Asset Pricing in Financial Markets

Transcription

1 Cognitive Biases, Ambiguity Aversion and Asset Pricing in Financial Markets E. Asparouhova, P. Bossaerts, J. Eguia, and W. Zame April 17, 2009

2 The Question

3 The Question Do cognitive biases (directly) affect asset prices?

4 The Question Do cognitive biases (directly) affect asset prices? Evidence abound that people are subject to cognitive biases. In the psychology literature, biases have been documented in experiments where subjects have no choice but to directly reveal them.

5 The Question Do cognitive biases (directly) affect asset prices? Evidence abound that people are subject to cognitive biases. In the psychology literature, biases have been documented in experiments where subjects have no choice but to directly reveal them. In financial markets agents biases, even if revealed in choices, might not be directly revealed in prices, if at all

6 Motivation

7 Motivation 1 Consider agents who improperly Bayesian update.

8 Motivation 1 Consider agents who improperly Bayesian update. 2 Those agents are likely to face market prices that contradict their computations. How do agents react to those prices?

9 Motivation 1 Consider agents who improperly Bayesian update. 2 Those agents are likely to face market prices that contradict their computations. How do agents react to those prices? 3 Well known that when confronted with conflicting expert opinion, people perceive ambiguity. Fox and Tversky (1995) refer to the phenomenon as comparative ignorance.

10 Motivation 1 Consider agents who improperly Bayesian update. 2 Those agents are likely to face market prices that contradict their computations. How do agents react to those prices? 3 Well known that when confronted with conflicting expert opinion, people perceive ambiguity. Fox and Tversky (1995) refer to the phenomenon as comparative ignorance. 4 We conjecture that in financial markets, comparative ignorance emerges when traders face market prices that contradict their beliefs.

11 Motivation

12 Motivation 5 Agents who perceive ambiguity and are averse to it (Ellsberg (1961)) actively seek ambiguity neutral positions for a wide range of prices.

13 Motivation 5 Agents who perceive ambiguity and are averse to it (Ellsberg (1961)) actively seek ambiguity neutral positions for a wide range of prices. Confirmed in experiments (Bossaerts, Ghirardato, Guarnaschelli, Zame (2008)).

14 Motivation 5 Agents who perceive ambiguity and are averse to it (Ellsberg (1961)) actively seek ambiguity neutral positions for a wide range of prices. Confirmed in experiments (Bossaerts, Ghirardato, Guarnaschelli, Zame (2008)). 6 As a result, the cognitive biases that cause agents to perceive ambiguity in the first place, while reflected in portfolio choices, would not be directly reflected in prices.

15 Motivation 5 Agents who perceive ambiguity and are averse to it (Ellsberg (1961)) actively seek ambiguity neutral positions for a wide range of prices. Confirmed in experiments (Bossaerts, Ghirardato, Guarnaschelli, Zame (2008)). 6 As a result, the cognitive biases that cause agents to perceive ambiguity in the first place, while reflected in portfolio choices, would not be directly reflected in prices.

16 Hypotheses

17 Hypotheses 1 Some agents are insensitive to prices

18 Hypotheses 1 Some agents are insensitive to prices 2 Those agents hold ambiguity neutral portfolios

19 Hypotheses 1 Some agents are insensitive to prices 2 Those agents hold ambiguity neutral portfolios 3 Those agents trade less that price-sensitive agents

20 Hypotheses 1 Some agents are insensitive to prices 2 Those agents hold ambiguity neutral portfolios 3 Those agents trade less that price-sensitive agents 4 Price quality improves the higher the number of price-sensitive agents

21 Hypotheses 1 Some agents are insensitive to prices 2 Those agents hold ambiguity neutral portfolios 3 Those agents trade less that price-sensitive agents 4 Price quality improves the higher the number of price-sensitive agents

22 Experiment and Results

23 Experiment and Results In experiments subjects trade two Arrow-Debreu assets whose value is determined by a difficult Bayesian updating problem.

24 Experiment and Results In experiments subjects trade two Arrow-Debreu assets whose value is determined by a difficult Bayesian updating problem. We use a Monty Hall-like games to determine the payoffs of the assets.

