Overconfidence

1. Overconfidence Professor Anne Sibert MSc Finance Spring 2013

2. “Hurrah, boys, we’ve got them!” General Armstrong Custer at the Little Big Horn

3. “Major combat operations in Iraq have ended!”

4. “The odds of a meltdown are one in 10,000 years.”The Ukrainian Minister of Power, February 1986

5. Why do market participants make systematic errors? • Bankers rashly bet that the US house bubble would continue long after economists predicted its demise. • Managers of insurance companies and pension funds did not exercise due diligence when they purchased collateralised debt obligations and mortgage-backed securities that they did not understand. • Bankers were over confident and they took on too much risk.

6. Overconfident Bankers • “We were hitting on all 99 cylinders, so you have to ask yourself, What can we do better? And I just can’t decide what that might be … Everyone says that when the markets turn around, we will suffer. But let me tell you we are going to surprise some people this time around. Bear Stearns is a great place to be.” James E. Cayne, Chairman and CEO of Bear Stearns, 2003.

7. The effects of overconfidence • Odean (1998), Barber and Odean (2001), Biais, Hilton, Mazurierand Pouget (2005) demonstrate that overconfidence can lead to excess trading and lower profits. • Daniel, Hirshleifer and Subrahmanyam (1998), Scheinkman and Xiong (2003) and Burnside, Han, Hershleifer and Wang (2011) show that it can lead to asset price anomalies such as overreactions, excess volatility and bubbles.

8. Some questions from Kahneman (2011) Kahneman, D., Thinking, Fast and Slow, London, Allen Lane, 2011. An individual has been described by a neighbour as follows: “Steve is very shy and withdrawn, invariably helpful but with little interest in people or the world of reality. A meek and tidy soul, he has a need for order and structure and a passion for detail.” Is Steve more likely to be a librarian or a farmer?

9. Fast and frugal heuristics • Humans have evolved to form impressions, make judgements and invent explanations quickly: Fast and frugal heuristics • A snap judgement: “This is dangerous” may be more apt to keep us alive than a slower and more finely nuanced thought. • But, the heuristics that promote speed may cause systematic biases.

10. An example of a heuristic • The representativeness heuristic is where we judge something by comparing it to our mental picture of a category. • An example from Myers (2008): “Linda, who is 31, single, outspoken, and very bright. She majored in philosophy in college. As a student she was deeply concerned with discrimination and other social issues, and she participated in anti-nuclear demonstrations. Based on that description, would you say it is more likely that • Linda is a bank teller • Linda is a bank teller and active in the feminist movement

11. Representativeness Heuristic • Most people say that the answer is b. (Mellor et al, 2001) But that cannot possibly be right! • Some other examples: (Myers, 2008) • Do more people live in Iraq or Tanzania? People usually answer according to how readily Iraqis and Tanzanians come to mind. • Vivid, easy to imagine events (shark attacks) seem more likely than hard-to-picture events. • People are quick to infer general conclusions from a single striking event: People switched from air travel to car travel after 11 September 2001.

12. Kahneman’s (2011) explanation • A person’s mental life can be described by the metaphor of two internal agents. The first produces that fast and frugal heuristics; the second produces slow and deliberative thought. Call these System 1 and System 2, respectively. • System 1 can be very good. A team of fire fighters is trying to douse a fire in a kitchen when the chief, without knowing why, heard himself yell to get out. Immediately after the floor collapsed. Only later did he realise that the fire had been unusually quiet and his ears unusually hot. The heart of the fire was in the basement below.

13. Another problem from Kahneman (2011) A bat and a ball cost $1.10. The bat costs one dollar more than the ball. How much does the ball cost?

14. System 1 vs. System 2 • Do the math: • Let bat := price of the bat ball := price of the ball bat + ball = 1.10 bat = ball + 1.00 This implies that 2 x ball + 1.00 = 1.10 or that 2 x ball = 10 cents or that ball = five cents. Thus the bat cost 1.05. • Probably everyone who got this right immediately thought of the answer that the bat cost a dollar and the ball ten cents, but they managed to resist it.

15. Another example from Kahneman (2011) ANN APPROACHED THE BANK

16. System 1 is not good at thinking statistically. • Going back to the introverted Steve. Our System 1 thinking associated Steve’s personality traits with those of a librarian. • Unless our System 2 overrules our System 1 we will say that Steve is more likely to be a librarian. • There are far more farmers than librarians. It is more likely that Steve is a farmer.

17. Another example from Kahneman (2011) A study of the incidence of kidney cancer in 3,141 counties of the United States reveals a remarkable pattern. The counties in which the incidence is lowest are mostly rural, sparsely populated and located in traditionally Republican states in the Midwest, the South and the West. What do you make of this?

18. But it is also true that: The counties in which the incidence of kidney cancer is highest are mostly rural, sparsely populated and located in traditionally Republican states in the Midwest, the South and the West. What do you make of this?

19. The key feature is “sparsely populated” Suppose an urn is filled with marbles. One fifth of the marbles are red and four-fifths are blue. Suppose we consider a scenario where we draw three marbles. The probability that all are red is 1/125. In a scenario where we draw seven marbles the probability that they are all red is 1/78,125.

