Course 9: Behavioral Perspectives

Behavioral Finance: Psychology Meets Markets

How cognitive biases, emotions, and bounded rationality shape investment decisions and create market anomalies

Learning Objectives

1.Master Prospect Theory and understand loss aversion and probability weighting
2.Identify major cognitive biases: overconfidence, anchoring, and mental accounting
3.Analyze market anomalies through behavioral lens: momentum, value, post-earnings drift
4.Understand limits to arbitrage and why mispricing persists
5.Apply behavioral insights to improve investment decision-making
6.Evaluate the debate between behavioral and rational perspectives in finance

1. Prospect Theory and Loss Aversion

Definition 1.1: Prospect Theory

Prospect Theory (Kahneman & Tversky, 1979) describes how people make decisions under risk, replacing expected utility theory:

V = \sum_i w(p_i) v(x_i)

where:

$v(x)$ is the value function (replaces utility)
$w(p)$ is the probability weighting function
$x_i$ are outcomes relative to a reference point

Theorem 1.1: Value Function

The value function $v(x)$ has three key properties:

v(x) = \begin{cases} x^\alpha & \text{if } x \geq 0 \\ -\lambda(-x)^\beta & \text{if } x < 0 \end{cases}

Typical parameters: $\alpha = \beta \approx 0.88$ , $\lambda \approx 2.25$

Properties:

Reference dependence: Value defined relative to reference point, not absolute wealth
Loss aversion: $\lambda > 1$ means losses hurt more than equivalent gains feel good
Diminishing sensitivity: Concave for gains ( $\alpha < 1$ ), convex for losses ( $\beta < 1$ )

Example 1.1: Loss Aversion in Action

Gamble: Win $100 with 50% probability, lose $100 with 50% probability

Expected utility (risk-neutral): $0.5 \times 100 + 0.5 \times (-100) = 0$ → Indifferent

Prospect Theory value (with $\lambda = 2.25$ ):

V = 0.5 \times 100^{0.88} - 0.5 \times 2.25 \times 100^{0.88} \approx -31.2

Most people reject this gamble! Need potential gain of ~$225 to compensate for $100 loss risk.

Definition 1.2: Probability Weighting

People overweight small probabilities and underweight moderate/high probabilities:

w(p) = \frac{p^\gamma}{(p^\gamma + (1-p)^\gamma)^{1/\gamma}}

Typical $\gamma \approx 0.65$

Implications: $w(0.01) \approx 0.06$ (overweight), $w(0.50) \approx 0.42$ (underweight)

Proposition 1.1: Fourfold Pattern of Risk Attitudes

Prospect Theory predicts different risk attitudes by domain and probability:

	Gains	Losses
High probability	Risk averse (prefer sure gain)	Risk seeking (gamble to avoid loss)
Low probability	Risk seeking (lottery tickets)	Risk averse (insurance)

Remark 1.1: Contrast with Expected Utility Theory

Expected Utility Theory assumes:

Utility depends on final wealth levels (not changes)
Consistent risk aversion (concave utility everywhere)
Probabilities enter linearly

Prospect Theory better explains real behavior: disposition effect, equity premium puzzle, insurance + lottery purchases.

2. Cognitive Biases and Heuristics

Definition 2.1: Overconfidence

People systematically overestimate their knowledge, abilities, and precision of information:

Overestimation: Belief in superior skills (e.g., "above-average driver")
Overplacement: Overestimate relative ranking
Overprecision: Excessive certainty (confidence intervals too narrow)

Example 2.1: Overconfidence in Investing

Evidence:

Individual investors trade too much (turnover correlates with underperformance)
Men trade 45% more than women, earn 2.65% less (Barber & Odean, 2001)
Professional forecasters give 90% confidence intervals that contain actual outcome only 50% of time

Consequence: Excessive trading, insufficient diversification, holding concentrated positions.