25 Experiment and Results In experiments subjects trade two Arrow-Debreu assets whose value is determined by a difficult Bayesian updating problem. We use a Monty Hall-like games to determine the payoffs of the assets. We find that many agents cannot solve the updating problem (as proxied by price-insensitivity)

26 Experiment and Results In experiments subjects trade two Arrow-Debreu assets whose value is determined by a difficult Bayesian updating problem. We use a Monty Hall-like games to determine the payoffs of the assets. We find that many agents cannot solve the updating problem (as proxied by price-insensitivity) Those who do not solve the problem achieve (significantly) more balanced positions and trade (marginally) less than the subjects who solve the problem.

27 Experiment and Results In experiments subjects trade two Arrow-Debreu assets whose value is determined by a difficult Bayesian updating problem. We use a Monty Hall-like games to determine the payoffs of the assets. We find that many agents cannot solve the updating problem (as proxied by price-insensitivity) Those who do not solve the problem achieve (significantly) more balanced positions and trade (marginally) less than the subjects who solve the problem. The higher the number of subjects who can solve the problem, the closer the prices to their theoretical levels.

28 Literature Kluger and Wyatt (2004) conjecture that prices are right if at least two agents know the prices due to Bertrand competition. Coval and Shumway (2005) present evidence of short term effect of behavioral biases on prices on the Chicago Board of Trade. Maciejovsky and Budescu (2005); Bossaerts, Copic, and Meloso (2008) on financial markets facilitating social cognition.

29 Ambiguity Aversion

30 Ambiguity Aversion Two-date, two-state economy. States r(ed) and b(lack); corresponding Arrow securities R and B, in equal aggregate supply.

31 Ambiguity Aversion Two-date, two-state economy. States r(ed) and b(lack); corresponding Arrow securities R and B, in equal aggregate supply. Objective probabilities of the two states not common knowledge but can be computed; π R and π B.

32 Ambiguity Aversion Two-date, two-state economy. States r(ed) and b(lack); corresponding Arrow securities R and B, in equal aggregate supply. Objective probabilities of the two states not common knowledge but can be computed; π R and π B. If all agents are expected utility maximizers, and subjective probabilities equal the objective probabilities, prices equal expected values (which equal the objective probabilities).

33 Ambiguity Aversion Two-date, two-state economy. States r(ed) and b(lack); corresponding Arrow securities R and B, in equal aggregate supply. Objective probabilities of the two states not common knowledge but can be computed; π R and π B. If all agents are expected utility maximizers, and subjective probabilities equal the objective probabilities, prices equal expected values (which equal the objective probabilities). If all agents are expected utility maximizers but with different subjective probabilities, prices depend on the vector of subjective probabilities

34 Ambiguity Aversion

35 Ambiguity Aversion If some agents perceive ambiguity, we assume they have α max min preferences, so that they maximize: U(R, B) = α min{u(r), u(b)}+(1 α) max{u(r), u(b)}

36 Ambiguity Aversion If some agents perceive ambiguity, we assume they have α max min preferences, so that they maximize: U(R, B) = α min{u(r), u(b)}+(1 α) max{u(r), u(b)} An agent with α max min preferences acts as if with probability α, the worst possible state will occurs, and with probability 1 α, the best possible state occurs.

37 Ambiguity Aversion If some agents perceive ambiguity, we assume they have α max min preferences, so that they maximize: U(R, B) = α min{u(r), u(b)}+(1 α) max{u(r), u(b)} An agent with α max min preferences acts as if with probability α, the worst possible state will occurs, and with probability 1 α, the best possible state occurs. The FOC with the α max min preferences imply that ambiguity averse agents (α > 0.5) balance their portfolio for any price vector in the interval [ 1 α, α ]. α 1 α

38 Assumptions Agents who compute the correct probabilities do not feel comparative ignorance and do not adopt α max min preferences at any price level they face.

39 Assumptions Agents who compute the correct probabilities do not feel comparative ignorance and do not adopt α max min preferences at any price level they face. Halevy (2007): 95% of agents who fail at the standard calculation task of reducing compound lotteries avoid ambiguity in the Ellsberg experiment, whereas only 4% of agents who correctly reduce compound lotteries exhibit this behavior.

