Chapter 13 Risk Attitudes .

Chapter 13, Risk Attitudes Learning Objectives: Utility Function Risk Premium Utility Function Assessment Exponential utility Function

Risk Attitudes This chapter will discuss the problems associated with risk and return trade-off. Study of preference for decision making It is important for decision maker to consider their attitudes toward risk

Risk Basic decision on expected monetary values (EMVs) is convenient, but it can lead to decision that may not seem intuitively appealing. Using expected Values to make decision means that the decision maker is considering only the average payoff EMV does not capture the risk attitudes.

Utility Function The utility Function represents a way to translate dollars into “Utility Units”. A utility function might be specified in terms of : Graph Tabular form Mathematical expression.

Risk Attitude Utility Function is only a model of an individual’s attitude toward risk. Three different shapes for utility functions: Risk-Seeking Risk-Neutral Risk-Avers

Risk Attitude Risk neutrality is reflected by a utility curve that is simply a straight line. For Risk Neutral person , maximizing EMV is the same as maximizing expected utility A convex (opening upward) utility curve indicates risk-seeking behavior A concave (opening downward) utility curve indicates risk-averse behavior

Risk Attitude The purpose of a utility function is to help decision maker to choose from among alternatives that have uncertain payoffs. Instead of maximizing expected value, the decision maker should maximize expected utility.

Risk Attitudes Expected Utility Using Expected Utility to rank alternatives in order of preference Two concepts are closely linked to the idea of expected utility: Certainty Equivalent Risk Premium

Risk Attitudes Certainty Equivalent: the amount of money that is equivalent in your mind to given situation that involves uncertainty. Ranking alternatives by their certainty equivalents is the same as ranking them by their expected utilities.

Risk Attitude The notation of a Risk Premium can be thought of as a measure of how risk-averse a decision maker is in regard to a particular risky situation. The risk premium is defined as the difference between the EMV and the certainty equivalent. Risk Premium=EMV - Certainty Equivalent

Risk Attitudes Certainty equivalent is a dollar amount, whereas expected utility is in utility units A certainty equivalent is not the same as the expected utility The two measurements translate through the utility function.

Utility Function Assessment The basic procedure for assessing a utility function requires comparison of lotteries with riskless payoffs Different people have different risk attitudes and thus are willing to accept different level of risk. Assessing a utility function is a matter of subjective judgment, just like assessing subjective probability.

Utility Function Assessment Two utility-Assessment approaches: Assessment using Certainty Equivalents Requires the decision maker to assess several certainty equivalents Assessment using Probabilities This approach use the probability-equivalent (PE) for assessment technique Exponential Utility Function: U(x) = 1-e-x/R R is called risk tolerance

Risk Attitudes Summary Basic concepts that underlie risk and return trade-offs Basic procedure for assessing utility function Certainty Equivalents and Risk Premium