Introduction
Traditional finance assumes investors make rational decisions based on expected utility theory. Yet, real-world behavior often deviates from this ideal. Prospect Theory, developed by Kahneman and Tversky (1979), explains how people evaluate gains and losses relative to a reference point rather than absolute wealth. In this article, I explore how asset allocation decisions change under Prospect Theory, why standard models fail, and how behavioral biases shape portfolio choices.
Table of Contents
What Is Prospect Theory?
Prospect Theory argues that people:
- Evaluate outcomes relative to a reference point (e.g., initial investment).
- Feel losses more intensely than gains (loss aversion).
- Overweight small probabilities and underweight large ones.
The value function V(x) in Prospect Theory is S-shaped: concave for gains, convex for losses, and steeper for losses. Mathematically:
V(x) = \begin{cases} x^\alpha & \text{if } x \geq 0 \ -\lambda(-x)^\beta & \text{if } x < 0 \end{cases}Where:
- \alpha, \beta < 1 (diminishing sensitivity).
- \lambda > 1 (loss aversion coefficient).
Example: Loss Aversion in Stocks
Suppose an investor faces two scenarios:
- Gain $1,000 → perceived utility = 1000^{0.88} \approx 275.
- Lose $1,000 → perceived utility = -2.25 \times (-1000)^{0.88} \approx -618.
The pain of losing outweighs the joy of gaining, explaining why investors hold losing stocks too long.
Asset Allocation Under Prospect Theory
1. Reference Points Matter
Investors compare returns to benchmarks (e.g., S&P 500). If a portfolio underperforms, they take excessive risks to “break even.”
Example:
- Reference point = 5% annual return.
- If YTD return = 3%, the investor may chase high-risk assets to recover.
2. Mental Accounting and Portfolio Segregation
Investors divide wealth into mental buckets (e.g., “safe money” vs. “play money”). This violates the principle of diversification.
| Mental Account | Allocation | Risk Tolerance |
|---|---|---|
| Retirement | 60% Bonds | Low |
| Discretionary | 90% Stocks | High |
3. Probability Weighting and Skewness Preferences
Investors overweight lottery-like payoffs (e.g., meme stocks). The decision weight w(p) distorts true probabilities:
w(p) = \frac{p^\gamma}{(p^\gamma + (1-p)^\gamma)^{1/\gamma}}Where \gamma < 1 leads to overestimating tiny probabilities.
Example:
- True probability of a 10x return = 1%.
- Perceived probability = w(0.01) \approx 5\%.
Empirical Evidence
Case Study: 401(k) Plans
Benartzi & Thaler (1995) found that employees:
- Overweight recent performance (“recency bias”).
- Use naïve diversification (1/n heuristic).
| Fund Option | Allocation (%) |
|---|---|
| S&P 500 | 40 |
| Bonds | 30 |
| Int’l Stocks | 30 |
Many split contributions equally across options, ignoring correlations.
Practical Implications
1. Dynamic Asset Allocation
Adjust portfolios based on gains/losses relative to a reference:
\text{If } W_t > W_{ref}, \text{ reduce risk.} \ \text{If } W_t < W_{ref}, \text{ increase risk.}2. Framing Effects
Presenting the same strategy as “loss protection” vs. “gain potential” alters choices.
Example:
- Frame A: “This strategy has a 95% chance of not losing money.”
- Frame B: “This strategy has a 5% chance of losing money.”
Prospect Theory predicts Frame A attracts more investors.
Limitations
- Parameter Sensitivity – Small changes in \alpha, \beta, \lambda drastically alter outcomes.
- Market Equilibrium – If all investors follow Prospect Theory, asset prices adjust, altering expected returns.
Conclusion
Prospect Theory reshapes asset allocation by incorporating human biases. Investors should:
- Define rational reference points (e.g., inflation + 4%).
- Avoid mental accounting traps.
- Use probability-weighted scenarios in planning.
By blending behavioral insights with traditional finance, we build portfolios that align with how people actually think—not just how they should.
References
- Kahneman, D., & Tversky, A. (1979). “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica.
- Benartzi, S., & Thaler, R. (1995). “Myopic Loss Aversion and the Equity Premium Puzzle.” QJE.
