Economic Theory of Choice Certainty

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VII. Choices Among Risky Portfolios
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Choices Among Risky Portfolios

• Utility Analysis
• Safety First

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Utility Analysis Choice among risky portfolios
depends on risk return trade off More formally
depends on maximizing value to me or utility of
outcomes Utility functions are a mathematical
way of determining the value of different choices
to the investor
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• Properties we believe utility functions for most
  individual should have
• Prefer more to less non satiation
• Require compensation for taking risk
• Risk Aversion
• Additional Qualities to Consider
• More of less dollars at risk as wealthier
• Larger or smaller percentage of wealth at risk as
  wealthier

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• What happen to willingness to take a bet (put a
  sum of money at risk) as wealth changes.
• Investor Absolute risk Aversion Measured by

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What happens to willingness to risk a fraction of
money as wealth changes
Relative Risk Aversion
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• What do we know most individuals exhibit
• Non Satiation
• Risk Aversion
• Decreasing Absolute Risk Aversion
• Either Constant or decreasing relative risk
  aversion

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• Other Portfolios Selection Criteria
• Safety First
• Maximize Geometric Mean

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• Safety First
• Investors wont go through complex Utility
• Calculations but need a simpler way to select a
  portfolio.
• Investors thinks in terms of bad outcomes.
• Criteria
• Telser
• Kataoka
• Roy

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Roys Criteria Minimize Prob Rp lt RL
Minimize the probability of a return lower than
some limit e.g minimize the Probability of the
return below zero
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Tesler Criteria Maximize expected return
subject to the Probability of a lower limit is no
greater than some number e.g., Maximize
expected return given that the chance of having a
negative return is no greater than 10 e.g.,
Maximize expected return given that the chance of
not earning the actuarial rate is no greater then
5.
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• Maximize the Geometric Mean Return
• Has the highest expected value of terminal
• wealth
• Has the highest probability of exceeding given
  wealth level
• What is geometric mean

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• Maximizing the geometric Mean
• In general will not maximize expected utility
• May select a portfolio not on the efficient
• frontier
• If the portfolio is on the efficient frontier it
• involves a particular risk return trade
  off
• If returns are log normally distributed or
  utility
• Functions are log normal
• U(W) ln (W)
• Then we can show that the portfolio which has
• Maximum geometric mean return lies on the
• Efficient frontier.