Unit 3: Prospect Theory, Framing and Mental Accounting

Prospect Theory, Framing & Mental Accounting

1. Errors in Bernoulli’s Theory (Expected Utility Theory)

Bernoulli’s Expected Utility Theory (EUT) assumed:

People make rational choices
Utility depends only on final wealth
People are risk-averse for gains and risk-seeking for losses consistently

But real human behaviour violates these assumptions.

Key Errors / Limitations

1. People evaluate outcomes relative to a reference point

Bernoulli assumed utility depends on final wealth, but people think in terms of gains and losses from a baseline.

2. Losses hurt more than gains feel good

Bernoulli assumed equal sensitivity to gains and losses.
However:

Losing ₹100 hurts more than gaining ₹100 feels good.
→ Loss aversion

3. Diminishing sensitivity

People feel differences less intensely as amounts grow. Example: Saving ₹100 on a ₹500 product feels larger than saving ₹100 on a ₹50,000 product.

4. Probability weighting

People don’t see probabilities correctly:

Overweight small probabilities (lotteries)
Underweight large probabilities

EUT cannot explain phenomena like:

Gambling and insurance at the same time
Reference dependence
Loss aversion
Framing effects

Thus, Prospect Theory was introduced to correct these errors.

2. Prospect Theory (Daniel Kahneman & Amos Tversky)

Prospect Theory explains how real people make decisions under risk.

It includes two main components:

A) Value Function (S-shaped curve)

Key features:

Reference-dependent: People evaluate outcomes relative to a reference point (current wealth, expectations).
Loss aversion: Losses are about 2x more painful than equivalent gains are pleasurable.
Diminishing sensitivity:

Gain side: Concave → risk-averse
Loss side: Convex → risk-seeking

Graph shape:

Steeper for losses
Flatter for large gains/losses

B) Probability Weighting Function

Humans distort probabilities:

Overweight low probability events

Lotteries
Rare catastrophic risks

Underweight high probability events

Insurance lapses
Conservatism in investing

Thus, decisions deviate from rational predictions.

3. SP/A Theory (Security-Potential/Aspiration Theory)

Developed by Lola Lopes, it expands Prospect Theory by adding emotional and motivational goals.

Key elements:

Security (S) orientation: Focus on avoiding negative outcomes (risk-averse individuals).
Potential (P) orientation: Focus on achieving high gains (risk-seeking individuals).
Aspiration (A): Desired target or goal influencing decisions.

How it differs from Prospect Theory

Aspect	Prospect Theory	SP/A Theory
Focus	Psychological biases	Goals & aspirations
Behaviour Depends on	Gains/losses from reference point	Desire for security or potential
Emotional Role	Implicit	Explicit

SP/A explains why different individuals may react differently to the same decision scenario depending on aspiration levels.

4. Framing

Framing refers to how the presentation or wording of choices affects decisions.

Even when alternatives are identical, people choose differently depending on the frame.

A) Gain vs. Loss Framing

People prefer:

Risk-averse choices when framed as gains
Risk-seeking choices when framed as losses

Example: “90% survival rate” vs. “10% mortality rate”
→ Same information, but different choices.

B) Attribute Framing

Highlighting a positive or negative attribute changes judgment. Example: “80% lean meat” vs. “20% fat meat”

C) Goal Framing

Emphasizing benefits of action or costs of inaction.

Example: “Vaccination saves lives” vs. “Not vaccinating increases death risk”

5. Mental Accounting (Richard Thaler)

Mental accounting is the tendency of individuals to categorize money into separate “accounts” in their minds, affecting spending and investment decisions.

Key Principles

1. Segregation of Money

People treat money differently depending on its source or purpose.

Example:

Salary vs. bonus money
Tax refund vs. hard-earned savings

2. Sunk Cost Fallacy

People continue a losing investment because they mentally account for past costs.

3. Budgeting in Categories

People create mental budgets:

Food
Entertainment
Investments
Travel

Even when money is fungible, they restrict spending based on these mental budgets.

4. House Money Effect

People take higher risks with money earned easily (e.g., lottery, profit) than with their own savings.

5. Narrow Framing

Viewing decisions in isolation rather than as part of a portfolio.

Example: An investor treats each stock separately instead of considering total portfolio risk.

