Experiments on Risk Taking and Evaluation Periods Misread as Evidence of Myopic Loss Aversion Ganna Pogrebna June 30, 2007 Experiments on Risk Taking and Evaluation Periods Misread as Evidence of Myopic Loss Aversion Blavatskyy, Pavlo and Ganna Pogrebna (2007) “Experiments on Risk Taking and Evaluation Periods Misread as Evidence of Myopic Loss Aversion”

Presentation Overview Introduction Introduction Experimental evidence Experimental evidence Gneezy and Potters (QJE, 1997) Gneezy and Potters (QJE, 1997) Haigh and List (JF, 2005) Haigh and List (JF, 2005) Langer and Weber (JEBO, 2005) Langer and Weber (JEBO, 2005) Bellemare et al. (EL, 2005) Bellemare et al. (EL, 2005) Reexamination of experimental results Reexamination of experimental results Discussion Discussion Conclusion Conclusion

Introduction Bernartzi and Thaler (1995) propose MLA as an explanation for equity premium puzzle Bernartzi and Thaler (1995) propose MLA as an explanation for equity premium puzzle MLA combines two behavioral concepts: MLA combines two behavioral concepts: Loss aversion Loss aversion Mental accounting (how often evaluate financial outcomes) Mental accounting (how often evaluate financial outcomes) MLA: MLA: lotteries with positive EV and a possibility of a loss lotteries with positive EV and a possibility of a loss If frequently evaluated – losses are more likely to be detected… If frequently evaluated – losses are more likely to be detected… … which averts loss averse investors … which averts loss averse investors

Experimental Evidence Subjects choose how much of their endowment ($1-$4) to invest into a risky lottery: Subjects choose how much of their endowment ($1-$4) to invest into a risky lottery: If x invested, lottery yields –x with prob. 2/3 and 2.5x with prob. 1/3 If x invested, lottery yields –x with prob. 2/3 and 2.5x with prob. 1/3 Two treatments: Two treatments: (H) make 9 investment decisions in 9 rounds (H) make 9 investment decisions in 9 rounds (L) make 3 investment decisions each binding for 3 consecutive rounds (only cumulative earnings for three rounds are observed) (L) make 3 investment decisions each binding for 3 consecutive rounds (only cumulative earnings for three rounds are observed)

Treatment H Individual choice pattern Number (percentage) of subjects Gneezy and Potters (1997) Langer and Weber (2005) Haigh and List (2005), students Haigh and List (2005), traders Invest 100% of endowment in the majority of rounds11 7 (17.1 %) 2 (12.5%) 5 (15.7 %) 6 (22.2 %) Invest 1%-99% of endowment in the majority of rounds 27 (65.8 %) 13 (81.2%) 25 (78.1 %) 17 (63.0 %) Invest 0% of endowment in the majority of rounds 4 (9.8 %) 1 (6.3%) 1 (3.1 %) 2 (7.4 %) Other 3 (7.3 %) 0 (0.0%) 1 (3.1 %) 2 (7.4 %) 11 Majority is defined as 5 rounds for experiments of Gneezy and Potters (1997) and Haigh and List (2005) and 10 rounds for the experiment of Langer and Weber (2005).

Treatment L Individual choice pattern Number (percentage) of subjects Gneezy and Potters (1997) Langer and Weber (2005) Haigh and List (2005), students Haigh and List (2005), traders Invest 100% of endowment in the majority of rounds 15 (35.7 %) 3 (15.0%) 6 (18.8 %) 10 (37.0 %) Invest 1%-99% of endowment in the majority of rounds 27 (64.3 %) 17 (85.0%) 26 (81.2 %) 17 (63.0 %) Invest 0% of endowment in the majority of rounds 0 (0.0 %) 0 (0.0%) 0 (0.0 %) 0 (0.0 %)

Observation In the majority of rounds subjects invest an intermediate fraction of their initial endowment. In the majority of rounds subjects invest an intermediate fraction of their initial endowment. Only a handful of subjects abstain from betting. Only a handful of subjects abstain from betting. 12%-22% (15%-37%) of subjects consistently bet all their endowment on the risky lottery in treatment H (L). 12%-22% (15%-37%) of subjects consistently bet all their endowment on the risky lottery in treatment H (L). Let us now focus on subjects who consistently bet an intermediate fraction of their endowment on the risky lottery. Let us now focus on subjects who consistently bet an intermediate fraction of their endowment on the risky lottery.

