.
Narrow framing prevents the CEO from getting the twenty-three projects he would like, and instead getting only three. When broadly considering the twenty-three projects as a portfolio, it is clear that the firm would find the collection of investments highly attractive, but when narrowly considering them one at a time, managers will be reluctant to bear the risk. The firm ends up taking on too little risk. One solution to this problem is to aggregate investments into a pool where they can be considered as a package.
The value of this sort of aggregation was brought home to me on a brief consulting job with a large pharmaceutical company. Like all major drug companies, this one spent over a billion dollars a year on research and development, investigating thousands of new compounds in the hope of finding the next blockbuster drug. But blockbuster drugs are rare. Even for a large firm, finding one every two or three years would be considered good, and with so many drugs being investigated, any one of them has expected returns that look a lot like a lottery ticket—there is a very small chance of a very large prize. You might think a company that lays out billions on investments that offer very small chances of an occasional windfall has figured out how to think about risk, but you would be wrong, because they had only figured this out with respect to research and development.
The project I happened to be working on was related to marketing and pricing, not research and development. An employee came up with a proposal to run experiments investigating different ways that certain drugs might be priced, with one of the goals being to improve “compliance,” which is medical parlance for taking the medicine that your doctor has prescribed. For some drugs, especially those that do not relieve pain or have other obvious beneficial effects for the user, many patients stop taking their medicine. In certain cases, such as taking the recommended drugs after having a heart attack, the benefits are demonstrably large. Any improvement to compliance offered the chance for a true win-win. Patients would be healthier, medical spending would fall, and the drug company would make more money since it would sell more pills. In spite of this potential upside, we were told that running the trials to attempt to communicate directly with consumers that we had devised would be too risky. This was wrongheaded thinking. Of course the idea might not pan out—that is why you run experiments.* But the cost of the experiment was tiny, compared to the size of the company. It just looked risky compared to the particular manager’s budget. In this example, narrow framing prevented innovation and experimentation, two essential ingredients in the long-term success of any organization.
Both this example of the risk-averse manager and the story of the CEO who would have liked to take on twenty-three risky projects, but would only get three, illustrate an important point about principal–agent problems. In the economics literature, such failures are usually described in a way that implicitly puts the “blame” on the agent for taking decisions that fail to maximize the firm, and acting in their own self-interest instead. They are said to make poor decisions because they are maximizing their own welfare rather than that of the organization. Although this depiction is often apt, in many cases the real culprit is the boss, not the worker.
In order to get managers to be willing to take risks, it is necessary to create an environment in which those managers will be rewarded for decisions that were value-maximizing ex ante, that is, with information available at the time they were made, even if they turn out to lose money ex post. Implementing such a policy is made difficult by hindsight bias. Whenever there is a time lapse between the times when a decision is made and when the results come in, the boss may have trouble remembering that he originally thought it was a good idea too. The bottom line is that in many situations in which agents are making poor choices, the person who is misbehaving is often the principal, not the agent. The misbehavior is in failing to create an environment in which employees feel that they can take good risks and not be punished if the risks fail to pay off. I call these situations “dumb principal” problems. We will discuss a specific example of such a case a bit later in the context of sports decision-making.
The previous stories illustrate Danny’s take on narrow framing. My own project on this topic was with a PhD student who had arrived recently at Cornell to study finance, Shlomo Benartzi. Shlomo would turn out to be an important solution to my laziness problem. Shlomo is high-energy and impossible to discourage. He also mastered the fine art of “bugging me,” as we came to define it. Often I would say to Shlomi, as everyone calls him, “I am just too busy, I can’t think about this right now.” Shlomi: “Okay, when do you think you can get to it?” Me: “Oh, maybe two months from now, not before.” Two months to the day later, Shlomi would call. Are we ready to work? Of course Shlomi had figured out that I was taking the inside view in thinking that I would have more time in just two months, but he would call nonetheless, and eventually I would get around to working on his current project. As a result of his “bugging,” as well as a fountain of interesting ideas, I have written more papers with him than anyone else.
Shlomo and I were interested in an anomaly called the equity premium puzzle. The puzzle was first announced, and given the name, by Raj Mehra and Edward Prescott in a 1985 paper. Prescott was a surprising person to announce an anomaly. He was and remains a hard-core member of the conservative, rational expectations establishment. His work in this domain, called “real business cycles,” would later win him a Nobel Prize. And unlike me, Prescott did not have declaring anomalies as part of his agenda. I suspect he found this one to be a bit embarrassing given his worldview, but he and Mehra knew they were on to something interesting.
The term “equity premium” is defined as the difference in returns between equities (stocks) and some risk-free asset such as short-term government bonds. The magnitude of the historical equity premium depends on the time period used and various other definitions, but for the period that Mehra and Prescott studied, 1889–1978, the equity premium was about 6% per year.
