# chapter13 by xiangpeng

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```									               Chapter 13
• Risk Attitudes

1
Chapter 13, Risk Attitudes
• Learning Objectives:

•   Utility Function
•   Utility Function Assessment
•   Exponential utility Function

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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

3
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.
4
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.

5
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

6
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

7
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.

8
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

9
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.

10
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
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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.

12
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.                      13
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
14
Risk Attitudes
• Summary
• Basic concepts that underlie risk and return
• Basic procedure for assessing utility
function
• Certainty Equivalents and Risk Premium

15

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