Chapter06-07RiskRatesReturnCAPM

Chapter06-07RiskRatesReturnCAPM - OEM 2009 Program...

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OEM 2009 Program Risk and Rates of Return Page 1 CHAPTERS 6 AND 7 Risk and Rates of Return 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: z Risk of a single stock or project (sigma or standard deviation) z Risk in a portfolio sense (beta) ± Risk can also be measured on an ex ante or ex post basis. Probability Distributions -15 -10 -5 0 5 10 15 20 25 30 35 Firm B 0 14 Expected Rate of Return risk? Basic Statistics - Ex Ante r = Σ P i r i σ 2 = Σ P ( - r 2 i = 1 N N ^ ^ P i (r i r) σ = Variance = √σ 2 CV = σ / r i = 1 ^ Basic Statistics - Ex Ante JK M a r k e t Boom 0.30 0.40 0.20 0.20 Security or Portfolio State of Nature Probability of State Normal 0.40 0.10 0.40 0.10 Recession 0.30 0.00 - 0.20 - 0.10
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OEM 2009 Program Risk and Rates of Return Page 2 r J (.30)(.40) + (.40)(.10) + (.30)(.00) 16% ^ ^ Basic Statistics - Ex Ante r K (.30)(.20) + (.40)(.40) + (.30)(-.20) 16% r M (.30)(.20) + (.40)(.10) + (.30)(-.10) 7% ^ 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 Security or Portfolio Standard Deviation Mean or Average Variance Summary of Basic Statistics J 0.16 0.0264 0.1625 K 0.16 0.0624 0.2498 Market 0.07 0.0141 0.1187 ± Clear All .40 Σ + (enter 3 times) .10 Σ + (enter 4 times) Statistics with 10B Calculator For Security J .00 Σ + (enter 3 times) ± x,y Î 0.1600 = mean ± σ x , σ y Î 0.1625 = standard deviation __ ± Clear All .20 Σ + (enter 3 times) .40 Σ + (enter 4 times) Statistics with 10B Calculator For Security K .20 ±Σ + (enter 3 times) ± x,y Î 0.1600 = mean ± σ x , σ y Î 0.2498 = standard deviation Basic Statistics - Ex Ante ² How could we compare the relative stand-alone risk of Securities J and K if their di t ib ti h d diff distributions had different expected returns? ± Calculate the coefficient of variation.
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OEM 2009 Program Risk and Rates of Return Page 3 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 Coefficient of Variation CV A B Firm B Firm A Coefficient of Variation CV A B Firm B Basic Statistics - Ex Post r Avg =[ Σ r t ] / [N] V = [ Σ ( 2 ]/[N 1 t = 1 N N __ __ V = [ (r t - r Avg ) ] / [N-1] s = V t = 1 Basic Statistics - Ex Post JK M a r k e t Prior Years Security or Portfolio 1 - 0.0 5 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
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OEM 2009 Program Risk and Rates of Return Page 4 Basic Statistics - Ex Post r Avg =[ Σ r t ] / [N] = [ 05) + ( 25) + ( 15) + ( 20 t = 1 N __ __ r J [(-.05) + (.25) + (.15) + (.20) + (.25)] / [ 5 ] = 0.16 r K =0 . 1 6 r M = 0.07 __ __ Basic Statistics - Ex Post V = [ Σ (r t -r Avg ) 2 ] / [N-1] V J = [ (-.05 - .16) 2 + (.25 - .16) 2 t = 1 N __ + (.15 - .16) 2 + (.20 - .16) 2 + (.25 - .16) 2 ] / [5 - 1] = 0.0155 S J = 0.0155 = 0.1245 Basic Statistics – Ex Post Summary of Basic Statistics Security or Portfolio Mean or Average Variance Standard Deviation J 0.16 0.0155 0.1245 K 0.16 0.0643 0.2535 Market 0.07 0.0060 0.0771 ± Clear All .05 ±Σ + .25 Σ + Statistics with 10B Calculator For Security J .15 Σ + .20 Σ + .25 Σ + ± x,y Î 0.1600 = mean ± s x ,s y Î 0.1245 = standard deviation _ _ ± Clear All .10 Σ + .40 Σ + Statistics with 10B Calculator For Security K .25 + .30 Σ + .25 Σ + ± x,y Î 0.1600 = mean ± s x ,s y Î 0.2535 = standard deviation _ _ Normal Distribution r ^ 1 σ 2 σ 3 σ + _ + _ + _
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OEM 2009 Program Risk and Rates of Return Page 5 Z-Scores ± 1 σ = 68.26 % ± 2 σ = 95.46 % ± 3 σ =9 97 4% Cumulative probabilities for a normal distribution 3 = 99.74 %
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This note was uploaded on 05/12/2010 for the course FIN 5405 taught by Professor Tapley during the Summer '08 term at University of Florida.

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Chapter06-07RiskRatesReturnCAPM - OEM 2009 Program...

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