Investor behavior",

What Is Prospect Theory?

Prospect theory is a cognitive theory in behavioral finance that describes how individuals make decision-making under risk when evaluating potential gains and losses. Unlike traditional utility theory, which assumes rational economic behavior, prospect theory posits that people evaluate outcomes relative to a subjective reference point and exhibit different attitudes toward risk depending on whether they perceive a situation as involving gains or losses. This often leads to deviations from pure rationality in financial choices.

History and Origin

Prospect theory was developed by psychologists Daniel Kahneman and Amos Tversky, who challenged the prevailing assumptions of traditional economic models that suggested individuals always act rationally. Their groundbreaking work emerged from observations that people's choices often violated the axioms of expected utility theory. A key turning point was their 1979 paper, "Prospect Theory: An Analysis of Decision under Risk," published in Econometrica.⁵ This seminal paper introduced core concepts like loss aversion and the framing effect, which became foundational elements of behavioral economics. Their collaboration, beginning in the 1970s, laid the groundwork for understanding how psychological heuristics and cognitive biases influence economic choices.⁴

Key Takeaways

Prospect theory highlights that individuals evaluate outcomes relative to a subjective reference point, not in terms of absolute wealth.
It proposes that the psychological impact of a loss is generally greater than the joy derived from an equivalent gain, a phenomenon known as loss aversion.
The theory suggests that people tend to be risk aversion when facing potential gains but become risk seeking when facing potential losses.
The way a decision problem is presented, or "framed," significantly influences choices, even if the underlying objective outcomes are the same.
Prospect theory explains various market anomalies and observed irrationalities in financial behavior.

Formula and Calculation

Prospect theory models the subjective value of an outcome using a value function and transforms objective probabilities into subjective decision weights. The overall subjective value ($V$) of a prospect (a risky choice) is given by:

V(P) = \sum_{i=1}^{n} v(x_i) \cdot \pi(p_i)

Where:

$P$ represents a prospect (a set of possible outcomes and their probabilities).
$x_i$ is the $i$-th outcome, defined as a deviation (gain or loss) from a reference point.
$v(x_i)$ is the value function that assigns a subjective value to each outcome $x_i$. This function is typically S-shaped: concave for gains (implying diminishing sensitivity to increasing gains) and convex for losses (implying diminishing sensitivity to increasing losses), and steeper for losses than for gains (loss aversion).
$p_i$ is the objective probability of outcome $x_i$.
$\pi(p_i)$ is the probability weighting function, which transforms the objective probability $p_i$ into a subjective decision weight. This function typically overweights small probabilities and underweights large probabilities.

The value function and probability weighting function are central to understanding how prospect theory deviates from standard utility theory.

Interpreting Prospect Theory

Interpreting prospect theory involves understanding that individuals do not make choices based purely on expected monetary value, but rather on subjective psychological value. A critical element is the role of the reference point, which can shift depending on circumstances, influencing whether an outcome is perceived as a gain or a loss. For example, an investor who bought a stock at $50 might consider a current price of $45 a loss, even if their overall portfolio management is still profitable from other holdings. The theory suggests that the pain of a $5 loss from the reference point is felt more intensely than the pleasure of a $5 gain. This helps explain phenomena like selling winning stocks too early or holding onto losing stocks too long.

Hypothetical Example

Consider an investor, Sarah, who purchased 100 shares of Company A at $100 per share. Her investment decisions are about to be tested.

Scenario 1: Potential Gain
Company A's stock price has risen to $120. Sarah is considering selling. According to traditional economic theory, she should consider the $20 profit per share. However, under prospect theory, she might be more risk-averse regarding this gain. If offered a choice between:

Selling now for a guaranteed $2,000 profit (100 shares * $20 profit).
Holding the stock for a 50% chance of gaining another $2,000 (total $4,000 profit) or a 50% chance of the price falling back to $100 (total $0 profit).

Sarah, influenced by the concavity of the value function in the gain domain, is likely to choose the guaranteed $2,000 profit, exhibiting risk aversion. She prefers the certainty of a smaller gain over the possibility of a larger gain with risk, even if the expected value is higher for the risky option.

