Chapter 13

1. Chapter 13 • Risk Attitudes

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

3. 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

4. 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.

5. 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.

6. 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

7. 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

8. 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.

9. 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

10. 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.

11. 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

12. 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.

13. 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.

14. 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

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