40 Assumptions Agents who compute the correct probabilities do not feel comparative ignorance and do not adopt α max min preferences at any price level they face. Halevy (2007): 95% of agents who fail at the standard calculation task of reducing compound lotteries avoid ambiguity in the Ellsberg experiment, whereas only 4% of agents who correctly reduce compound lotteries exhibit this behavior. Proportion ρ of agents who compute wrong probabilities feel comparative ignorance when confronted with market prices that do not correspond to their subjective probabilities. Proportion 1 ρ act according to their biased subjective probabilities.

41 Implications If (some of) the individuals who cannot compute the correct probabilities become price insensitive and those who know how to compute the probabilities change the composition of their portfolio according to the prevailing prices then:

42 Implications If (some of) the individuals who cannot compute the correct probabilities become price insensitive and those who know how to compute the probabilities change the composition of their portfolio according to the prevailing prices then: The deviation of the market price from the expected value of the asset (mispricing) is negatively related to the number of price sensitive subjects.

43 Implications If (some of) the individuals who cannot compute the correct probabilities become price insensitive and those who know how to compute the probabilities change the composition of their portfolio according to the prevailing prices then: The deviation of the market price from the expected value of the asset (mispricing) is negatively related to the number of price sensitive subjects. Given some mispricing, price insensitive subjects hold more balanced portfolios than price insensitive subjects.

44 Implications If (some of) the individuals who cannot compute the correct probabilities become price insensitive and those who know how to compute the probabilities change the composition of their portfolio according to the prevailing prices then: The deviation of the market price from the expected value of the asset (mispricing) is negatively related to the number of price sensitive subjects. Given some mispricing, price insensitive subjects hold more balanced portfolios than price insensitive subjects. Price insensitive subjects trade less than price sensitive subjects.

45 The Securities Two Arrow securities, Red and Black; Bond

46 The Securities Two Arrow securities, Red and Black; Bond Two states of the world: red and black.

47 The Securities Two Arrow securities, Red and Black; Bond Two states of the world: red and black. The color of the last card in a game of cards determines the state.

48 The Securities Two Arrow securities, Red and Black; Bond Two states of the world: red and black. The color of the last card in a game of cards determines the state. Last Card Red Stock Black Stock Bond red black Trading only in Red Stock and Bond; endowments in all 3 securities.

49 The Card Game

50 The Card Game Four cards face down

51 The Card Game Four cards face down One card randomly discarded

52 The Card Game Four cards face down One card randomly discarded One card face up but never

53 The Card Game Four cards face down One card randomly discarded One card face up but never Last card randomly chosen

54 The Card Game Four cards face down One card randomly discarded TRADE PERIOD 1 One card face up but never Last card randomly chosen

55 The Card Game Four cards face down One card randomly discarded TRADE PERIOD 1 One card face up but never TRADE PERIOD 2 Last card randomly chosen

56 Timeline Trade Trade

57 Timeline P(Red)=Prob(Last Card is Red) Trade Trade

58 Timeline P(Red)=Prob(Last Card is Red) Trade P(Red)= Trade P(Red)=

59 Timeline P(Red)=Prob(Last Card is Red) Trade P(Red)= 7 12 Trade P(Red)=

60 Timeline P(Red)=Prob(Last Card is Red) Trade P(Red)= 7 12 Trade P(Red)= 11 16

61 Experimental Sessions 20 subjects per session 3 minute trading periods Market for Red Stock and Bond open; Black market always closed. Initial endowment Holdings carry over from Period 1 to Period 2 of trading

62 Trading: jmarkets

63 Prices: UCLA

64 Prices: Utah

65 Prices: Utah-Caltech

66 Identifying Price-Sensitivity Subjects Correct Price = Expected Payoff of Red Stock. MISPRICE=Market Price-Correct Price. For each subject and each treatment perform the regression

67 Identifying Price-Sensitivity Subjects Correct Price = Expected Payoff of Red Stock. MISPRICE=Market Price-Correct Price. For each subject and each treatment perform the regression RedStock,m = a + b MISPRICE m + e m

68 Identifying Price-Sensitivity Subjects Correct Price = Expected Payoff of Red Stock. MISPRICE=Market Price-Correct Price. For each subject and each treatment perform the regression RedStock,m = a + b MISPRICE m + e m Misprice m is avg. mispricing in minute m of trading.

