Chapter 3 Risk Attitudes: Expected Utility Theory and Demand for Hedging

Determining an Individual’s Level of Satisfaction Classical economic theory assumes that individuals make rational decisions in order to enhance their level of satisfaction in any given situation. Behavioral economics recognizes that an individual’s emotional needs can override rational decision-making. The rational economic approach assumes that greater wealth (a larger budget) leads to choices yielding higher levels of personal satisfaction than choices available to lower budgets.

Expected Utility Utility theory is interested in people’s perceptions of the most satisfying outcome of situations whose outcomes are uncertain. Expected utility theory (EU) deals with choices that individuals make when the outcomes they face are uncertain. Utility theory assumes that when faced with either certainty or uncertainty, individuals try to maximize their utility in different outcomes.

Utility Theory Utility theory postulates that people can consistently rank their choices based on their personal preferences. To rank is to mentally list items from their highest to lowest perceived value. One can know that a particular item is worth more than another without necessarily being able to assign each item a specific number value.

Utility Theory (continued) Positive theory seeks to explain an individual’s observed behavior and choices. Normative theory dictates the manner in which people should behave.

Utility Theory (continued) Utility function: A mathematical formulation that ranks an individual’s preferences in terms of the satisfaction various consumption bundles stand to provide. Ordinal utility: Ranking utility that compares the relative satisfaction levels associated with two or more alternatives. Cardinal utility: Utility that represents an individual’s absolute satisfaction level.

Assumptions Underlying Utility Theory 1.Completeness: Every person can rank all possible bundles according to individual preferences. 2.Monotonicity: More consumption is always better. 3.Mix-is-better: A mix of consumption bundles is better than stand-alone choices. 4.Rationality: A person’s rank order of preferences always stays fixed.

Well-behaved Utility Function A well-behaved utility function is one for which all four of the underlying utility assumptions have been met. Note that in this process, individuals begin with wealth that can be directed at choices selected to maximize their utility and their satisfaction, but not their wealth itself.

Uncertainty, Expected Value and Fair Games Subjective probability measures the perceived probability of a given outcome based on an individual’s feelings and/or experience, rather than on mathematical calculation. Empirical or mathematical probability records outcomes, and divides the number of adverse outcomes by the total number of events that could generate each one. *For example, for every 100 homes, there are 2 house fires each year. 2/100 (1/50) is the probability of any house having a fire over the next 12 months.

Expected Value Expected value, also called average value, is critical in risk management and insurance. Expected value enables people and enterprises to reduce uncertainty, thereby reducing risk. Expected value is calculated by taking the sum of the products of two numbers (a dollar loss and a probability percentage) for a number of possible loss outcomes.

Fair Game A Fair game is a game in which the cost of playing equals the expected winnings, so that net value of the game equals zero. Although a game’s expected utility to an individual is finite, playing nevertheless provides satisfaction.

Maximizing Expected Utility Expected utility applies to situations in which outcomes are uncertain. In spite of uncertainty, it is assumed that the individual wants to maximize expected utility, as opposed to maximizing expected wealth.

A Utility Function for a Risk-Averse Individual Wealth Utility Of Wealth

Considerations for the risk-averse individual’s graph (just above) Concavity: Property of a curve such that a chord connecting any two points on the curve will lie below the curve. Diminishing marginal utility: Utility is always increasing, but at a decreasing rate (as shown in the graph of the risk-averse individual).

Actuarially Fair Premium The actuarially fair premium is the expected loss or average loss for an individual. It is one of three major components of the gross premium that is charged to a customer for an insurance policy. A risk-averse person is willing to pay more than the actuarially fair premium for an insurance policy in order to achieve peace of mind in case of a loss occurring.

A Utility Function for a Risk-Seeking Individual Utility Of Wealth

Considerations for the risk-seeking individual’s graph (just above) Convex utility function: The curve lies strictly below the chord joining any two points on the curve. Increasing marginal utility: Feature of a utility function such that utility (not wealth) is always increasing at an increasing rate.

Biases Affecting Choices Under Uncertainty Behavioral economics: The realm of academic study dealing with departures from expected utility, or E(U), maximization behavior. E(U) does not always explain the choices that individuals actually make under uncertainty. Emotions and feelings can influence choices. Framing effect: different wording or presentation of choices can influence decisions. Value function: A mathematical formulation that seeks to explain observed behavior with no consideration of preferences.

Biases Availability bias: Tendency to work with only information that is easily available. Experience bias: Tendency to assign more weight (importance) to what one has personally experienced. Anchoring bias: Tendency to base subsequent assessments of outcomes upon an initial assessment. Sunk cost: Money already spent that cannot be recovered.

Losses-0-Gains Value Function of Kahneman and Tversky

Considerations of value function graph (just above) This value function (viewed as a purely descriptive device) is much steeper in losses than in gains. In mathematical terms, this value function is convex in losses and concave in gains. This value function is risk-seeking in losses and risk-averse in gains.

Risk Aversion and the Price of Hedging A risk-averse person is willing to pay the actuarially fair price (AFP) in premium to hedge his or her risk. However, at the AFP, the insurer makes no profit. A risk-averse person is also willing to pay more than the AFP to hedge risk, up to a point. If the premium exceeds this point, a risk-averse individual will not buy full insurance.

Information Asymmetry Problem in Economics Information asymmetry: A problem of one party in a contract having more relevant information than another party. Adverse selection: Situation in which a person with a higher risk chooses to hedge the risk, preferably without paying more to do so. The impact of adverse selection is to increase premiums for all people who hedge (e.g. in buying insurance).

Out-of-Pocket Payments Rather than offer full insurance, insurers often sell a contract that is viewed as partial insurance. In a claim, the customer absorbs part of the loss through deductibles and/or coinsurance payments. A deductible, usually the initial part of the loss, is absorbed by the customer with the loss. In coinsurance, the customer shares with the insurer in absorbing the loss.

Moral Hazard Another form of asymmetry exists such that the insured can fail to exercise the degree of care necessary to avoid or reduce loss by the insurer. This is one type of moral hazard. An insured can try to take advantage of the insurer by misrepresenting information and/or behavior. This is another type of moral hazard. An insurer can gather additional information about the insured to try to reduce moral hazard. However, gathering more information creates more underwriting costs for the insurer.

Why Corporations Hedge 1)Managers hedge because they are undiversified. 2)Managers want to lower expected bankruptcy costs. 3)Risk bearers may be in a better position to bear risk.

Why Corporations Hedge (continued) 4) Hedging can increase debt capacity. 5) Hedging may lower tax liability. 6) Regulation may limit the amount of risk taking; some insurance (such as workers’ compensation) must be purchased as a sign of credit-worthiness.

End of Chapter 3