Prospect theory

What Is Prospect Theory?

Prospect theory is a groundbreaking concept in Behavioral Finance that describes how individuals make choices under risk and uncertainty. Unlike traditional economic models that assume rational decision-making, prospect theory posits that people evaluate potential outcomes based on perceived gains and losses from a reference point, rather than on absolute final wealth. This psychological framework highlights that individuals tend to be risk-aversion when facing potential gains but become risk-seeking when confronted with potential losses. It also introduces the idea that people do not evaluate probabilities linearly, often overweighing small probabilities and underweighing large ones. Prospect theory is a cornerstone of understanding cognitive-biases and their impact on financial decision-making.

History and Origin

Prospect theory was developed by psychologists Daniel Kahneman and Amos Tversky and introduced in their seminal 1979 paper, "Prospect Theory: An Analysis of Decision under Risk." Their research challenged the prevailing utility-theory by demonstrating that human choices often deviate from purely rational calculations. Kahneman and Tversky conducted numerous experiments that revealed systematic patterns in how people perceive risk and make choices, particularly concerning gains and losses. This pioneering work earned Daniel Kahneman the Nobel Memorial Prize in Economic Sciences in 2002, recognizing his profound influence on the field of economics.,⁷

Key Takeaways

• Prospect theory explains that individuals evaluate potential outcomes relative to a reference point, not absolute wealth.
• It highlights loss-aversion, where the psychological impact of a loss is greater than that of an equivalent gain.
• The theory suggests people are typically risk-averse regarding gains but risk-seeking regarding losses.
• It introduces a probability weighting function, indicating that individuals distort objective probabilities in their minds.
• Prospect theory is a fundamental concept in behavioral economics, offering insights into irrational investment-decisions.

Formula and Calculation

Prospect theory models the subjective value of a prospect (a potential outcome or gamble) through a value function and a probability weighting function. The overall subjective value (V) of a prospect with multiple outcomes is given by:

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

Where:

• (V) = The overall perceived value of the prospect.
• (x_i) = The outcome (i), measured as a deviation (gain or loss) from a reference point.
• (v(x_i)) = The value function that assigns subjective value to each outcome (x_i). This function is typically S-shaped, concave for gains and convex for losses, and steeper for losses than for gains, illustrating loss aversion.
• (p_i) = The objective probability of outcome (i).
• (\pi(p_i)) = The probability weighting function that transforms objective probabilities into subjective decision weights. This function often overweighs small probabilities and underweighs large probabilities.

This formula demonstrates how subjective perceptions of both magnitude and probability contribute to an individual's evaluation of a prospect. The concept of a reference-point is crucial here, as all outcomes are evaluated relative to it.

Interpreting Prospect Theory

Interpreting prospect theory involves understanding that human beings are not always rational maximizers of utility. Instead, their choices are influenced by psychological factors and how information is presented. A core tenet is that individuals assess gains and losses from a subjective reference point, which can shift. For instance, an investor might consider their initial purchase price as a reference point for a stock; any movement below this point is perceived as a loss, while movement above is a gain.

The theory also reveals how heuristics and cognitive biases impact financial choices. People tend to feel the pain of a loss much more intensely than the pleasure of an equivalent gain, a phenomenon known as loss-aversion. This can lead to irrational behaviors, such as holding onto losing investments longer than they should in the hope of recovering the initial loss, or selling winning investments too early to "lock in" a gain. The way a choice is "framed"—as a gain or a loss—can significantly alter a person's ultimate investment-decisions, demonstrating the powerful framing-effect.

Hypothetical Example

Consider an investor, Sarah, who purchased 100 shares of Company A at $50 per share.

Scenario 1: Gain
Company A's stock price rises to $60. Sarah is now sitting on a $10 per share gain, totaling $1,000. According to prospect theory, Sarah, being risk-averse in the domain of gains, might be tempted to sell her shares quickly to realize the profit, even if there's a good chance the stock will continue to rise. Her perceived "value" of the $1,000 gain diminishes as the gain increases, making her more willing to lock it in.

Scenario 2: Loss
Company A's stock price drops to $40 per share. Sarah is now facing a $10 per share loss, totaling $1,000. In this domain of losses, prospect theory suggests Sarah might become risk-seeking. Instead of selling to cut her losses, she might hold onto the stock, or even buy more, hoping it will rebound to her original purchase price of $50. The pain of realizing the $1,000 loss is so strong that she is willing to take on more risk (holding a declining asset or buying more) to avoid that pain, potentially falling victim to the sunk-cost-fallacy.

