chapter13 by xiangpeng

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									               Chapter 13
• Risk Attitudes




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      Chapter 13, Risk Attitudes
• Learning Objectives:

•   Utility Function
•   Risk Premium
•   Utility Function Assessment
•   Exponential utility Function

                                   2
             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.

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              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



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                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.


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             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

                                                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
                                              11
             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
  trade-offs
• Basic procedure for assessing utility
  function
• Certainty Equivalents and Risk Premium


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