Ambiguity Attitudes for Real-World Sources: Field Evidence from a Large Sample of Investors

Show that ambiguity aversion helps explain low household stock market participation


Ambiguity
"Since Keynes (1921) and Knight (1921) it has been understood that economists should look into ambiguity (unknown probabilities) more than risk (known probabilities).Yet it took till the end of the 1980s before people (Gilboa and Schmeidler) came clever enough to invent such models, because this invention took exceptional creativity.As things go, it then takes decades before the ideas get generally understood and applied, which is happening today, as an important part of the behavioral approach."Peter Wakker

" " Ambiguity
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Things that cannot be explained by traditional risk models.➢ Ambiguity aversion tends to arise when people feel relatively unknowledgeable or incompetent about the source of ambiguity.
Existing evidence about ambiguity attitudes uses artificial Ellsberg urns or student samples.

Our Research:
❑ Measures ambiguity attitudes for relevant natural sources: The matching probability is the known probability of winning at which the respondent is indifferent between Option A (winning €15 if the event happens) and Option B (winning €15 with known chance).

Control for Subjective Beliefs
The matching probabilities of an event and its complement depends in exactly opposite ways on the unknown subjective probability P(E1).
• Subjective beliefs will be cancelled out in the process • Three single events • The tendency to treat all uncertain events as 50-50%, ignoring the likelihood of events.
• Insensitivity, Index a

Findings
Majority of investors is ambiguity averse for investments, but aversion is not universal.
" " Some people are ambiguity averse, some are seeking.
Findings: Ambiguity Aversion, Index b

Findings: Ambiguity Aversion for Investments
• Majority of investors is ambiguity averse for investments, but aversion is not universal.
• Lots of heterogeneity between subjects.

Findings: Ambiguity Aversion for Investments
Findings: Ambiguity Aversion for Investments • Ambiguity aversion is highly correlated within subjects and driven by one factor.
• Supports theoretical models where the investor's ambiguity aversion is modeled by one preference parameter (e.g., alpha, index b) Findings: A-Insensitivity, Index a Findings: A-Insensitivity, Index a • Most investors (≥ 80%) are insensitive to event likelihoods, with Index a > 0.
• About 66% of the investors have index a between 0 and 1.This supports an interpretation of index a as perceived ambiguity.
Findings: A-Insensitivity, Index a Findings: Perceived Ambiguity about Investments • Perceived Ambiguity about the 4 investments tends to differ more depending on the specific source considered (not driven by 1 factor).
• Supports theoretical models where the investor's perceived level of ambiguity is different for each investment (e.g.familiar stock, index, Bitcoin, etc.) Mean of b and a index

Panel regression of b and a index on other variables
• Ambiguity Aversion positively related to Risk Aversion (r = 0.49), but not with education, suggesting it is a preference component.
• Perceived Ambiguity is lower for people with higher education and better financial literacy, suggesting it is a cognitive component.

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αMin PϵQ E P [U(W;a)] + (1-α)Max PϵQ E P [U(W;a)] } ◼ Q is a set of prior probability distributions ◼ α ϵ [0, 1] is the ambiguity aversion parameter Maximize expected utility over all actions a, using a mixture of the best and worst probability distribution  Ghirardato, Maccheroni and Marinacci (2004) Prior Set Decision maker has degree of confidence (1 − δ) in his reference probability distribution π ◼ C δ is a set of prior probability distributions ◼ π is the reference probability distribution ◼ (1 − δ) is confidence level in the reference distribution, while 0 ≤ δ ≤ 1 is the perceived level of ambiguity.Proposed in: Chateauneuf,Eichberger and Grant (2007)

subjective beliefs, using Baillon et al. (2018)
A: Win €15 if the AEX index decreases by 4% or more in 1 month time A: Win €15 if the AEX does n ot decrease by 4% or more Show that ambiguity aversion helps explain low household stock market participation, low equity fractions and low foreign stock ownership Abdellaoui, Baillon, Placido & Wakker (AER, 2011) ◼ Measure weighting functions for natural sources ◼ Introduce index b and index a ◼ Method requires measuring utility and probability weighting functions to isolate ambiguity attitudes ◼ Measure ambiguity aversion with matching probs.◼ Ellsberg urns, Dutch general population  Dimmock, Kouwenberg, Mitchell & Peijnenburg (JRU, 2015) ◼ Estimate α-MaxMin model and perceived ambig.() ◼ Ellsberg urns, US general population  Dimmock, Kouwenberg, Mitchell & Peijnenburg (JFE, 2016) ◼ ◼ Ellsberg urns, US general population Related Literature  ◼ Student sample  Baillon, Huang, Selim & Wakker (Econometrica, 2018) ◼ Measure ambiguity aversion for natural sources ◼ New simple method that controls for beliefs ◼ Student sample