20. Overconfidence • Also known as the “Lake Woebegone Effect”. • Overconfidence is pervasive. • Fischhoff (1977) found that when people claimed to be 100 percent confident, they were right 70 – 80 percent of the time. • Most of us are sure that we are better drivers than average. Svenson (1891), for example, found that 80 percent of survey respondents claimed to be in the top 30 percent of all drivers.

21. More Experiments Kahneman, D. a nd Tversky, A. (1797), “Intuitive Prediction: Biases and Corrective Procedures,” Managnement Science 12, 313-327. Daniel Kahneman and Amos Tversky (1979) asked people to fill in the gaps in statements such as “I fell 98 percent certain that the air distance between New Delhi and Beijing is more than ___ miles but less than ___ miles.” About 30 percent of the time the answers lay outside the range they felt 98 percent confident about.

22. Confirmation Bias • Overconfidence may lead to a failure to look for disconfirming evidence. • In psychology experiments, the failure of subjects to look for disconfirming evidence has “raised more doubts over human rationality than any other psychological tasks.” Oaksford and Chator (1993)

23. Wason’s test (P.C. Wason, 1960) • Wason gave participants in his test a sequence: 2,4,6. He asked participants to guess the rule that generated the sequence. • The rule was: Any three ascending numbers. • The subjects were allowed to discover the rule by generating sequences of three numbers. They were then told whether there sequence conformed to the rule or not.

24. 23 of 29 particpants got it wrong • Participants typically formed a belief about what the rule was: say, counting by twos. • They then tested this by seeking for confirming evidence, rather than attempting to look for evidence that might disprove their theories.

25. Men appear to be more overconfident than women • There is a sizable literature documenting that men are more confident of their abilities at activities that are perceived as traditionally male. • Using data on 35,000 households from a large brokerage firm, Barber and Odean (2001) argue that men are substantially more overconfident than women in financial markets.

26. Overconfidence is not related to ability • Overconfidence is not related to ability: it is found even when women perform as well or better than men. • Using undergraduate and graduate students, Lundeberg et al (1994) found that most students were over confident, but women were less overconfident then men, “who tended to show high degrees of confidence when wrong.”

27. Feedback loops in overconfidence • Campbell and Sedikides (1999) document the importance of the self-serving bias: a tendency to attribute success to one’s own ability and failure to external factors. • Beyer (1990) and others, however, find that this effect is stronger in men than in women. Thus, if confidence helps produce successful outcomes, there is more likely to be strong feedback loop in confidence in men than in women.

28. Coates and Herbert (2008) • In a fascinating and innovative study, Coates and Herbert (2008) consider the effect of testosterone on both risk aversion and overconfidence. • They explain that testosterone – a steroid hormone -- rises in athletes preparing for a contest; it rises further in winners and falls in losers. • Because increased testosterone increases confidence and risk taking, this produces a positive feedback loop in the winners as it improves their chances of winning again. • They hypothesised that something similar might happen in financial market participants.

29. The test • To test this, they took samples of testosterone levels of 17 male traders on a typical London trading floor (which had 260 traders, only four of whom were female) twice a day for eight days. • (They controlled for food, medications and whether the traders had received any important news from outside work.) • They found that testosterone was significantly higher on days when traders made more than their daily one-month average profit. • Furthermore, higher levels of testosterone led to greater profitability – presumably because of greater confidence and risk taking.

30. It gets worse … • The authors hypothesise that if raised testosterone were to persist for several weeks the elevated appetite for risk taking might have important behavioural consequences and there might be cognitive implications as well. • Testosterone, they say, has receptors throughout the areas of the brain that neuroeconomic research has identified as contributing to irrational financial decisions. • They also point to a study where testosterone was administered to a group of subjects playing a gambling task and it led to irrational behaviour: subjects preferred options with high variance and a negative expected return to options with a low variance and a positive expected return. • They speculate that steroid feedback loops may help explain why bankers behave irrationally when caught up in bubbles.

31. An economic model: Sabourian and Sibert (2011)

32. confidence

33. Objective function

34. Equilibrium ρ The announced accuracy ρis increasing in competency (although not necessarily as a straight line) up to some point where experts they are perfectly accurate. This point can be at one half or at one. 1 π 1/2 π* 1/2 1

35. What the market believes

36. Find the cutoff point

37. Find the optimum

38. Derivatives of Inverse Functions • Let y = f(x). Then f-1(y) = f-1(f(x)) = x. Differentiating yields f-1’(f(x)) f’(x) = 1 and thus f-1’(y) = 1/ f’(x). The derivative of the inverse function is the reciprocal of the derivative of the original function. • Differentiating f-1’(f(x)) f’(x) = 1 yields f-1’’(f(x)) f’(x)2 + f-1’(f(x)) f’’(x)= 0. This implies f-1’’(y) = - f-1’(y) f’’(x)/ f’(x)2 = f’’(x)/ f’(x)3 .

39. Using this we have the second-order condition is satisfied and

40. Separating equilibrium

41. Equilibrium

42. Separating Equilibrium • Relatively incompetent experts would be willing to say that they are more confident than they are to be perceived as more competent than they are. • But, relatively competent experts avoid being imitated (and thus be perceived as less competent than they are) by saying they are more competent than they are. • It is less costly for a competent expert to exaggerate his competency because he is less likely to be wrong. So, relatively competent experts avoid being imitated.

43. Pooling part There is an upper bound on how confident you can be. So there is a region where relatively competent experts cannot separate themselves.