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ch06 - 6-1 Lecture II(Chapter 6(7th/8th/9th edition 6-2 6-3...

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6-1 Lecture II (Chapter 6 (7 th /8 th /9 th edition)) 6-2 6-3 FIN 275 (Part I) Lecture II – p. 3 W = $100 W 1 = $150 Profit = $50 W 2 = $80 Profit = $-20 p = .6 1-p = .4 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 σ = 34.293 Risk - Uncertain Outcomes
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6-4 FIN 275 (Part I) Lecture II – p. 4 W = 100 W 2 = 80 Return 2 = -0.20 p = .6 1-p = .4 E(r) = pr 1 + (1-p)r 2 = .6 (0.50) + .4(-0.20) = 0.22 = .6 (50%) + .4(-20%) = 22% σ 2 = p[r 1 - E(r)] 2 + (1-p) [r 2 - E(r)] 2 = = .6 (0.5-0.22) 2 + .4(-0.2-0.22) 2 = 0.1176 σ = 0.34293 = .6 (50%-22%) 2 + .4(-20%-22%) 2 = 1,176% σ = 34.293% Risk - Uncertain Outcomes W 1 = 150 Return 1 = 0.50 m 6-5 FIN 275 (Part I) Lecture II – p. 5 p = .6 1-p = .4 100 Risky Inv. Risk Free T-bills W Rf =105 Return Rf = 0.05 Risk Premium = E(r) –r Rf = 0.22 – 0.05 = 0.17 Risky Investments with Risk-Free Investment W 1 = 150 Return 1 = 0.50 W 2 = 80 Return 2 = -0.20 6-6 FIN 275 (Part I) Lecture II – p. 6 Speculation Assumption of considerable business risk in obtaining commensurate gain (i.e. a sufficient risk premium) Gamble Bet or wager on an uncertain outcome No mention of commensurate gain The difference may be due to “ heterogeneous expectations Two speculators may take the opposites sides of a gamble if they assign different probabilities to the possible outcomes. Risk - Speculation vs. Gambling
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6-7 FIN 275 (Part I) Lecture II – p. 7 Investor’s view of risk Risk Averse Risk Neutral Risk Seeking Who will accept a “fair game”? Utility - describes preferences Utility Function: U = E ( r ) - .005 A σ 2 A measures the degree of risk aversion Estimating the degree of risk aversion: Use questionnaires, e.g. http://njaes.rutgers.edu/money/riskquiz/default.asp Observe individual decisions when confronted with risk Observe how much people are willing to pay to avoid risk Risk Aversion & Utility 6-8 FIN 275 (Part I) Lecture II – p. 8 Risk Aversion and Value: Using the Sample Investment U % = E ( r ) - .005 A σ 2 (in percentages) = 22 - .005 A (34) 2 U D = E ( r ) - .5 A σ 2 (in decimals) = 0.22 - .5 A (0.34) 2 Risk Aversion A U % U D U T-Bill High 5 -6.90 -0.069 5 3 4.66 0.0466 5 Low 1 16.22 0.1622 5 6-9 FIN 275 (Part I) Lecture II – p. 9 Mean-Variance (M-V) Criterion Portfolio A dominates portfolio B if: And If both conditions are not met, A does not dominate B
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6-10 FIN 275 (Part I) Lecture II – p. 10 Dominance Principle 1 2 3 4 Expected Return Standard Deviation
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