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ajaz_204_2009_lecture_22

ajaz_204_2009_lecture_22 - University of Toronto Department...

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University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 22 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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Today From last time: certainty equivalence Risk Premium (or discount due to risk) Discount for risk = Max payment made to avoid risk Risk premium = Min payment required to absorb risk Insurance Actuarially fair insurance Credit default swaps Interest rate swaps Decisions under uncertainty with information Ajaz Hussain. Department of Economics. University of Toronto (St. George) 2
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Ajaz Hussain. Department of Economics. University of Toronto (St. George) 3 Recall: Certainty Equivalence $ Utility $5 U($5) $10 U($10) EV $8.5 U(EV) 0.7 0.3 0.7 0.3 0.7 0.3 U(X) EU CE U(CE) = EU U(CE) =
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A Gamble: { x 1 , x 2 ; p, 1 p} Ajaz Hussain. Department of Economics. University of Toronto (St. George) 4 Gamble x 1 x 2 p 1 p Suppose: x 1 < x 2 By definition: U(CE) = EU EV CE = “Risk Premium”
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Ajaz Hussain. Department of Economics. University of Toronto (St. George) 5 Risk Premium for Risk Averse $ Utility x 1 U(x 1 ) x 2 U(x 2 ) EV U(EV) 1 - p p 1 - p p 1 - p p U(X) EU CE U(CE) = EU Risk Premium = EV CE > 0 RP Risk Premium aka Discount due to risk
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Ajaz Hussain. Department of Economics. University of Toronto (St. George) 6 Risk Premium for Risk Neutral $ Utility x 1 U(x 1 ) x 2 U(x 2 ) EV U(EV) 1 - p p 1 - p p 1 - p p U(X) EU = CE U(CE) = EU Risk Premium = EV CE = 0
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Risk Premium If you face gamble and want a certain outcome Risk premium = Maximum you’ll pay to avoid risk If you have certain outcome and are asked to gamble Risk premium = Minimum you’ll want to absorb risk Ajaz Hussain. Department of Economics. University of Toronto (St. George) 7
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