Scenario 2: Potential Loss
Company A's stock price has fallen to $80. Sarah is considering selling. According to traditional theory, she should minimize losses. Under prospect theory, she might be more risk-seeking in the loss domain. If offered a choice between:

Selling now for a guaranteed $2,000 loss (100 shares * $20 loss).
Holding the stock for a 50% chance of the price returning to $100 (total $0 loss) or a 50% chance of it falling further to $60 (total $4,000 loss).

Sarah, influenced by the convexity of the value function in the loss domain and loss aversion, is likely to hold onto the stock, hoping it recovers, exhibiting risk-seeking behavior to avoid the certain loss. The psychological pain of realizing the $2,000 loss is disproportionately high, making the risky option of avoiding it more appealing.

Practical Applications

Prospect theory has profound practical applications in finance and economics, offering insights into why investors often deviate from what is considered rational. It helps explain common investor behaviors such as the disposition effect, where investors are prone to selling assets that have increased in value too soon while holding assets that have decreased in value for too long. This behavior is a direct manifestation of risk aversion in the gain domain and risk-seeking in the loss domain, as described by prospect theory. The insights from prospect theory have also been applied to understand macroeconomic phenomena, such as consumer spending habits and even the origins of financial crises.³ Financial advisors and policymakers can use these insights to design better communication strategies, default options in retirement plans, and regulatory frameworks that account for predictable human biases. Understanding these behavioral pitfalls can help individuals make more informed decisions and avoid common errors in investing.²

Limitations and Criticisms

While prospect theory offers a powerful descriptive model of human choice under risk, it is not without limitations. Some criticisms revolve around its descriptive rather than normative nature; it explains how people do behave, not how they should behave. The precise shape of the value function and probability weighting function can vary between individuals and contexts, making precise predictions challenging. Furthermore, defining the "reference point" can be ambiguous and context-dependent, which can make applying the theory difficult in certain complex real-world scenarios. It primarily focuses on choices under explicit risk with known probabilities, which may not always reflect the uncertainty prevalent in real financial markets. While an excellent descriptive model, some argue that its complexity makes it less amenable to certain forms of economic modeling compared to simpler utility theory.¹

Prospect Theory vs. Expected Utility Theory

Prospect theory is often contrasted with Expected Utility Theory (EUT), which served as the dominant framework for describing decision-making under risk prior to the advent of behavioral economics.

Feature	Expected Utility Theory	Prospect Theory
Reference Point	Evaluates choices based on final wealth states.	Evaluates choices based on gains and losses relative to a reference point.
Risk Attitude	Assumes consistent risk aversion (or neutrality/seeking) across all wealth levels.	Risk-averse for gains, risk-seeking for losses.
Probabilities	Uses objective probabilities directly.	Transforms objective probabilities into subjective decision weights.
Value Function	Utility function is typically concave, reflecting diminishing marginal utility of wealth.	Value function is S-shaped (concave for gains, convex for losses) and steeper for losses.
Description	Normative: How people should make decisions.	Descriptive: How people actually make decisions.

The fundamental difference lies in their approach: EUT provides a normative framework for rational choice, while prospect theory offers a descriptive account of observed human behavior, including common deviations from perfect rationality.

FAQs

Why is prospect theory important in finance?

Prospect theory is important in finance because it provides a more realistic model of investor behavior than traditional economic theories. It helps explain why investors might make seemingly irrational investment decisions, such as holding onto losing stocks or being overly cautious with small gains, by incorporating psychological factors like loss aversion and framing effects.

What is the main difference between prospect theory and expected utility theory?

The main difference is that expected utility theory is a normative model, describing how rational individuals should make choices, while prospect theory is a descriptive model, explaining how people actually make choices. Prospect theory introduces concepts like a reference point, an S-shaped value function, and subjective decision weights that account for observed biases.

Can prospect theory help investors make better decisions?

While prospect theory describes how people behave, understanding its principles can help investors recognize and mitigate their own cognitive biases. By being aware of tendencies like loss aversion or the framing effect, investors can consciously try to make more disciplined and rational choices, aligning their decisions more closely with their long-term financial goals.