Prospect Theory – Gains, Losses & Risk Behavior

Introduction

Prospect Theory, developed by Daniel Kahneman and Amos Tversky (1979), revolutionized economics by describing how people actually make decisions under risk. It remains the most influential alternative to Expected Utility Theory and forms the foundation of modern behavioral finance.

Core Principles of Prospect Theory

Reference Dependence

The Breakthrough Insight

Traditional Finance (Expected Utility Theory):

• Utility defined over final wealth states
• Example: Two scenarios give you ₹1 million final wealth → Same utility

Prospect Theory:

• Value defined over gains and losses from a reference point
• Example: Gain of ₹50,000 (from ₹950K to ₹1M) feels different from losing ₹30,000 (from ₹1.03M to ₹1M)
• Both end at ₹1M, but how you got there matters psychologically

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Same ending (₹120K), different emotions! This violates EUT which says only final wealth matters.

Investment Implications

Purchase Price as Reference Point:

• Bought stock at ₹500 (reference point)
• Current price ₹400
• Psychological reality: Down ₹100 (loss!) → Hold hoping to break even
• Rational reality: Stock worth less than ₹400 fundamentally → Should sell

Mental Accounting: Different reference points for different "buckets"—retirement savings (long-term reference) vs emergency fund (short-term reference).

Loss Aversion

The Asymmetry

Key Finding: Losses hurt approximately 2-2.5 times more than equivalent gains feel good.

Mathematical Expression:

• Gain of ₹100: Value = +10 utils
• Loss of ₹100: Value = -25 utils (2.5x pain!)

Experimental Evidence:

Gamble	Acceptance Rate
50% win ₹100, 50% lose ₹100	15% (should be ~50% if symmetric)
50% win ₹200, 50% lose ₹100	45% (need 2:1 upside to accept!)
50% win ₹250, 50% lose ₹100	65% (2.5:1 typical threshold)

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Why Loss Aversion Exists

Evolutionary Psychology Explanation:

• In ancestral environment, losses threatened survival more than gains helped
• Food loss = potential starvation
• Territory loss = vulnerability to predators
• Gains were nice, but losses were dangerous

Result: Human brains evolved to weight losses heavily → Carried into modern financial decisions where it's often maladaptive.

Diminishing Sensitivity

The Value Function Shape

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Investment Behavior Consequences

Risk Aversion in Gains (Being Ahead):

• Stock up 30% from purchase → "Lock in gains, sell!"
• Behavior: Sell winners too early
• Outcome: Miss further upside (disposition effect)

Risk Seeking in Losses (Being Behind):

• Stock down 30% from purchase → "It could come back, I'll hold/double down!"
• Behavior: Hold or average down on losers
• Outcome: Throw good money after bad

Classic Error: "I'm not selling tillit gets back to my price!" (Risk-seeking in loss domain driven by diminishing sensitivity and loss aversion combination.)

Probability Weighting

How We Distort Probabilities

People don't weight probabilities linearly. Instead:

True Probability	Psychological Weight	Distortion
0.1% (1 in 1000)	Feels like 5-8%	Overweight by 50-80x!
1%	Feels like 5-6%	Overweight by 5-6x
10%	Feels like 14-16%	Slight overweight
50%	Feels like 40-45%	Underweight
90%	Feels like 84-87%	Underweight
99%	Feels like 95%	Underweight
99.9%	Feels like 91%	Massive underweight

Pattern:

• Small probabilities overweighted → Why agitatary tickets sell, terrorism fear
• Moderate probabilities underweighted → Why people underinsure realistic risks
• Near-certainty underweighted → Why 99% isn't treated as "basically certain"

Financial Market Examples

Lottery Stocks: Investors pile into penny stocks with tiny probability of 100x return.

• Rational: Expected value negative
• Behavioral: Overweight small probability of huge win → Makes terrible bets feel attractive

Insurance Demand: People buy insurance even when premiums exceed expected payout.

• Rational: Violation of EUT (should self-insure at fair odds)
• Behavioral: Overweight small probability of catastrophe → Willing to pay premium

IPO Oversubscription: Overweight small probability of "next Google" → Massive oversubscription (100x in India for hot IPOs).

The Four-Fold Pattern

Combining diminishing sensitivity and probability weighting gives Kahneman & Tversky's famous preference pattern:

Situation	Probability	Typical Choice	Explanation
Gains, Low Prob	Lottery (1% win ₹100K)	Risk-seeking (buy ticket)	Overweight small prob + dream of gain
Gains, High Prob	Sure ₹45K vs 90% of ₹50K	Risk-averse (take sure thing)	Certainty effect + concave value
Losses, Low Prob	1% lose ₹100K	Risk-averse(buy insurance)	Overweight small prob + fear of loss
Losses, High Prob	Sure -₹45K vs 90% of -₹50K	Risk-seeking (gamble!)	Avoid sure loss, convex value in losses

Investment Manifestation:

• Sell winners quickly (risk-averse in gains) → Disposition effect
• Hold losers hoping for bounce (risk-seeking in losses) → Disposition effect
• Buy lottery stocks (low prob gains, overweighted) → Overallocation to speculative investments
• Under-diversify (perceive portfolio loss as low prob) → Concentration risk

Implications for Investors

Individual Mistakes

Disposition Effect Quantified:

• Studies show investors sell winners 50-70% more readily than losers
• Cost: ~2-4% annual underperformance
• Driven by: Loss aversion + reference dependence

Break-Even Effect:

• Holding losing stocks until they return to purchase price
• Ignoring: Opportunity cost, new information, fundamentals

House Money Effect:

• After gains, take excessive risk ("playing with house money")
• Reality: All money is your money! Prior gains irrelevant to new decision

Portfolio Implications

Under-Diversification: Losses loom larger → Hold fewer stocks ("protect what I have").

Excessive Cash: Loss aversion → Keep too much idle cash (avoiding risk of stock losses).

Home Bias: Domestic stocks feel less risky (familiarity) → Overweight home market.

Using Prospect Theory Productively

For Investors

Reframe Decisions:

• Don't ask: "Did I lose money vs my purchase price?"
• Do ask: "If I had cash today, would I buy this stock at current price?"

Ignore Sunk Costs: Purchase price is irrelevant. Only forward-looking value matters.

Pre-Commit to Rules:

• "Rebalance to 60/40 when stocks drift >5% from target"
• "Stop-loss at -15% from purchase"
• Remove reference dependence from moment-to-moment decisions

For Financial Professionals

Frame Recommendations Carefully:

• Don't say: "This strategy could lose 10%"
• Do say: "This strategy protects 90% in worst case, gains typically 12%/year"

Avoid Loss-Framed Anchors: Don't remind clients of purchase prices during bear markets.

Automatic Rebalancing: Remove behavioral temptation by automating.

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Key Takeaways

• Prospect Theory: People evaluate outcomes as gains/losses from reference points, not final wealth
• Loss aversion: Losses hurt ~2-2.5x more than equivalent gains feel good
• Diminishing sensitivity: Concave for gains (risk-averse), convex for losses (risk-seeking)
• Probability weighting: Overweight small probabilities, underweight moderate/high ones
• Disposition effect: Combination of loss aversion + reference dependence → Sell winners, hold losers
• Applications: Explains insurance demand, lottery sales, stock trading patterns, IPO fr

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