Decisions under uncertainty Flashcards
What is the Allais Paradox and what does it reveal about decision-making under uncertainty?
The Allais Paradox is a choice problem that violates the independence axiom of expected utility theory. People prefer a certain outcome in one scenario (Gamble A over B) but then switch preferences in a similar setup (Gamble D over C), showing inconsistency. It demonstrates that individuals do not always follow expected utility maximisation.
What is the Ellsberg Paradox and what behaviour does it illustrate?
The Ellsberg Paradox involves choosing between bets with known and unknown probabilities. Most people prefer the bet with known probability (Gamble A) and simultaneously choose the ambiguous one with less unknown risk (Gamble D), revealing ambiguity aversion—people prefer known risks over unknown ones.
What did Kahneman, Knetsch, & Thaler (1990) find about the endowment effect?
They found that people value items more once they own them. In experiments, participants with mugs demanded more to give them up (WTA) than others were willing to pay (WTP), contrary to standard theory. This supports the endowment effect and highlights loss aversion.
How did Thaler (1980) explain the endowment effect?
Thaler explained the endowment effect as a manifestation of loss aversion: giving up an item is seen as a loss, which is more painful than the pleasure of gaining it. This causes owners to value items more highly than non-owners.
What is the equity premium puzzle and how did Benartzi and Thaler (1997) explain it?
The equity premium puzzle is the observation that stocks offer much higher returns than bonds, more than standard risk aversion can explain. Benartzi and Thaler used prospect theory to show that myopic loss aversion—frequent evaluation of outcomes and loss aversion—makes investors demand high premiums for risky assets like stocks.
What is the disposition effect in behavioural finance?
It is the tendency for investors to sell winning investments too early and hold onto losing ones too long. This contradicts rational investment theory and is explained by prospect theory, where losses are more psychologically painful, making people reluctant to realise them.
What did Odean (1998) find about the disposition effect?
By analysing trading records from 10,000 accounts, Odean found that investors consistently realised gains more than losses, supporting the disposition effect and the idea that people are averse to recognising financial losses.
How does prospect theory explain investor behaviour in the disposition effect?
When a stock gains, it moves into the concave (risk-averse) part of the value function, prompting selling. If it loses, it’s in the convex (risk-seeking) part, encouraging investors to hold on, hoping it recovers. This aligns with the asymmetric value function in prospect theory.
What was the key finding of Tanaka, Camerer, & Nguyen (2010) in Vietnam?
They found that risk and loss aversion vary by demographics and income. Poorer villages showed more loss aversion. Their findings rejected expected utility theory and supported prospect theory, with estimated parameters σ ≈ 0.6, α ≈ 0.74, and λ ≈ 2.63—close to values from Kahneman & Tversky.
What is the significance of the parameters σ, α, and λ in prospect theory?
σ measures the concavity of the value function (risk attitude), α captures the probability weighting (how people perceive probabilities), and λ reflects the degree of loss aversion. Values from Tanaka et al. (2010) support prospect theory: people distort probabilities and are more sensitive to losses.
What are the four axioms of Expected Utility Theory (EUT)?
- Completeness: Preferences are defined between any two lotteries.
- Transitivity: If X ≻ Y and Y ≻ Z, then X ≻ Z.
- Continuity: If X ≻ Y ≻ Z, there is some mix of X and Z that is equally preferred to Y.
- Independence: Preference between X and Y remains unchanged if they are both mixed with a third lottery Z in the same proportions.
Why is the Independence Axiom often violated in real-world decision-making?
It assumes preferences are stable under probabilistic mixtures, but examples like the Allais Paradox show that people change preferences when certainty is introduced, revealing an overweighting of certain outcomes—a violation known as the ‘certainty effect’.
How is Expected Utility (EU) calculated, and how does it differ from Expected Value (EV)?
EU = Σpᵢu(xᵢ), where u(xᵢ) is the utility of outcome xᵢ and pᵢ its probability. EV = Σpᵢxᵢ. EU incorporates risk preferences via the utility function, while EV treats all outcomes at face value.
What is the shape of the Prospect Theory value function and what does it imply?
The value function is concave for gains (risk aversion), convex for losses (risk seeking), and steeper for losses than gains (loss aversion). It reflects reference dependence and diminishing sensitivity.
What is the mathematical form of the Prospect Theory value function used by Tanaka et al. (2010)?
v(x) = x^σ for gains (x > 0); v(x) = -λ(-x)^σ for losses (x < 0). σ measures curvature (risk aversion); λ is the loss aversion coefficient.
What is the weighting function in Prospect Theory and what shape does it have?
π(p) = 1 / exp[ln(1/p)^α]. It is concave for small p and convex for larger p, meaning people overweight small probabilities and underweight larger ones. α < 1 implies deviation from EUT.
What is mental accounting and how does it deviate from rational choice?
Mental accounting refers to how people categorise and treat money differently depending on its source or intended use. For example, they may prefer segregating gains (viewing a £100 gift and a £50 lottery win separately) or aggregating losses (viewing a £100 ticket and £50 scam as a single £150 loss). This violates the fungibility of money.
Why does the Ron Weasley example illustrate decision-making under uncertainty?
Ron doesn’t know if there will be a quiz, so he must choose between uncertain outcomes (lotteries). His preferences depend on the expected utility of each action under uncertainty, showing how EUT is used to model such decisions.
What does it mean if a subject has α < 1 in the weighting function of Prospect Theory?
They distort probabilities: overweighting small probabilities and underweighting large ones. This shows deviation from objective probability and supports the non-linear weighting proposed by Prospect Theory.
How does ambiguity aversion explain the Ellsberg Paradox?
People prefer known risks (e.g. a red ball with known probability) over ambiguous ones (e.g. blue or yellow with unknown proportions), even when this contradicts EUT predictions. Ambiguity aversion is the preference for known probabilities over unknown ones.
