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# Ch6_1 - Risk and Risk Aversion Chapter 6 Risk altitude Risk...

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Risk and Risk Aversion Chapter 6

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Risk altitude Risk neutral Only care about expected return Risk seeking Pay to take risk Risk averse Compensated to take risk Assumption of portfolio theory Utility function Positive in expected return Negative in risk
Prospect W = 100 W 1 = 150 Profit = 50 W 2 = 80 Profit = -20 p = .6 E(W) = pW 1 + (1-p)W 2 = .6 (150) + .4(80) = 122 σ 2 = p[W 1 - E(W)] 2 + (1-p) [W 2 - E(W)] 2 = .6 (150-122)2 + .4(80=122)2 = 1,176,000 σ = 34.293

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Prospect with riskfree investment W 1 = 150 Profit = 50 W 2 = 80 Profit = -20 p = .6 1-p = .4 Risky Inv. Risk Free T-bills Risk Premium = 17 Profit = 5 W = 100
Utility function Fair game – zero risk premium Risk averse investors reject fair game Utility Function of risk averse investor U = E ( r ) - .005 A σ 2 A’ measures the degree of risk aversion

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Example U = E ( r ) - .005 A σ 2 = .22 - .005 A (34%) 2 Risk Aversion A Value T-bill (5%) High 5 -6.90 5 3 4.66 5 Low 1 16.22 5 -Certainty equivalent rate
Dominance Principle 1 2 3 4 Expected Return Variance or Standard Deviation 2 dominates 1; has a higher return • 2 dominates 3; has a lower risk • 4 dominates 3; has a higher return

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Ch6_1 - Risk and Risk Aversion Chapter 6 Risk altitude Risk...

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