# Cumulative Prospect Theory Explained

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Cumulative prospect theory, or CPT, was introduced in 1992 by Amos Tversky and Daniel Kahneman. CPT differs from the standard prospect theory by adding weight to the cumulative probability distribution function. It suggests that people think of possible outcomes based on a certain point of reference instead of a final status or outcome.

This creates what is called the framing effect. The goal is often to maintain the status quo, which means there are different risk perceptions when looking at gains or losses from their point of reference. One of the greatest influences, in fact, are the most extreme, but most unlikely, events that occur.

In CPT, people add more weight to what might happen and less weight to what will probably happens. That skews their perception of what can happen and that changes their reactions and behaviors to life events.

In other words, everyone is always trying to plan for the worst-case scenario economically under the cumulative prospect theory.

### What Is Prospect Theory and Why Is It Important?

Prospect theory is a behavioral economic theory. It dictates how people choose to spend or invest their wealth. It states that people make decisions based on the prospect of value in gains or losses instead of trying to create a specific final outcome.

A common example of this theory involves a decision to purchase an insurance policy. In this example, we’re going to assume the probability of risk to the insured is 2%. The potential maximum loss that could occur is \$5,000. The insurance company will set a premium of \$25.

To apply the concepts of prospect theory, we must have a point of reference. We could use the worst-case scenario where \$5,000 is lost. Most people, however, will base a decision on their current wealth.

That means a person is left with a specific choice. They can pay the \$25 and be left with a utility loss of -25 to their wealth. They could also enter into what prospect theory describes as a “lottery” of possible outcomes.

In the lottery, the person will evaluate all possible outcomes to determine a risk level. That risk level will be associated with a specific monetary loss. Is the cost of the insurance premium greater than or less than the risk of not carrying insurance at all?

This creates a four-fold series of possible outcomes that involve gains or losses. There are high probability gains and losses and low probability gains or losses. Let’s say the insurance policy is purchased, a loss occurs, but the company refuses to honor the claim. In this example, the affected person decides to file a civil lawsuit for double damages.

High Probability Gain: The defendant is given an 80% chance to win \$10,000, but they are given a 100% chance to settle for \$8,500. 80% x \$10,000 equals a possible outcome of \$8,000, which is less than the guaranteed settlement of \$8,500. Although the settlement is unfavorable, it would be risk averse to accept it.
Low Probability Gain: The defendant is given a 10% chance to win \$10,000, but a 100% chance to settle for \$500. In this instance, 10% x \$10,000 = \$1,000. The hope of a larger gain comes from a refusal to settle.
High Probability Loss: The opposite applies to situations of loss. If there is a 80% chance to lose \$10,000, but a 100% chance to lose \$8,500, the hope to avoid loss is greater so there is a rejection of the settlement.
Low Probability Loss: If there is a 10% chance to lose \$10,000, but a 100% chance to lose \$500, the decision to accept the unfavorable settlement is better because it avoids a potentially great loss.

### How Is CPT Different from Standard Prospect Theory?

Tversky and Kahneman incorporated rank-dependent functionals into their theory. This transforms cumulative probabilities instead of individual probabilities. This was done to satisfy stochastic dominance, which the original prospect theory did not take into account.

At the same time, the two primary components of the standard prospect theory are retained in CPT.

• Gains or losses are based on value carriers instead of final assets or overall wealth.
• Outcome values are multiplied by decision weight instead of additive probabilities.

People will deal with risk in many different ways. Every situation that a person will encounter offers risk. Managing that risk depends on whether or not it is identified as being acceptable or unacceptable. There are 4 basic methods of handling risk that can be incorporated into CPT by merging the principles of enterprise risk management structures with it.

1. Avoidance. This method of risk management means nothing will be done. The risk is recognized, but then it is ignored.
2. Mitigation. This method of management implements control factors, countermeasures, and specific fixes that target high risk situations. There will always be some level of risk, but the implemented mitigating factors make it easier to manage.
3. Transfer. Instead of dealing with risk, one method of dealing with it is to transfer it to a different entity. One way to transfer risk would be to purchase an insurance policy. In CPT, risk transfer might mean shifting responsibilities to other entities.
4. Acceptance. In this method, the risk is identified and actions are taken despite its presence. Unknowns are still present, but do not stop individuals or organizations from taking an action.

The problem with CPT is that most people do not look at the value of probability in a uniform way. Lower probability issues are usually over-weighted and higher probability issues are usually over-weighted. Going back to the gains and losses listed above, the average person will put more weight on the most favorable outcome and then ignore the risks that come with that decision.

Instead of accepting the 100% probability of winning \$8,500 in the lawsuit, the individual involved would choose the 80% probability of winning \$10,000. The fact that they could not win anything because of the 20% reduction in probability is ignored, with the focus placed on the larger monetary amount instead.

This affects the economics on local, regional, national, and even international levels, depending on the amount in question and how much risk is being ignored or avoided. The 2007 Great Recession, which affected economies around the world, is an example of risk avoidance where the short-term gains, not the long-term potential outcome, were evaluated for risk. Eventually, the risk percentages grew to the point where it became more likely for failure to occur and it eventually did.

On a personal level, purchasing a stock to sell tomorrow no matter what instead of holding onto it to maximize its growth could be an example of local CPT application.

Risk will always be present. If we evaluate it fairly, we can make risk averse decisions more often, and that will benefit us all from an economic point of view.