The fact that stocks earn higher rates of return than Treasury bills is not surprising. Any model in which investors are risk averse predicts it: because stocks are risky, investors will demand a premium over a risk-free asset in order to be induced to bear that risk. In many economics articles, the analysis would stop at that point. The theory predicts that one asset will earn higher returns than another because it is riskier, the authors find evidence confirming this prediction, and the result is scored as another win for economic theory.
What makes the analysis by Mehra and Prescott special is that they went beyond asking whether economic theory can explain the existence of an equity premium, and asked if economic theory can explain how large the premium actually is. It is o
ne of the few tests I know of in economics where the authors make a statement about the permissible magnitude of some effect.† After crunching the numbers, Mehra and Prescott concluded that the largest value of the equity premium that they could predict from their model was 0.35%, nowhere near the historical 6%.‡ Investors would have to be implausibly risk averse to explain the historical returns. Their results were controversial, and it took them six years to get the paper published. However, once it was published, it attracted considerable attention and many economists rushed in to offer either excuses or explanations. But at the time Shlomo and I started thinking about the problem, none of the explanations had proven to be completely satisfactory, at least to Mehra and Prescott.
We decided to try to find a solution to the equity premium puzzle. To understand our approach, it will help to consider another classic article by Paul Samuelson, in which he describes a lunchtime conversation with a colleague at the MIT faculty club. Samuelson noted that he’d read somewhere that the definition of a coward is someone who refuses to take either side of a bet at 2-to-1 odds. Then he turned to one of his colleagues, an economic historian named E. Carey Brown, and said, “Like you, Carey.”
To prove his point, Samuelson offered Brown a bet. Flip a coin, heads you win $200, tails you lose $100. As Samuelson had anticipated, Brown declined this bet, saying: “I won’t bet because I would feel the $100 loss more than the $200 gain.” In other words, Brown was saying: “I am loss averse.” But then Brown said something that surprised Samuelson. He said that he did not like one bet, but would be happy to take 100 such bets.
This set Samuelson thinking, and he soon came back with a proof that Brown’s preferences were not consistent, and therefore not rational by economics standards. Specifically, he proved, with one proviso, that if someone is not willing to play one bet, then he should not agree to play multiple plays of that bet. The proviso is that his unwillingness to play a single bet is not sensitive to relatively small changes in his wealth, specifically any wealth level that could be obtained if he played out all of the bets. In this case, he could lose as much as $10,000 (if he loses all 100 bets) and win as much as $20,000 (if he wins every bet). If Brown had a substantial retirement nest egg he probably made or lost that amount of money frequently, so it was probably safe to assume that his answer to Samuelson’s question would not change if he were suddenly $5,000 richer or poorer.§
Here is the logic of Samuelson’s argument. Suppose Brown agrees to play the 100 bets, but after playing 99 of the bets, Samuelson offers him the chance to stop, thus making the last bet optional. What will Brown do? Well, we know that he does not like one bet, and we are in the range of wealth for which this applies, so he stops. Now, suppose that we do the same thing after 98 bets. We tell him that each of the last two bets is now optional. What will Brown do? As a trained economist, he will use backward induction, which just means starting at the end and working back. When he does, he will know that when he reaches the choice of taking the single bet number 100 he will turn it down, and realizes that this implies that bet 99 is also essentially a single bet, which he again does not like, so he also says no to bet 99. But if you keep applying this logic sequentially, you get to the result that Brown will not take the first bet. Thus Samuelson’s conclusion: If you don’t like one bet, you shouldn’t take many.
This result is quite striking. It does not seem unreasonable to turn down a wager where you have a 50% chance to lose $100, especially since $100 in the early 1960s was worth more than $750 now. Not many people are willing to risk losing that much money on a coin flip, even with a chance to win twice as much. Although the 100-bet combination seems quite attractive, Samuelson’s logic is unassailable. As he restated it once in another of his short papers, this time consisting entirely of words with one syllable:¶ “If it does not pay to do an act once, it will not pay to do it twice, thrice, . . . or at all.” What is going on here?
Samuelson did more than point out that his colleague had made a mistake. He offered a diagnosis teased at in the title of the paper: “Risk and Uncertainty: A Fallacy of Large Numbers.” In Samuelson’s view, the mistake Brown made was to accept the 100 plays of the gamble, and he thought Brown made this mistake because he misunderstood the statistical principle called the law of large numbers. The law of large numbers says that if you repeat some gamble enough times, the outcome will be quite close to the expected value. If you flip a coin 1,000 times, the number of heads you get will be pretty close to 500. So Brown was right to expect that if he played Samuelson’s bet 100 times, he was unlikely to lose money. In fact, his chance of losing money is just 1 in 2300. The mistake Samuelson thought Brown was making was to ignore the possibility of losing a substantial amount. If you play the bet once you have a 50% chance of losing, but the most you can lose is $100. If you play it 100 times, your chance of losing is tiny, but there is some, admittedly infinitesimal, chance of losing $10,000 by flipping 100 tails in a row.
