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IFT_Chapt5_sli - 5.2 Risk Aversion and Portfolio Allocation...

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5.2 Risk Aversion and Portfolio Allocation; Risk Free vs. Risky Assets 5.3 Portfolio Composition, Risk Aversion and Wealth 5.4 Risk Aversion and Risky Portfolio Composition 5.5 Risk Aversion and Saving Behavior 5.6 Key Concepts and Results Intermediate Financial Theory Chapter V. Risk Aversion and Investment Decisions, Part I June 26, 2006 Intermediate Financial Theory
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5.2 Risk Aversion and Portfolio Allocation; Risk Free vs. Risky Assets 5.3 Portfolio Composition, Risk Aversion and Wealth 5.4 Risk Aversion and Risky Portfolio Composition 5.5 Risk Aversion and Saving Behavior 5.6 Key Concepts and Results The Canonical Portfolio Problem The various problems considered in this chapter (and the next) max a EU ( ˜ Y 1 ) = max EU ( Y 0 ( 1 + r f ) + a r - r f )) , (1) Consider first an agent solving the following two period consumption-savings problem: max s E { U ( Y 0 - s ) + δ U ( s ˜ R ) } , s.t. Y 0 s 0 (2) max { a , s } U ( Y 0 - s ) + δ EU ( s ( 1 + r f ) + a r - r f )) , (3) Intermediate Financial Theory
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5.2 Risk Aversion and Portfolio Allocation; Risk Free vs. Risky Assets 5.3 Portfolio Composition, Risk Aversion and Wealth 5.4 Risk Aversion and Risky Portfolio Composition 5.5 Risk Aversion and Saving Behavior 5.6 Key Concepts and Results The Canonical Portfolio Problem max a EU ( ˜ Y 1 ) = max EU ( Y 0 ( 1 + r f ) + a r - r f )) , (4) First order condition (FOC): E U ( Y 0 ( 1 + r f ) + a r - r f )) (˜ r - r f ) = 0 (5) Theorem (Theorem 5.1:) Assume U ( ) > 0 , and U ( ) < 0 and let ˆ a denote the solution to problem (1). Then ˆ a > 0 E ˜ r > r f ˆ a = 0 E ˜ r = r f ˆ a < 0 E ˜ r < r f Intermediate Financial Theory
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5.2 Risk Aversion and Portfolio Allocation; Risk Free vs. Risky Assets 5.3 Portfolio Composition, Risk Aversion and Wealth 5.4 Risk Aversion and Risky Portfolio Composition 5.5 Risk Aversion and Saving Behavior 5.6 Key Concepts and Results
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