6. From Theory to Practice

How these behavioural concepts apply in real-life and business:

A) In Marketing

Framing used in pricing (“Save ₹500!” vs. “20% discount”)
Product bundles leverage mental accounting
Prospects respond differently to loss/gain messages

B) In Investing

Loss aversion leads to holding losing stocks too long
Mental accounting causes improper diversification
Framing affects risk preferences
Overweighting low probabilities → speculative trading

C) In Financial Planning

Clients avoid selling stocks at a loss (loss aversion)
Reference points change expectations
Narrow framing → poor asset allocation decisions

D) In Policy Making

Framing messages improves public compliance
Understanding loss aversion helps design effective tax laws
Mental accounting aids behavioural nudges

Quick Summary Table

Topic	Meaning	Key Insight
Error in Bernoulli’s Theory	EUT fails to explain real behavior	People are irrational, reference-dependent, loss-averse
Prospect Theory	Describes actual decisions under risk	Loss aversion, probability weighting
SP/A Theory	Security vs. Potential vs. Aspiration	Decisions depend on motivational goals
Framing	Presentation changes choices	Gain frames → risk-averse; loss frames → risk-seeking
Mental Accounting	People mentally separate money into accounts	Leads to irrational spending & investment behaviour

Challenge to Market Efficiency

Theoretical Foundations of EMH, Empirical Evidence, Challenges, Noise Trading, Limits to Arbitrage, Keynesian Beauty Contest, Guess-a-Number Game & Assessment

1. Theoretical Foundations of EMH

Efficient Market Hypothesis (EMH) argues that financial markets fully reflect all available information. It was developed by Eugene Fama (1970).

Types of EMH

Type	Meaning	Implication
Weak Form	Prices reflect all past price data	Technical analysis cannot beat market
Semi-Strong Form	Prices reflect all public information	Fundamental analysis cannot beat market
Strong Form	Prices reflect all public + private information	Even insiders can’t beat market

Assumptions underlying EMH

Investors are rational
Markets react quickly to new information
Prices represent true intrinsic value
No investor can consistently earn abnormal returns

2. Empirical Evidence for EMH

Evidence supporting EMH

Random Walk Theory Prices follow a random path; tomorrow’s price cannot be predicted by past data.
Event Studies Markets quickly incorporate earnings announcements, mergers, interest rates, etc.
Index Funds outperform active funds Because markets already reflect available information.

Evidence against EMH (anomalies)

Anomaly	Meaning
January Effect	Stocks earn abnormal returns in January
Momentum Effect	Past winners continue to outperform
Value Effect	Low P/E, low P/B stocks outperform
Post-Earnings Announcement Drift (PEAD)	Markets react slowly to earnings
Bubbles & Crashes	Prices deviate from fundamentals

3. Theoretical Challenges to EMH

Behavioral finance shows investors are not fully rational. Key challenges:

1. Cognitive biases

Overconfidence
Loss aversion
Anchoring
Herd behavior

These lead to predictable mispricing, contradicting EMH.

2. Investors have different information-processing abilities

People may misinterpret or ignore information.

3. Limited arbitrage

Even if mispricing occurs, arbitrage is risky and costly.

4. Market frictions

Taxes, transaction costs, liquidity constraints prevent continuous price adjustment.

4. Noise Trading & Limits to Arbitrage

Noise Trading

Noise traders make decisions based on:

rumors
emotions
wrong beliefs
overreaction

They cause irrational price movements.

Example

Buying a stock just because:

it is trending on social media
a celebrity endorsed it
there is panic selling

Noise traders can push prices far from intrinsic value.

Limits to Arbitrage

Arbitrage = opportunity to profit from mispricing (buy low, sell high).

However, arbitrage is limited because:

1. Fundamental Risk

Mispricing can worsen before correcting. Example: A stock undervalued today may fall even more tomorrow.

2. Noise Trader Risk

Noise traders can stay irrational longer than traders can stay solvent.

3. Implementation Costs

Short selling constraints
Transaction costs
Borrowing costs

4. Time horizon risk

Markets take time to correct; arbitrageurs may run out of capital. Conclusion: Mispricing can persist → market is not always efficient.

5. Keynesian Beauty Contest & Guess-a-Number Game

Keynesian Beauty Contest

John Maynard Keynes compared the stock market to a newspaper beauty contest where:

You must pick the face that others think will win,
not the one you find beautiful.

This shows:

Investors try to predict others’ behavior, not fundamentals.
Leads to herd behavior and speculative bubbles.

Example Investors buy a stock not because it’s good, but because they think others will buy it.

Guess-a-Number Game

(Also known as “Guess 2/3 of the average”)

Steps:

Everyone chooses a number from 0–100.
The winner is the one closest to 2/3 of the average guess.

Results

Rational players choose lower numbers.
Ultimately, the equilibrium is 0.
But people rarely pick 0 → indicates bounded rationality.

Lesson: Investors do not think infinitely about others' thoughts → markets are not perfectly rational.

6. Assessment of EMH

Strengths of EMH

✔ Explains why active fund managers often fail to beat market
✔ Encourages disciplined investing & index funds
✔ Market prices incorporate information rapidly

Weaknesses of EMH

❌ Behavioral biases cause predictable mispricing
❌ Bubbles and crashes contradict rationality
❌ Arbitrage cannot always eliminate mispricing
❌ Real-world evidence shows anomalies

Final Assessment

EMH is a useful but incomplete theory.
Markets are efficient most of the time, but not all the time due to:

human psychology
irrational behavior
noise trading
arbitrage limits

This is why behavioral finance complements EMH