Definition 2.2: Anchoring and Adjustment

People anchor on initial information and adjust insufficiently:

Initial value serves as mental anchor
Subsequent adjustments are inadequate
Affects valuation, forecasts, and negotiations

Example 2.2: 52-Week High as Anchor

Stock trading near 52-week high:

Investors anchor on past peak price
Reluctant to buy if above 52-week high ("too expensive")
Slow price adjustment to new information (momentum effect)

George & Hwang (2004): Stocks near 52-week highs outperform by 8% annually.

Definition 2.3: Mental Accounting

People segregate decisions into separate mental accounts, violating fungibility of money:

Different attitudes toward "house money" vs. own money
Reluctance to realize losses (disposition effect)
Narrow framing (evaluate investments in isolation)

Example 2.3: Disposition Effect

Behavior: Investors sell winners too early and hold losers too long

Evidence (Odean, 1998):

Proportion of gains realized (PGR) = 15%
Proportion of losses realized (PLR) = 10%
Ratio PGR/PLR ≈ 1.5 (should be 1 if rational)

Explanation: Loss aversion + reference point = purchase price → reluctance to realize losses.

Proposition 2.1: Representativeness and Availability Heuristics

Representativeness: Judge probability by similarity to stereotypes

Leads to base rate neglect
Gambler's fallacy ("due for a win")
Extrapolating small samples (hot hand fallacy)

Availability: Judge probability by ease of recall

Recent/vivid events weighted heavily
Recency bias in forecasts
Overreaction to news

Remark 2.1: Confirmation Bias

Tendency to seek information confirming existing beliefs and ignore contradictory evidence:

Selective attention to bullish news when long
Echo chambers in social media
Reluctance to change investment thesis

3. Market Anomalies and Behavioral Explanations

Definition 3.1: Market Anomalies

Patterns in stock returns that violate the Efficient Market Hypothesis and cannot be fully explained by risk:

Theorem 3.1: Momentum Effect

Past winners continue outperforming and past losers continue underperforming (3-12 month horizon):

\text{Momentum return} \approx 1\% \text{ per month}

Behavioral explanations:

Underreaction: Anchoring causes slow incorporation of news
Herding: Investors follow trends, amplifying momentum
Confirmation bias: Positive feedback loop

Theorem 3.2: Value Effect (Book-to-Market)

High book-to-market (value) stocks outperform low B/M (growth) stocks:

\text{Value premium} \approx 5\% \text{ annually}

Behavioral explanations:

Overreaction: Excessive pessimism about value stocks, optimism about growth
Extrapolation bias: Projecting past growth too far into future
Representativeness: Glamorous growth stocks seem like "good companies"

Example 3.1: Post-Earnings Announcement Drift (PEAD)

Phenomenon: Stocks with positive earnings surprises continue to drift upward for 60-90 days

Magnitude: Approximately 4-6% annualized abnormal return

Behavioral explanation:

Underreaction to earnings information
Anchoring on pre-announcement expectations
Limited attention (investors miss earnings reports)

Proposition 3.1: Other Documented Anomalies

Size effect: Small caps outperform (though diminished recently)
January effect: Abnormal returns in January (tax-loss selling)
Weekend effect: Monday returns lower than other days
IPO underperformance: Long-run underperformance after IPO
Accruals anomaly: Firms with high accruals underperform

Remark 3.1: Risk vs. Behavioral Interpretations

Debate: Are anomalies compensation for risk or behavioral mispricing?

Risk-based view (Fama-French): Value and size premiums reflect compensation for systematic risk

Behavioral view: Anomalies arise from predictable investor mistakes and limits to arbitrage

Consensus: Likely combination of both factors, varying by anomaly.

4. Limits to Arbitrage

Definition 4.1: Limits to Arbitrage

Frictions that prevent rational traders from fully exploiting and eliminating mispricings:

Theorem 4.1: Implementation Costs

Trading costs reduce arbitrage profitability:

Transaction costs: Commissions, bid-ask spreads (can be 1-2% round-trip for small caps)
Market impact: Large trades move prices unfavorably
Short-sale costs: Borrowing fees, margin requirements, limited supply

Small mispricings (1-2%) may not be exploitable after costs.

