Prospect theory Study Guide

📖 Core Concepts Prospect Theory – Behavioral model describing how people evaluate gains and losses relative to a reference point rather than final wealth. Reference Dependence – Outcomes are judged as gains or losses compared to a neutral benchmark (often status‑quo or expectation). Loss Aversion – Psychological pain of a loss ≈ 2 ×  pleasure of an equivalent gain. Value Function \(v(x)\) – S‑shaped: concave for gains (diminishing sensitivity → risk‑averse), convex for losses (diminishing sensitivity → risk‑seeking), steeper for losses. Probability‑Weighting Function \(\pi(p)\) – Inverse‑S curve: overweights small probabilities (\(\pi(p) > p\) for low p) and underweights large probabilities (\(\pi(p) < p\) for high p). Fourfold Pattern – Risk‑averse for moderate‑probability gains & low‑probability losses; risk‑seeking for low‑probability gains & moderate‑probability losses. Two‑Stage Decision Process – (1) Editing: set reference, order outcomes, label gains/losses. (2) Evaluation: compute weighted value of each prospect and choose the highest. 📌 Must Remember Loss aversion coefficient ≈ 2 (loss feels twice as bad as gain feels good). Value function: \(v(x) = \begin{cases} x^\alpha & x \ge 0\\ -\lambda (-x)^\beta & x < 0 \end{cases}\) with \(\lambda > 1\) (loss‑aversion), \(\alpha,\beta \in (0,1)\). Probability weighting: \(\pi(p) = \frac{p^\gamma}{[p^\gamma + (1-p)^\gamma]^{1/\gamma}}\) (Tversky‑Kahneman 1992) – \(\gamma < 1\) gives inverse‑S shape. Overall utility: \[ U = \sumi \pi(pi)\, v(xi) \] Fourfold risk attitudes – memorize the 2 × 2 matrix (gain vs loss × low vs high probability). Myopic Loss Aversion (MLA) – short‑term focus + loss aversion → investors over‑react to recent dips. 🔄 Key Processes Editing Stage Identify reference point (status‑quo, expectation). Classify each outcome as gain (\(xi>0\)) or loss (\(xi<0\)). Order outcomes by magnitude, combine similar prospects if allowed. Evaluation Stage Apply value function \(v(xi)\) to each outcome. Apply probability‑weighting \(\pi(pi)\) to each associated probability. Compute total prospect utility \(U = \sum \pi(pi) v(xi)\). Choose prospect with highest \(U\). 🔍 Key Comparisons Prospect Theory vs. Expected Utility Theory Reference: PT uses gains/losses relative to a point; EU uses final wealth. Risk attitudes: PT is concave for gains, convex for losses; EU’s curvature is uniform. Probability: PT distorts probabilities; EU treats them linearly. Loss Aversion vs. Endowment Effect Loss Aversion: General tendency to weigh losses > gains. Endowment Effect: Specific manifestation where ownership increases perceived value (a form of loss aversion). Description‑Experience Gap vs. Standard PT Description: Overweight rare events (as PT predicts). Experience: Tend to underweight rare events, opposite of PT’s probability weighting. ⚠️ Common Misunderstandings “Prospect Theory predicts rational choices.” – It describes actual (often irrational) behavior, not normative optimality. “The reference point is always zero.” – Reference is context‑dependent (status‑quo, expectations, aspirations). “Loss aversion means people always avoid losses.” – Because the value function is convex for losses, people may become risk‑seeking when facing potential losses. “Probability weighting only matters for tiny probabilities.” – It also underweights high probabilities, influencing decisions like insurance purchase. 🧠 Mental Models / Intuition “Gain‑Loss Lens” – Visualize outcomes on a mountain slope: gains on the gentle right slope (concave), losses on the steep left slope (convex). “Weighting Scale” – Small probabilities sit on a “magnifying glass” (overweighted), large probabilities on a “sieve” (underweighted). “Two‑Stage Funnel” – First, the funnel edits (filters) outcomes; second, it evaluates (adds weighted values). 🚩 Exceptions & Edge Cases Description‑Experience Gap – When probabilities are learned through sampling, rare events are underweighted (reverse of \(\pi(p)\) rule). Cross‑Cultural Variation – Parameters (\(\alpha,\beta,\lambda,\gamma\)) shift across societies; loss aversion may be weaker in collectivist cultures. Cumulative Prospect Theory – Extends original model to handle mixed prospects; weighting applied to cumulative probabilities rather than each \(pi\) individually. 📍 When to Use Which Insurance vs. Lottery Decision – Use PT’s overweighting of low‑probability losses to explain why people buy insurance (high \(\pi(p{1\%})\)). Investment Choices – Apply Myopic Loss Aversion when evaluating frequent portfolio monitoring vs. long‑term holding. Policy Design – Leverage probability weighting to predict response to low‑probability, high‑impact risks (e.g., disaster preparedness). 👀 Patterns to Recognize Fourfold Risk Pattern – Spot if a problem mentions low‑probability gain (risk‑seeking) or moderate‑probability loss (risk‑seeking). Reference Shift – Look for cues like “after a windfall” or “following a loss” indicating the reference point has moved. Overweighting Cue – Phrases such as “despite a 1 % chance” often signal PT’s probability distortion will dominate the decision. 🗂️ Exam Traps Trap 1: Assuming linear probabilities – Answer choices that treat \(p\) as linear ignore \(\pi(p)\); they are wrong under PT. Trap 2: Confusing risk‑aversion with loss aversion – Selecting “risk‑averse for all losses” is incorrect; PT predicts risk‑seeking for losses. Trap 3: Mis‑identifying the reference point – Answers that fix the reference at zero without context ignore the key PT premise. Trap 4: Ignoring the two‑stage process – Choosing an option that jumps straight to utility calculation without editing skips a crucial PT step. Trap 5: Overgeneralizing the fourfold pattern – Applying risk‑seeking to high‑probability gains (or risk‑averse to low‑probability losses) reverses PT predictions. --- If any section lacked sufficient source material, the placeholder “- Not enough information in source outline.” would be shown, but all headings above are fully supported by the provided outline.