Theoretical Prediction An individual betting amount x on the lottery in treatment H receives utility An individual betting amount x on the lottery in treatment H receives utility An individual betting amount x on the lottery in treatment H obtains utility An individual betting amount x on the lottery in treatment H obtains utility Let Let and and

Predicted Behavior in Treatments H and L According to MLA Index of loss aversion Betting on the risky lottery in treatment H everything anythingnothing Betting on the risky lottery in treatment L everything anythingnothing

Testable Implications A. % of subjects, who bet all their endowment on the risky lottery, is higher in treatment L than in treatment H; - confirmed B. % of subjects, who abstain from betting, is higher in treatment H than in L; - confirmed C. % of subjects, who bet all their endowment in treatment L, is higher than the percentage of subjects, who bet an intermediate fraction of endowment in treatment H; - violated D. % of subjects, who bet nothing in treatment H, is higher than the percentage of subjects, who bet an intermediate fraction of their endowment in treatment L. - violated

Inconsistency The majority of subjects bet an intermediate fraction of their endowment The majority of subjects bet an intermediate fraction of their endowment The fraction of subjects who consistently bet an intermediate fraction of their endowment is nearly identical across two treatments The fraction of subjects who consistently bet an intermediate fraction of their endowment is nearly identical across two treatments Between 65% and 85% across different experiments Between 65% and 85% across different experiments Their intermediate bets are not significantly different across two treatments (except for the field experiment of Haigh and List (2005)). Their intermediate bets are not significantly different across two treatments (except for the field experiment of Haigh and List (2005)).

Inconsistency, continued MLA can explain this finding only if for the majority of subjects in both treatments. MLA can explain this finding only if for the majority of subjects in both treatments. But for that we need to assume unconventional parameterizations of cumulative prospect theory But for that we need to assume unconventional parameterizations of cumulative prospect theory In contradiction with the existing experimental evidence (e.g. Tversky and Kahneman (1992), Abdellaoui (2000)). In contradiction with the existing experimental evidence (e.g. Tversky and Kahneman (1992), Abdellaoui (2000)). Moreover in this case MLA cannot explain implications A and B that apparently lead to statistically significant difference between aggregate choice patterns in treatments H and L. Moreover in this case MLA cannot explain implications A and B that apparently lead to statistically significant difference between aggregate choice patterns in treatments H and L.

Discussion Decreasing risk aversion Decreasing risk aversion Mixture model Mixture model Fechner model of random errors Fechner model of random errors Financial asset pricing model Financial asset pricing model

Fechner model of random errors

FMRE, continued Fechner model suggests that an individual evaluates risky lotteries according to a deterministic decision theory, but this evaluation is affected by random errors. Fechner model suggests that an individual evaluates risky lotteries according to a deterministic decision theory, but this evaluation is affected by random errors. The smaller the difference between two lotteries in terms of utility, the more likely are random errors to reverse deterministic preferences. The smaller the difference between two lotteries in terms of utility, the more likely are random errors to reverse deterministic preferences. A simple model of expected value maximization combined with a Fechner model of random errors explains the experimental data. A simple model of expected value maximization combined with a Fechner model of random errors explains the experimental data.

FMRE, continued Consider an individual who places bets in both treatments according to a simple algorithm. Starting from status quo, she compares betting zero versus betting a fraction of her endowment. Consider an individual who places bets in both treatments according to a simple algorithm. Starting from status quo, she compares betting zero versus betting a fraction of her endowment. According to the Fechner model of random errors (e.g. Fechner (1860)) an individual prefers to abstain from betting rather than to bet in treatment H if According to the Fechner model of random errors (e.g. Fechner (1860)) an individual prefers to abstain from betting rather than to bet in treatment H if And in treatment L if And in treatment L if

FMRE, continued The chance of observing zero bet is The chance of observing zero bet is H: H: L: L: Since for any positive Since for any positive the likelihood that an individual abstains from betting is higher in H than L. the likelihood that an individual abstains from betting is higher in H than L. probability that an individual bets 100% is H: probability that an individual bets 100% is H: and L: and L: an individual is more likely to invest 100% in L rather than in H. an individual is more likely to invest 100% in L rather than in H.

FMRE, continued Probability that an individual bets an intermediate fraction of her endowment is Probability that an individual bets an intermediate fraction of her endowment is H: H: L: L: Which of these two probabilities is larger depends on the additional assumptions about the step size and the function. Which of these two probabilities is larger depends on the additional assumptions about the step size and the function. Chances of observing an intermediate bet can be of a similar magnitude in both treatments. Chances of observing an intermediate bet can be of a similar magnitude in both treatments.

Financial asset pricing model

Conclusion We reexamine the experimental evidence on risk taking and evaluation periods. We reexamine the experimental evidence on risk taking and evaluation periods. Behavioral patterns of the majority of subjects contradict to the MLA explanation: Behavioral patterns of the majority of subjects contradict to the MLA explanation: Subjects invest intermediate fractions of their endowment Subjects invest intermediate fractions of their endowment These intermediate bets do not appear to vary greatly across treatments with different length of evaluation period. These intermediate bets do not appear to vary greatly across treatments with different length of evaluation period. Alternative explanations Alternative explanations

Conclusion, continued Experiments on risk taking and evaluation periods have been incorrectly interpreted as evidence of MLA. (critique of loss aversion literature by Plott and Zeiler (2005, 2006)). Experiments on risk taking and evaluation periods have been incorrectly interpreted as evidence of MLA. (critique of loss aversion literature by Plott and Zeiler (2005, 2006)). The question of comparing expected utility theory and MLA approaches in the laboratory remains unanswered. The question of comparing expected utility theory and MLA approaches in the laboratory remains unanswered. There is much work to be done in developing a model, which would allow to explain the data on risk taking and evaluation periods. There is much work to be done in developing a model, which would allow to explain the data on risk taking and evaluation periods.