This example illustrates how the same individual can exhibit different risk attitudes depending on whether they are facing potential gains or losses relative to their reference-point.

Practical Applications

Prospect theory has numerous practical applications across finance and economics, shedding light on real-world phenomena often unexplained by traditional models.

• Investor Behavior: It helps explain why investors exhibit behaviors like the disposition effect (selling winners too early and holding losers too long) or the endowment-effect (overvaluing assets they already own). Financial professionals use this understanding to provide behavioral coaching, helping clients overcome these tendencies.,
• ^{6 5} Marketing and Sales: Companies can frame product benefits in terms of avoided losses rather than achieved gains to increase appeal, leveraging consumers' loss-aversion.
• Insurance Industry: Prospect theory helps explain why people are willing to pay a premium for insurance (a certain small loss) to avoid a larger, uncertain loss, even if the expected value of not insuring is higher.
• Public Policy: Policymakers can design interventions that leverage insights from prospect theory, such as framing public health messages or financial literacy programs to emphasize the losses of inaction rather than the gains of compliance.
• Regulatory Insights: Regulators, such as the U.S. Securities and Exchange Commission (SEC), acknowledge behavioral patterns influenced by cognitive biases, including those described by prospect theory, when considering investor protection and education., Th⁴e³se insights help address how investors make suboptimal choices under uncertainty.

Limitations and Criticisms

While prospect theory revolutionized the understanding of decision-making under uncertainty, it faces certain limitations and criticisms.

One common critique is that the model's parameters (the specific shape of the value function and weighting function) are derived empirically rather than from a foundational theoretical framework. This means they describe observed behavior but do not fully explain the underlying psychological mechanisms that generate these preferences. Critics argue that while the theory describes what happens, it doesn't always explain why in deep psychological terms.

An²other limitation is its reliance on a "reference point," which can be ambiguous or variable in real-world scenarios. Identifying the precise reference point an individual uses can be challenging, and shifts in this point can alter predictions. Furthermore, some argue that prospect theory, like other behavioral models, might oversimplify complex emotional and cognitive processes that influence financial choices. While it accounts for some market-anomalies, it doesn't provide a comprehensive explanation for all irrational behaviors.

Additionally, while prospect theory highlights that individuals overweigh small probabilities (leading to lottery ticket purchases) and underweigh large probabilities, some argue that real-world risk-taking behavior can be far more nuanced and context-dependent than the theory fully captures. Economic letters from institutions like the Federal Reserve acknowledge the complexities of monetary-policy and decision-making in highly uncertain environments, suggesting that factors beyond those directly modeled by prospect theory often come into play.

##¹ Prospect Theory vs. Expected Utility Theory

Prospect theory is often contrasted with Expected-Utility-Theory (EUT), which was the dominant paradigm for describing rational choice under risk before prospect theory emerged.

While EUT provides a normative framework for rational choice, prospect theory offers a more descriptive account of human decision-making, particularly in financial contexts. Prospect theory highlights that individuals are not always rational in the classical economic sense, often exhibiting predictable deviations from the assumptions of EUT due to psychological factors like regret-aversion and how options are presented.

FAQs

What is the main idea of prospect theory?

The main idea of prospect theory is that people make decisions based on the potential value of gains and losses, rather than the final outcome. They evaluate these gains and losses relative to a specific starting point, or "reference point." This means that the psychological impact of losing $100 is generally greater than the psychological impact of gaining $100.

Who developed prospect theory?

Prospect theory was developed by two psychologists, Daniel Kahneman and Amos Tversky, in 1979. Their work laid the foundation for the field of behavioral-economics, integrating psychological insights into economic theory.

How does prospect theory affect investing?

Prospect theory explains several common behaviors observed in behavioral-investing. For instance, it accounts for why investors might hold onto losing stocks for too long (to avoid realizing the pain of a loss) or sell winning stocks too soon (to lock in a gain, even if the stock has more upside). It also helps understand how the way an investment opportunity is "framed" can influence an investor's willingness to take on risk.

Is prospect theory considered a behavioral finance concept?

Yes, prospect theory is a core concept within behavioral-finance. It directly challenges traditional finance theories by demonstrating that psychological factors and cognitive biases significantly influence individuals' financial decisions, leading to systematic deviations from purely rational behavior.