69 Identifying Price-Sensitivity Subjects Correct Price = Expected Payoff of Red Stock. MISPRICE=Market Price-Correct Price. For each subject and each treatment perform the regression RedStock,m = a + b MISPRICE m + e m Misprice m is avg. mispricing in minute m of trading. RedStock,m is change in holdings in minute m.

70 Identifying Price-Sensitivity Subjects Correct Price = Expected Payoff of Red Stock. MISPRICE=Market Price-Correct Price. For each subject and each treatment perform the regression RedStock,m = a + b MISPRICE m + e m Misprice m is avg. mispricing in minute m of trading. RedStock,m is change in holdings in minute m. Those who know the correct probabilities have b < 0

71 Identifying Price-Sensitivity Subjects Correct Price = Expected Payoff of Red Stock. MISPRICE=Market Price-Correct Price. For each subject and each treatment perform the regression RedStock,m = a + b MISPRICE m + e m Misprice m is avg. mispricing in minute m of trading. RedStock,m is change in holdings in minute m. Those who know the correct probabilities have b < 0 Those who do not know probabilities have b = 0

72 Identifying Price-Sensitivity Subjects Correct Price = Expected Payoff of Red Stock. MISPRICE=Market Price-Correct Price. For each subject and each treatment perform the regression RedStock,m = a + b MISPRICE m + e m Misprice m is avg. mispricing in minute m of trading. RedStock,m is change in holdings in minute m. Those who know the correct probabilities have b < 0 Those who do not know probabilities have b = 0 We use the t-statistics of the regression to determine price sensitivity.

73 Mispricing by Treatment Experiment Treatment Mean Absolute Number of (T < 1.65) Number of (T > 1.9) Mispricing Subjects Subjects Caltech Utah Utah-Caltech UCLA Utah Utah-Caltech

74 Mispricing and Price-sensitivity Result The correlation between the number of price-sensitive subjects and average absolute mispricing equals (st. error=0.146). Thus, the larger the number of subjects who appear to know the probabilities, the closer the prices to their theoretical levels.

75 End-of-game Imbalances by Treatment I i = a + bx i + e i I i = Holdings Red Holdings Black of subject i. X i = t i M i. t i =t-stat from RedStock,t = a + b MISPRICE t + e t M i = MISPRICE i.

76 End-of-game Imbalances by Treatment I i = a + bx i + e i I i = Holdings Red Holdings Black of subject i. X i = t i M i. t i =t-stat from RedStock,t = a + b MISPRICE t + e t M i = MISPRICE i. Theory: b < 0.

77 End-of-game Imbalances by Treatment b b Treatment all t i (t i > 1.9) included excluded (0.159) (0.172) (0.099) (0.117) (0.094) (0.125) (0.188) (0.228)

78 End-of-game Imbalances: All Treatments I it = I i + ɛ it, I i = E(I it i) X it = X i + ξ it, X i = E(X it i) I i = a + bx i + e i corr(ɛ it, ξ it ) = ρ b b All all t i (t i > 1.9) Treatments included excluded (0.646) (0.762) R

79 Mid-game Imbalances by Treatment b b Treatment all t i (t i > 1.9) included excluded (0.127) (0.132) (0.082) (0.100) (0.075) (0.099) (0.167) (0.208)

80 Mid-game Imbalances by Treatment b b All all t i (t i > 1.9) Treatments included excluded (0.583) (0.777) R

81 Imbalance Price-sensitivity Relation Result Consistent with the the prediction of the theory, price-insensitive subjects hold more balanced portfolios than price-sensitive subjects both mid-game and at conclusion of the trading periods.

82 Number of Trades by Treatment N i = a + bx i + e i b b Treatment all t i (t i > 1.9) included excluded (0.101) (0.280) (0.146) (0.190) (0.174) (0.205)) (0.291) (0.367)

83 Number of Trades: All Treatments b b All all t i (t i > 1.9) Treatments included excluded (1.135) (1.398) R

84 Number of Trades Price-sensitivity Relation Result The hypothesis that numbers of trades of price sensitive and price insensitive subjects are equal cannot be rejected.

85 In Conclusion... Hypothesis Cognitive biases may not directly affect prices in financial markets because they may translate into perception of ambiguity, and hence, price insensitivity. Evidence Large number of price insensitive subjects exists Price insensitive tend to hold balanced portfolios The price quality improves with the number of price sensitive subjects.