Theorem 4.2: Noise Trader Risk

Mispricing can worsen before correcting, causing losses for arbitrageurs:

Problem: Noise traders (irrational) can push prices further from fundamentals

Consequence: Arbitrageurs face:

Mark-to-market losses
Forced liquidation if leveraged
Client withdrawals

$\Rightarrow$ Short horizons limit arbitrage even when ultimately correct.

Example 4.1: Long-Term Capital Management (1998)

LTCM exploited arbitrage opportunities (convergence trades) with high leverage:

Russian default crisis → spreads widened (mispricings worsened)
Forced liquidation due to margin calls
Lost $4.6 billion, nearly collapsed

Lesson: "Markets can stay irrational longer than you can stay solvent" (Keynes)

Proposition 4.1: Synchronization Risk

Arbitrageurs may liquidate simultaneously, amplifying mispricing:

Similar strategies → correlated positions
Market stress → synchronized selling
Positive feedback: selling begets more selling

Remark 4.1: Implications for Market Efficiency

Limits to arbitrage mean:

Mispricings can persist for extended periods
Behavioral biases have real price impact
Markets are not perfectly efficient
But: difficult to systematically exploit anomalies after costs

Key Takeaways

1.Prospect Theory: Loss aversion (λ ≈ 2.25) and reference dependence better explain risk behavior than expected utility
2.Cognitive biases (overconfidence, anchoring, mental accounting) lead to systematic investment errors
3.Market anomalies (momentum, value, PEAD) challenge efficient markets and have behavioral explanations
4.Limits to arbitrage (costs, noise trader risk, synchronization) allow mispricings to persist
5.Behavioral finance complements, not replaces, traditional finance—both perspectives needed
6.Awareness of biases can improve decision-making: diversify, rebalance systematically, avoid overtrading

Practice Problems

Behavioral Finance

Questions

Correct

Accuracy

In Prospect Theory, the loss aversion parameter λ is typically around:

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The disposition effect refers to:

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Which cognitive bias explains why investors anchor on 52-week highs?

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Momentum anomaly suggests that:

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The value effect (high B/M outperforming) can be explained behaviorally by:

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Post-earnings announcement drift (PEAD) is evidence of:

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Which is NOT a limit to arbitrage?

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Overconfidence in investing typically leads to:

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Mental accounting explains:

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The Long-Term Capital Management (LTCM) collapse illustrates:

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Probability weighting in Prospect Theory means people:

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Which statement about behavioral vs. traditional finance is TRUE?

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The representativeness heuristic can lead to:

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Confirmation bias in investing means:

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To combat behavioral biases, investors should:

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Frequently Asked Questions

How does behavioral finance differ from traditional finance?

Traditional finance assumes rational agents with stable preferences. Behavioral finance incorporates psychology, showing that people exhibit systematic biases like loss aversion, overconfidence, and mental accounting that affect market prices.

What is the most important concept in behavioral finance?

Prospect Theory and loss aversion are foundational. People feel losses roughly twice as intensely as equivalent gains, leading to risk-seeking in losses and risk-averse in gains—contradicting expected utility theory.

Can behavioral biases explain market anomalies?

Yes, many anomalies (momentum, value effect, post-earnings drift) are consistent with investor biases like overreaction, underreaction, and anchoring. However, risk-based explanations also exist.

Why don't arbitrageurs eliminate behavioral mispricing?

Limits to arbitrage exist: implementation costs, noise trader risk, synchronization risk, and short-sale constraints. These prevent rational traders from fully correcting mispricings caused by behavioral biases.

Should individual investors care about behavioral finance?

Absolutely! Understanding your own biases (overconfidence, disposition effect, home bias) can improve investment decisions. Strategies like systematic rebalancing and diversification combat common behavioral mistakes.