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13 Pages

### Chap006

Course: FIR 7410, Fall 2008
School: U. Memphis
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Word Count: 377

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and Risk Risk Aversion Chapter 6 McGraw-Hill/Irwin Copyright 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Risk - Uncertain Outcomes p = .6 1 W = 150 Profit = 50 W = 100 1-p = .4 1 2 2 W = 80 Profit = -20 E(W) = pW + (1-p)W = 6 (150) + .4(80) = 122 2 1 2 2 2 = p[W - E(W)] + (1-p) [W - E(W)] = .6 (150-122)2 + .4(80=122)2 = 1,176,000 = 3 4 .2 9 3 6-2 Risky Investments with Risk-Free p = .6...

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and Risk Risk Aversion Chapter 6 McGraw-Hill/Irwin Copyright 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Risk - Uncertain Outcomes p = .6 1 W = 150 Profit = 50 W = 100 1-p = .4 1 2 2 W = 80 Profit = -20 E(W) = pW + (1-p)W = 6 (150) + .4(80) = 122 2 1 2 2 2 = p[W - E(W)] + (1-p) [W - E(W)] = .6 (150-122)2 + .4(80=122)2 = 1,176,000 = 3 4 .2 9 3 6-2 Risky Investments with Risk-Free p = .6 1 Risky Inv. W = 150 Profit = 50 1-p = .4 100 2 Risk Free T-bills W = 80 Profit = -20 Profit = 5 Risk Premium = 17 6-3 Risk Aversion & Utility Investor's view of risk Risk Averse Risk Neutral Risk Seeking Utility Utility Function U = E ( r ) - .005 A 2 A measures the degree of risk aversion 6-4 Risk Aversion and Value: U = E ( r ) - .005 A 2 = .22 - .005 A (34%) 2 Risk Aversion A Value High 5 -6.90 3 4.66 Low 1 16.22 T-bill = 5% 6-5 Dominance Principle Expected Return 4 2 1 Variance or Standard Deviation 3 2 dominates 1; has a higher return 2 dominates 3; has a lower risk 4 dominates 3; has a higher return 6-6 Utility and Indifference Curves Represent an investor's willingness to trade-off return and risk. Example Exp Ret 10 15 20 25 St Deviation U=E ( r ) - .005A 2 20.0 2 25.5 2 30.0 2 33.9 2 6-7 Indifference Curves Expected Return Increasing Utility Standard Return Rule Deviation 6-8 Expected 1 : The return for an asset is the probability weighted average return in all scenarios. E (r ) = P( s)r ( s) s 6-9 Variance of Return Rule 2: The variance of an asset's return is the expected value of the squared deviations from the expected return. = P( s )[r ( s ) - E (r )] s 2 2 6-10 Return on a Portfolio Rule 3: The rate of return on a portfolio is a weighted average of the rates of return of each asset comprising the portfolio, with the portfolio proportions as weights. r p = W 1 r1 + W 2 r2 W1 = Proportion of funds in Security 1 W2 = Proportion of funds in Security 2 r1 = Expected return on Security 1 r2 = Expected return on Security 2 6-11 Portfolio Risk with Risk-Free Asset Rule 4: When a risky asset is ...

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U. Memphis - FIR - 7721
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U. Memphis - FIR - 7721
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Minnesota - EE - 3161
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Minnesota - EE - 3161
Minnesota - EE - 3161
Minnesota - EE - 3161
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R cao 2 o t n eit n sl i s ti uoE 36 sr g 08 E 11 pi 20 n
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