Chemistry: Meaning, Criticisms & Real-World Uses

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. Developed by Daniel Kahneman and Amos Tversky, it posits that people value outcomes not in absolute terms, but relative to a specific reference point. Unlike traditional economic theories that assume rational actors, prospect theory accounts for common cognitive biases and emotional influences on financial choices. This theory highlights that the perception of a gain or a loss is more significant than the final state of wealth, and that individuals exhibit different attitudes towards risk depending on whether they are facing a potential gain or a potential loss.

History and Origin

Prospect theory was introduced in 1979 by psychologists Daniel Kahneman and Amos Tversky in their seminal paper, "Prospect Theory: An Analysis of Decision Under Risk."⁴ This groundbreaking work challenged the prevailing expected utility theory, which had long served as the cornerstone of economic thought regarding choices under uncertainty. Kahneman and Tversky observed that individuals' actual decision-making often deviated systematically from the predictions of expected utility theory, particularly when presented with choices involving risk. Their research, based on empirical studies and experiments, led to the formulation of a new descriptive model that better captured human psychology in financial contexts. Daniel Kahneman later received the Nobel Memorial Prize in Economic Sciences in 2002, in part for his contributions to prospect theory.

Key Takeaways

Prospect theory describes how people make decisions under risk, focusing on perceived gains and losses rather than absolute wealth.
It highlights the concept of loss aversion, where the psychological impact of a loss is greater than the pleasure from an equivalent gain.
The theory incorporates a "value function" that is concave for gains (indicating diminishing sensitivity) and convex for losses (also diminishing sensitivity).
It uses "decision weights" instead of objective probability to reflect how people subjectively perceive the likelihood of outcomes.
Prospect theory helps explain various cognitive biases observed in financial markets.

Formula and Calculation

Prospect theory does not rely on a single, universally defined mathematical formula in the same way traditional financial models might. Instead, it describes a framework characterized by a "value function" and "decision weights."

The overall value of a prospect, (V), is calculated as:

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

Where:

(x_i) represents the outcome (gain or loss) of prospect (i).
(v(x_i)) is the value assigned to outcome (x_i) by the individual's "value function." This function is typically s-shaped: concave for gains and convex for losses, and steeper for losses than for gains, reflecting loss aversion.
(p_i) is the stated probability of outcome (x_i).
(\pi(p_i)) is the "decision weight" assigned to probability (p_i) by the individual's "weighting function." This function often overweights small probabilities and underweights large probabilities, deviating from objective likelihood.

The value function, (v(x)), for an outcome (x) relative to a reference point (often zero, representing no change from the current state) is generally defined by:

v(x) = \begin{cases} x^\alpha & \text{if } x \ge 0 \quad \text{(for gains)} \\ -\lambda (-x)^\beta & \text{if } x < 0 \quad \text{(for losses)} \end{cases}

Where:

(\alpha) and (\beta) are parameters representing diminishing sensitivity, typically between 0 and 1.
(\lambda) (lambda) is the loss aversion coefficient, typically greater than 1 (often around 2 to 2.5), indicating that losses are felt more intensely than equivalent gains.

The probability weighting function, (\pi(p)), transforms objective probabilities into subjective decision weights. A common form is:

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

Where (\gamma) (gamma) is a parameter, typically less than 1, reflecting the curvature of the weighting function.

Interpreting the Prospect Theory

Interpreting prospect theory involves understanding how individuals deviate from purely rational economic models in their investment decisions. The core insight is that people evaluate potential outcomes in terms of changes from a perceived reference point, rather than absolute final wealth. This means that two individuals with the same absolute wealth might react differently to the same financial outcome if their starting reference points or framing of the situation differ.

The theory suggests that investors are generally risk aversion when facing choices involving potential gains, preferring a smaller, certain gain over a larger, uncertain one. Conversely, when faced with potential losses, individuals tend to be risk-seeking, willing to take on more risk to avoid a sure loss. This asymmetry, driven by the psychological impact of loss aversion, helps explain phenomena like holding onto losing investments for too long or quickly selling winning ones. Understanding these tendencies is crucial for financial professionals advising clients on their risk tolerance and for individuals seeking to mitigate the impact of their own biases.

Hypothetical Example

Consider an investor, Alice, who bought shares of TechCo for $100 per share. Her current financial situation represents her reference point.

Scenario 1: TechCo shares rise to $120.
Alice has a $20 per share gain. According to prospect theory, she is likely to exhibit risk aversion in the domain of gains. She might be tempted to sell her shares immediately to "lock in" this profit, even if there's a good chance the shares could rise further. The pleasure of the certain $20 gain outweighs the potential for a larger, but uncertain, future gain.

