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ch8 - CHAPTER 8 Risk and Rates of Return Investment Risk...

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Risk and Rates of Return CHAPTER 8

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Investment Risk Risk arises from and reflects uncertainty. Investment risk is the probability of earning less than some expected return.
Investment Risk Risk can be measured in two basic ways: Risk of a single stock or project (sigma or standard deviation) Risk in a portfolio sense (beta) Risk can also be measured on an ex ante or ex post basis.

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-15 -10 -5 0 5 10 15 20 25 30 35 Firm B Firm A 0 14 Expected Rate of Return Probability Distributions Which firm has more risk?
Basic Statistics - Ex Ante r = Σ P i r i σ 2 = Σ P i (r i - r) 2 σ = Variance = √σ 2 CV = σ / r i = 1 N i = 1 N ^ ^ ^

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Basic Statistics - Ex Ante J K Market Boom 0.30 0.40 0.20 0.20 Normal 0.40 0.10 0.40 0.10 Recession 0.30 0.00 - 0.20 - 0.10 Security or Portfolio State of Nature Probability of State
r J (.30)(.40) + (.40)(.10) + (.30)(.00) 16% r K (.30)(.20) + (.40)(.40) + (.30)(-.20) 16% r M (.30)(.20) + (.40)(.10) + (.30)(-.10) 7% ^ ^ ^ Basic Statistics - Ex Ante

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Basic Statistics - Ex Ante σ 2 = Σ P i (r i - r) 2 σ j 2 = (.3)(.40 - .16) 2 + (.4)(.10 - .16) 2 + (.3)(.00 - .16) 2 = .0264 σ J = .0264 = .1625 ^
Basic Statistics - Ex Ante J 0.16 0.0264 0.1625 K 0.16 0.0624 0.2498 Market 0.07 0.0141 0.1187 Security or Portfolio Standard Deviation Mean or Average Variance Summary of Basic Statistics

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Clear All .40 Σ + (enter 3 times) .10 Σ + (enter 4 times) .00 Σ + (enter 3 times) x,y 0.1600 = mean Statistics with 10B Calculator For Security J _ _
Clear All .20 Σ + (enter 3 times) .40 Σ + (enter 4 times) .20 ± Σ + (enter 3 times) x,y 0.1600 = mean Statistics with 10B Calculator For Security K _ _

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Basic Statistics - Ex Ante How could we compare the relative stand-alone risk of Securities J and K if their distributions had different expected returns? Calculate the coefficient of variation.
CV A < CV B Coefficient of Variation Firm A Firm B

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Basic Statistics - Ex Ante CV = σ / r CV J = (0.1625) / (0.16) = 1.0156 CV K = (0.2498) / (0.16) = 1.5613 CV M = (0.1187) / (0.07) = 1.6957 ^
Firm A Firm B Coefficient of Variation CV A < CV B

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Firm B Firm A Coefficient of Variation CV A < CV B
Basic Statistics - Ex Post r Avg = [ Σ r t ] / [N] V = [ Σ (r t - r Avg ) 2 ] / [N-1] s = V t = 1 t = 1 N N __ __

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Basic Statistics - Ex Post J K Market 1 - 0.05 0.10 - 0.03 2 0.25 0.40 0.05 3 0.15 - 0.25 0.05 4 0.20 0.30 0.10 5 0.25 0.25 0.18 Prior Years Security or Portfolio
Basic Statistics - Ex Post r Avg = [ Σ r t ] / [N] r J = [(-.05) + (.25) + (.15) + (.20) + (.25)] / [ 5 ] = 0.16 r K = 0.16 r = 0.07 t = 1 N __ __ __ __

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Basic Statistics - Ex Post V = [ Σ (r t - r Avg ) 2 ] / [N-1] V J = [ (-.05 - .16) 2 + (.25 - .16) 2 + (.15 - .16) 2 + (.20 - .16) 2 + (.25 - .16) 2 ] / [5 - 1] = 0.0155 S J = 0.0155 = 0.1245 t = 1 N __
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