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Chapter 13

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- Risk Attitudes

- Learning Objectives:
- Utility Function
- Risk Premium
- Utility Function Assessment
- Exponential utility Function

- 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

- 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.

- 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.

- 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 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

- 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.

- 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

- 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.

- 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

- 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.

- 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.

- 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

- Assessment using Certainty Equivalents
- Exponential Utility Function:
- U(x) = 1-e-x/R
- R is called risk tolerance

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