Transcription of Understanding Risk-Aversion through Utility Theory
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Understanding Risk-Aversion through Utility Theory
Understanding Risk-Aversion through Utility TheoryAshwin RaoICME, Stanford UniversityFebruary 3, 2020 Ashwin Rao (Stanford) Utility TheoryFebruary 3, 20201 / 14 Intuition on Risk-Aversion and Risk-PremiumLet s play a game where your payoff is based on outcome of a fair coinYou get $100 for HEAD and $0 for TAILHow much would you pay to play this game?You immediately say: Of course, $50 Then you think a bit, and say: A little less than $50 Less because you want to be compensated for taking the risk The wordRiskrefers to the degree of variation of the outcomeWe call this risk-compensation asRisk-PremiumOurpersonality-baseddegree of risk fear is known asRisk-AversionSo, we end up paying $50 minus Risk-Premium to play the gameRisk-Premium grows with Outcome-Variance & Risk-AversionAshwin Rao (Stanford) Utility TheoryFebruary 3, 20202 / 14 Specifying Risk-Aversion through a Utility functionWe seek a valuation formula for the amount we d pay that.
From the section on CRRA Utility, we know we need to maximize: r + ˇ( r) ˇ2˙2 2 + ˇ2˙2(1 ) 2 = r + ˇ( r) ˇ2˙2 2 So optimal investment fraction in risky asset ˇ = r ˙2 Ashwin Rao (Stanford) Utility Theory February 3, 2020 14/14
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