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Unformatted text preview: Risk and Rates of Return CHAPTER 8 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. 15105 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 ^ ^ ^ 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 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 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 _ _ Basic Statistics  Ex Ante How could we compare the relative standalone 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 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 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 ] / [N1] s = √ V t = 1 t = 1 N N __ __ 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 t = 1 N __ __ __ __ Basic Statistics  Ex Post V = [ Σ (r t r Avg ) 2 ] / [N1] 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 __ Basic Statistics – Ex Post J 0.16 0.0155 0.1245 K 0.16 0.0643 0.2535 Market 0.07 0.0060 0.0771 Summary of Basic Statistics Security or Portfolio Mean or Average Variance Standard Deviation...
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This note was uploaded on 04/08/2009 for the course FIN 3403 taught by Professor Tapley during the Spring '06 term at University of Florida.
 Spring '06
 Tapley
 Finance

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