Scenario 2: TechCo shares fall to $80.
Alice has a $20 per share loss. In the domain of losses, prospect theory suggests she will become risk-seeking. Instead of cutting her losses and selling the shares, she might hold onto them, or even buy more, hoping for the price to recover. The pain of realizing the $20 loss is so strong due to loss aversion that she prefers to gamble on a recovery, even if the probability of further decline is significant, rather than accept the sure loss. This behavior contrasts with a purely rational approach that would only consider the future prospects of TechCo's stock regardless of the initial purchase price.

Practical Applications

Prospect theory has profound practical applications across various areas of finance, offering insights into human behavior that traditional economic models often miss. In portfolio management, understanding this theory helps explain why investors might hold onto underperforming assets (due to loss aversion) or sell winning assets too early (due to risk aversion in gains). Financial advisors can use these insights to guide clients through potentially irrational investment decisions, emphasizing long-term goals over short-term emotional reactions to gains and losses.

The theory is also relevant in understanding market sentiment. Fluctuations in broad investor attitudes, influenced by collective cognitive biases, can significantly impact asset prices beyond what fundamental analysis alone would suggest.³ Furthermore, regulators and institutions increasingly acknowledge the role of human behavior. For instance, discussions around risk culture within financial firms implicitly recognize that individual and organizational biases can lead to misconduct and systemic risks.² By anticipating how individuals might react to different economic conditions, policymakers can design more effective regulations and communications. Even in areas like portfolio diversification, understanding an investor's emotional response to volatility, often influenced by their reference points, can shape the advice provided.¹

Limitations and Criticisms

While prospect theory offers a robust explanation for observed human decision-making under risk, it also has limitations and has faced criticisms. One common critique is the difficulty in precisely defining the " reference point" for individuals, as it can be subjective and vary across contexts and even over time. This makes precise quantitative predictions challenging in real-world scenarios.

Another limitation is its focus primarily on individual decisions rather than collective behavior in large financial markets. While the aggregation of individual biases can influence market movements, prospect theory itself doesn't fully explain phenomena like speculative bubbles or crashes driven by broader market dynamics. Some critics also argue that the theory's descriptive power comes at the expense of prescriptive guidance; while it explains how people behave, it doesn't necessarily dictate how they should behave to achieve optimal outcomes. Furthermore, the parameters used in the value and weighting functions (e.g., (\alpha), (\beta), (\lambda), (\gamma)) are typically derived from experimental settings and may not be universally applicable or stable in all real-world financial contexts. Despite these points, prospect theory remains a cornerstone of behavioral finance for its significant advancements in understanding cognitive biases and their impact on choices.

Prospect Theory vs. Expected Utility Theory

Prospect theory and expected utility theory are both frameworks for understanding decision-making under uncertainty, but they differ fundamentally in their assumptions about human rationality and behavior.

Feature	Prospect Theory	Expected Utility Theory
Core Principle	Values outcomes as gains and losses relative to a reference point; accounts for cognitive biases.	Maximizes expected utility of final wealth; assumes rational, consistent preferences.
Risk Attitude	Risk aversion for gains, risk-seeking for losses (due to loss aversion).	Consistent risk attitude (e.g., always risk-averse or risk-neutral).
Probability	Uses subjective "decision weights" that can distort objective probability.	Uses objective probabilities.
Value Basis	Value is assigned to changes in wealth (gains/losses).	Utility function is assigned to final states of wealth.
Nature	Descriptive (explains how people actually decide).	Normative (describes how rational people should decide).

The confusion between the two often arises because both deal with choices involving uncertainty. However, expected utility theory struggles to explain common behavioral anomalies observed in financial markets, such such as the endowment effect or framing effects, which prospect theory readily addresses by incorporating psychological realities like loss aversion and subjective probability weighting.

FAQs

What is the main idea behind Prospect Theory?

The main idea of prospect theory is that people evaluate financial outcomes as gains and losses relative to a specific reference point, rather than in terms of absolute final wealth. It highlights that the psychological impact of a loss is generally greater than the pleasure derived from an equivalent gain, a concept known as loss aversion.

How does Prospect Theory differ from traditional economic theories?

Prospect theory fundamentally differs from traditional economic theories, like expected utility theory, by acknowledging that individuals are not always perfectly rational. It integrates psychological insights and cognitive biases into its framework, providing a more accurate descriptive model of human decision-making under risk than normative models that assume ideal rationality.

Can Prospect Theory predict market movements?

While prospect theory helps explain the underlying psychological drivers of individual investment decisions and biases that can aggregate to influence financial markets, it is not a direct tool for predicting specific market movements. It offers a framework for understanding why certain behaviors occur, rather than a forecasting model for price changes.