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# Risk and Return Problem, Chapter 5

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Chapter 5, problem 5 from Essentials of Investments, by Bodie, Kane and Marcus, 8th edition.

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• ### Risk and Return Problem, Chapter 5

1. 1. Essentials of Investments BODIE, KANE, MARCUS, 8TH EDITION Problem + Solution for Chapter 5, Problem 5
2. 2. Compute mean and standard deviation of the market, given: State of the Probability HPR economySuppose this is your expectation of the Boom 0.3 44%return on the entire stock market NormalUse equations 5.6.-5.8 0.4 14 GrowthPages 114-115 of the textbook Recession 0.3 -16
3. 3. Expected Return = E(r)Expected return of the stock (s) is the mean value, or average of the return (r).The probabilities are weighted based on probability (p).
4. 4. Mean = Probability * Return State of the Probability HPR economyAll probabilities add up to equal 1,or 100% Boom 0.3 44%.3 + .4 + .3 = 1 Normal 0.4 14 Growth30% + 40% + 30% = 100% Recession 0.3 -16
5. 5. Calculate! State of the Probability HPR economy.3 * 44 = 13.2.4 * 14 = 5.6 Boom 0.3 44%.3 * -16 = -4.8 Normal 0.4 14 Growth13.2 + 5.6 + -4.8 = 14% