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is transparent and can be copied by other investors. To illustrate this point, assume that stocks are consistently found to earn excess returns in the month following a stock split. Since firms announce stock splits publicly and any investor can buy stocks right after these splits, it would be surprising if this inefficiency persisted over time. This can be contrasted with the excess returns made by some funds in index arbitrage, where index futures are bought (or sold), and stocks in the index are sold short (or bought). This strategy requires that investors be able to obtain information on index and spot prices instantaneously, have the capacity (in terms of margin requirements and resources) to buy and sell index futures and to sell short on stocks, and to have the resources to take and hold very large positions until the arbitrage unwinds. Consequently, inefficiencies in index futures pricing are likely to persist at least for the most efficient arbitrageurs with the lowest execution costs and the speediest execution times.

I N E F F I C I E N C Y O R A N O M A L Y : A S I M P L E T E S T

When you do find an investment strategy that seems to beat the market, it is always an open question as to whether you have found a market mistake that can be exploited for excess returns or just a phenomenon that occurs in financial markets that you are unable to explain because the models you use are incorrect or the data you use are incomplete or erroneous. You would categorize the first as an inefficiency and the second as an anomaly. The pragmatic difference is that you should try to make money off the first but not off the second.

One way to tell the difference is to observe what happens to the excess returns once a strategy has been uncovered and publicized. If it has uncovered an inefficiency, you should see the excess returns rapidly disappear after the strategy is made public. If it is an anomaly, you will see the excess returns continue unabated even after it is publicized.

B E H A V I O R A L F I N A N C E : T H E C H A L L E N G E T O

E F F I C I E N T M A R K E T S

Underlying the notion of efficient markets is the belief that investors are for the most part rational and even when not so, that irrationalities cancel out in the aggregate. Starting in the mid-1970s, a challenge was mounted by a subset of economists, with backing from psychologists, that the belief

in rational investors was misplaced. They pointed to the patterns that are observable in stock prices (that we will talk about in more depth in the next section), the recurrence of price bubbles in different asset markets, and the reaction to news announcements in markets as backing for their argument. In this section, we begin by considering some of the evidence accumulated by psychologists on human behavior. We will argue that almost all investment philosophies try to exploit one investor irrationality or another and that, ironically, investor failures in applying these philosophies can be traced back to other irrationalities. Put succinctly, you are your biggest enemy when it comes to investment success.

P s y c h o l o g i c a l S t u d i e s

At the risk of stating the obvious, investors are human and it is not surprising that financial markets reflect human frailties. In an extraordinary book (at least for an academic economist), Robert Shiller presented some of the evidence accumulated of human behavior by psychologists that may help us understand financial market behavior.5 He categorizes these findings into several areas, and we consider each one.

T h e N e e d f o r A n c h o r s When confronted with decisions, it is human nature to begin with the familiar and use it to make judgments. Kahneman and Tversky, whose research has helped illuminate much of what is called behavioral finance, ran an experiment where they used a wheel of fortune with numbers from 1 to 100 to illustrate this point.6 With a group of subjects, they spun the wheel to get a number and then asked the subjects numerical questions about obscure percentages—the percentage of the ancient Egyptians who ate meat, for instance. The subjects would have to guess whether the right answer was higher or lower than the number on the wheel and then provide an estimate of the actual number. They found that the answer given by subjects was consistently influenced by the outcome of the wheel spin. Thus, if the number on the wheel was 10, the answer was more likely to be 15 or 20 percent, whereas if the number on the wheel was 60 percent, it was more likely to be 45 or 50 percent. Shiller argues that market prices provide a similar anchor with publicly traded assets. Thus, an investor asked

5R. J. Shiller, Irrational Exuberance (Princeton, NJ: Princeton University Press, 2005).

6A. Tversky and D. Kahneman, “Judgment under Uncertainty: Heuristics and Biases,” Science 185 (1974): 1124–1131.

to estimate the value of a share is likely to be influenced by the market price, with the estimated value increasing as the market price rises.

T h e P o w e r o f t h e S t o r y For better or worse, human actions tend to be based not on quantitative factors but on storytelling. People tend to look for simple reasons for their decisions, and will often base their decision on whether these reasons exist. In a study of this phenomenon, Shafir, Simonson, and Tversky gave subjects a choice on which parent they would choose for sole custody of a child.7 One parent was described as average in every aspect of behavior and standing whereas the other was described more completely with both positive characteristics (very close relationship with child, above-average income) and negative characteristics (health problems, travels a lot). Of the subjects studied, 64 percent picked the second. Another group of subjects was given the same choice but asked which one they would deny custody to. That group also picked the second parent. These results seem inconsistent (the first group chose the second parent as the custodian and the second group rejected the same parent, given the same facts) but suggest that investors are more comfortable with investment decisions that can be justified with a strong story than one without.

O v e r c o n f i d e n c e a n d I n t u i t i v e T h i n k i n g As you have undoubtedly become aware from your interactions with friends, relatives, and even strangers over time, human beings tend to be opinionated about things they are not well informed on and to make decisions based on these opinions. In an illustrative study, Fischhoff, Slovic, and Lichtenstein asked people factual questions, and found that people gave an answer and consistently overestimated the probability that they were right. In fact, they were right only about 80 percent of the time that they thought they were.8 What are the sources of this overconfidence? One might just be evolutionary. The confidence, often in the face of poor odds, may have been what allowed us to survive and dominate as a species. The other may be more psychological. Human beings seem to have a propensity to hindsight bias; that is, they observe what happens and act as it they knew it was coming all the time. Thus, you have investors who claim to have seen the dot com crash, the housing bubble and the banking

7E. Shafir, I. Simonson, and A. Tversky, “Money Illusion,” Quarterly Journal of Economics 112 (1997): 341–374.

8B. Fischhoff, P. Slovic, and S. Lichtenstein, “Knowing with Uncertainty: The Appropriateness of Extreme Confidence,” Journal of Experimental Psychology 3 (1977): 522–564.

based on unrealistic expectations. They noted that a person who has not made peace with his losses is likely to accept gambles that would otherwise be unacceptable to him. Anyone who has visited a casino will attest to this finding.

In investing, Shefrin and Statman call this the disposition effect, i.e., the tendency to hold on to losers too long and to sell winners too soon.10 They argue that it is widespread and can cause systematic mispricing of some stocks. Terrance Odean used the trading records of over 10,000 customers at a discount brokerage house to examine whether there is evidence of this behavior among investors.11 He noted that investors realized only 9.8 percent of their losses each year, whereas they realized 14.8 percent of their gains.12 He also finds that investors seem to hold on to losers too long and to sell winners too soon. Overall, he argues that there is evidence of the disposition effect among investors.

T h e E v i d e n c e

While it is evident that human beings do not always behave rationally, it does not necessarily follow that markets will also be irrational. In fact, you could argue (as some believers in market efficiency do) that markets can be efficient even with irrational investors for several reasons. First, it is possible that there is a selection process that occurs in markets where irrational investors lose consistently to rational investors and eventually get pushed out of the market. Second, it is also possible that irrationalities cut in both directions—some leading investors to buy when they should not and others leading them to sell when they should not; if these actions offset each other, you could still have a market price that is unaffected by irrational investors. The only way to resolve this debate is to look at the evidence on the presence or absence of irrationality in market behavior.

One of the problems that we face when we test for irrationality in financial markets is the number of variables that cannot be controlled for. Investors enter and leave markets, new information arrives constantly, and the macroeconomic environment changes frequently, making it impossible to construct a controlled experiment. A few researchers have attempted to get around this problem by constructing experimental studies, similar

10H. Shefrin and M. Statman, “The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence,” Journal of Finance 40 (1985): 777–790.

11T. Odean, “Are Investors Reluctant to Realize Their Losses?” Journal of Finance

53(1998): 1775–1798.

12The only month in which more losses are realized than gains is December.

sequence of lotteries. In the first lottery, subjects were given a chance to win $15 and were offered a subsequent lottery where they had a 50–50 chance of winning or losing $4.50. While many of these same subjects would have rejected the second lottery if it had been offered as an initial choice, 77 percent of those who won the first lottery (and made $15) took the second lottery.17

Break-even effect. The break-even effect is the flip side of the house money effect and refers to the attempts of those who have lost money to make it back. In particular, subjects in experiments who have lost money seem willing to gamble on lotteries (that standing alone would be viewed as unattractive) that offer them a chance to break even. The study by Thaler and Johnson that uncovered the house money effect also found the break-even effect. In a study of sequenced lotteries, researchers found that subjects who lost money on the first lottery generally became more risk averse in the second lottery except when the second lottery offered them a chance to make up their first-round losses and break even.18

In summary, the findings from experimental studies offer grist for the behavioral finance mill. Whether or not we buy into all of the implications, it is clear that there are systematic quirks in human behavior that cannot be easily dismissed as irrational or aberrant since they are so widespread and long-standing.

As a side note, many of these experimental studies have been run using inexperienced subjects (usually undergraduate students) and professionals (traders in financial markets, experienced businesspeople) to see if age and experience play a role in making people more rational. The findings are not promising for the rational human school, since the consensus view across these studies is that experience and age do not seem to confer rationality in subjects and that some of the anomalies noted in this section are attenuated with experience. Professional traders exhibit more myopic loss aversion than undergraduate students do, for instance. The behavioral patterns indicated

17R. H. Thaler and E. J. Johnson, “Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice,” Management Science

36(1990): 643–660. They also document a house-loss effect, where those who lose in the initial lottery become more risk averse at the second stage, but the evidence from other experimental studies on this count is mixed.

18R. C. Battalio, J. H. Kagel, and K. Jiranyakul, “Testing between Alternative Models of Choice under Uncertainty: Some Initial Results,” Journal of Risk and Uncertainty

3(1990): 25–50.

in this section are also replicated in experiments using business settings (projects with revenues, profits, and losses) and experienced managers.19 Finally, we should resist the temptation to label these behaviors as irrational. Much of what we observe in human behavior seems to be hardwired into our systems and cannot be easily eliminated (if at all). In fact, a study in the journal Psychological Science examined the decisions made by 15 people with normal IQs and reasoning skills but with damage to the portions of the brain that control emotions.20 They confronted this group and a control group of normal individuals with 20 rounds of a lottery in which they could win $2.50 or lose a dollar, and found that the inability to feel emotions such as fear and anxiety made the brain-damaged individuals more willing to take risks with high payoffs and less likely to react emotionally to previous wins and losses. Overall, the brain-impaired participants finished with about 13 percent higher winnings than normal people who were offered the same gambles.

T e s t i n g M a r k e t E f f i c i e n c y

Tests of market efficiency look at whether specific investment strategies or portfolio managers beat the market. But what does beating the market involve? Does it just imply that someone earns a return greater than what the market (say, the S&P 500) earns in a specific year? We begin by looking at what beating the market requires and define what we mean be excess returns. We will then follow up by looking at three standard ways of testing market efficiency and when and why we may choose one over the other.

B e a t i n g t h e M a r k e t The fundamental question that we often attempt to answer when we test an investment strategy is whether the return we earn from the strategy is above or below a benchmark return on an alternative strategy of equivalent risk. But what should that benchmark return be? As we will see, it is almost impossible to measure the success or failure of an investment strategy without taking a point of view on how risk should be measured.

19K. Sullivan, “Corporate Managers’ Risky Behavior: Risk Taking or Avoiding,”

Journal of Financial and Strategic Decisions 10 (1997): 63–74.

20S. Baba, G. Lowenstein, A. Bechara, H. Damasio, and A. Damasio, “Investment Behavior and the Negative Side of Emotion,” Psychological Science 16 (2005): 435–

439.The damage to the individuals was created by strokes or disease and prevented them from feeling emotions.