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Behavioral Finance

Behavioral Finance. Economics 437. Utility Theory (Under Certainty). X. Ordinal Utility (only order matters). Y. But what happens with uncertainty. Suppose you know all the relevant probabilities Which do you prefer? 50 % chance of $ 100 or 50 % chance of $ 200

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Behavioral Finance

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  1. Behavioral Finance Economics 437

  2. Utility Theory (Under Certainty) X Ordinal Utility (only order matters) Y

  3. But what happens with uncertainty • Suppose you know all the relevant probabilities • Which do you prefer? • 50 % chance of $ 100 or 50 % chance of $ 200 • 25 % chance of $ 800 or 75 % chance of zero

  4. Use “Expected Value” to Decide • Which do you prefer? • 50 % chance of $ 100 or 50 % chance of $ 200 • 25 % chance of $ 800 or 75 % chance of zero • Expected Value (average result) • $ 150 • $ 200 • So, you would prefer the 2nd option to the 1st ?

  5. Bernoulli Paradox • Imagine flipping a “fair”coin (½ chance of flipping heads; ½ chance of flipping tails) • Suppose the first time you flip a heads you receive • 2N dollars, where N is the first time you flip heads: $ 2, $ 4, $ 8, $ 16, etc. • Expected value = 2(1/2) plus 4(1/4) plus 8(1/8) plus…………………. = 1 + 1 + 1 + …..

  6. Value of Bernoulli Game is Infinite • This means if you order things by expected value, you pay any price to play this game – any price! • This is known as the Bernoulli Paradox

  7. John Von Neumann (founder of game theory) • Four reasonable axioms: • Completeness: for every A and B either A ≥ B or B ≥ A (≥ means “at least as good as” • Transitivity: for every A, B,C with A ≥ B and B ≥ C then A ≥ C • Independence: let t be a number between 0 and 1; if A ≥ B, then for any C,: • t A + (1- t) C ≥ t B + (1- t) C • Continuity: for any A,B,C where A ≥ B ≥ C: there is some p between 0 and 1 such that: • B ≥ p A + (1 – p) C

  8. Conclusion • If those four axioms are satisfied, there is a utility function that will order “lotteries” • Known as “expected utility”

  9. For any two lotteries, calculate expected utility • p U(X) + (1 – p) U(Y) • q U(S) + (1 – q) U(T) • U(X) is the utility of X when X is known for certain; similar with U(Y), U(S), U(T)

  10. Mid Term Exam Tues Feb 19 • Will cover material through today • All of the reading • Nothing is left out • All of the classes through Tuesday Feb 12 • Does not include material covered today • Last name A, B, C, D report to Physics 204 • Everyone else in Wilson Auditorium

  11. The End

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