In our take on this betting scenario, Benartzi and I thought Samuelson was half right. He was right that his colleague had made a mistake. It is illogical, in Samuelson’s setup, to refuse one bet but accept many. But where Samuelson criticized Brown for taking the many bets, we thought his mistake was to turn down the one. Narrow framing was responsible. Criticizing the acceptance of the 100-bet option is really misplaced. On average Brown expects to win $5,000 by accepting this parlay, and the chance of losing any money is tiny. The chance of losing a lot of money is even tinier. Specifically, the chance of losing more than $1,000 is about 1 in 62,000. As Matthew Rabin and I wrote in an “Anomalies” column on this topic: “A good lawyer could have you declared legally insane for turning down this gamble.” But if it is crazy to turn down the 100 bets, the logic of Samuelson’s argument is just reversed; you should not turn down one! Shlomo and I called this phenomenon “myopic loss aversion.” The only way you can ever take 100 attractive bets is by first taking the first one, and it is only thinking about the bet in isolation that fools you into turning it down.
The same logic applies to investing in stocks and bonds. Recall that the equity premium puzzle asks why people would hold so many bonds if they expect the return on stocks to be 6% per year higher. Our answer was that they were taking too short-term a view of their investments. With a 6% edge in returns, over long periods of time such as twenty or thirty years, the chance of stocks doing worse than bonds is small, just like (though perhaps not as good odds as) the chance of losing money in Samuelson’s original 100-bet game.
To test this hypothesis, Shlomo and I ran an experiment using recently hired non-faculty employees at the University of Southern California, which has a defined contribution retirement plan in which employees have to decide how to invest their retirement funds. In the United States these are often called 401(k) plans, a term that is derived from a provision in the tax code that made them legal. We told each subject to imagine that there were only two investment options in this retirement plan, a riskier one with higher expected returns and a safer one with lower expected returns. This was accompanied by charts showing the distribution of returns for both of the funds based on the returns for the past sixty-eight years. The riskier fund was based on the returns of an index of large U.S. companies, while the safer fund was based on the returns of a portfolio of five-year government bonds. But we did not tell subjects this, in order to avoid any preconceptions they might have about stocks and bonds.
The focus of the experiment was on the way in which the returns were displayed. In one version, the subjects were shown the distribution of annual rates of return; in another, they were shown the distribution of simulated average annual rates of return for a thirty-year horizon (see figure 9). The first version captures the returns people see if they look at their retirement statements once a year, while the other represents the experience they might expect from a thirty-year invest-and-forget-it strategy. Note that the data being used for the two charts are exactly the same. This means that in a world o
f Econs, the differences in the charts are SIFs and would have no effect on the choices people make.
FIGURE 9
For our Human subjects, the presentation of the data had a huge effect. The employees shown the annual rates of return chose to put 40% of their hypothetical portfolio in stocks, while those who looked at the long-term averages elected to put 90% of their money into stocks. These results, and others, go against Samuelson’s hypothesis about people overestimating the risk-reducing effect of repeated plays. When people see the actual data, they love the riskier portfolio.
An implication of this analysis is that the more often people look at their portfolios, the less willing they will be to take on risk, because if you look more often, you will see more losses. And in fact, that is an implication I later explored with Kahneman and Tversky. This would be the only paper that Amos, Danny, and I published together (along with Danny’s then-student Alan Schwartz, now a professor of medical decision-making at the University of Illinois at Chicago). The paper was published in 1997 in a special issue of the Quarterly Journal of Economics dedicated to Amos’s memory. We had to finish the writing of the paper without him.
The paper reports an experiment in which student subjects at Berkeley were given the job of investing the money of a portfolio manager for a university endowment. Of course, they were only pretending to be portfolio managers, but the amount of money they earned in the experiment did depend on how their investments turned out. Their earnings varied from $5 to $35 in less than an hour, so it was real enough for them. As in the previous experiment, the subjects had only two investment options, a riskier one with higher returns and a safer one with lower returns. In this case, what we varied was how often the subjects got to look at the results of their decisions. Some subjects saw their results eight times per simulated calendar year of results, while others only saw their results once a year or once every five years. As predicted by myopic loss aversion, those who saw their results more often were more cautious. Those who saw their results eight times a year only put 41% of their money into stocks, while those who saw the results just once a year invested 70% in stocks.
Misbehaving: The Making of Behavioral Economics Page 21
