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) ² Discount for risk = Max payment made to avoid risk ² Risk premium = Min payment required to absorb risk ± Insurance ² Actuarially fair insurance ² Credit default swaps ² 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) U = 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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Risk Avoidance: Uncertainty to Certainty Ajaz Hussain. Department of Economics. University of Toronto (St. George) 8 Decision Gamble x 1 x 2 Certain Outcome 1 p p Examples Insurance Interest Rate Swaps
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Risk Avoidance If you face a gamble Risk premium is how much you’ll pay to avoid risk A risk averse person pays to avoid risk Ajaz Hussain. Department of Economics. University of Toronto (St. George) 9 Face Gamble Paid Max Risk Premium to Avoid Risk Outcome ($) EV EV RP = CE Utility EU U(CE)
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Ajaz Hussain. Department of Economics. University of Toronto (St. George) 10 Risk Avoidance $ Utility Wealth - Loss U(x 1 ) Wealth U(x 2 ) EV U(EV) 1 - p p 1 - p p 1 - p p U(X) EU CE U(CE) = EU Risk Premium > 0 RP
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Ajaz Hussain. Department of Economics. University of Toronto (St. George) 11 Differing Risk Aversion $ Utility Wealth - Loss Wealth EV A CE A Risk Premium B > Risk Premium A CE B B
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Risk Absorption: Certainty to Uncertainty Ajaz Hussain. Department of Economics. University of Toronto (St. George) 12 Decision? Gamble x 1 x 2 Certain Outcome 1 p p Examples Quit job to start new business Competing job offers
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Risk Absorption If you have a certain outcome Risk premium is how much you’ll want to absorb risk A risk averse person must be paid to absorb risk Ajaz Hussain. Department of Economics.
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ajaz_204_2009_lecture_22 - University of Toronto Department...

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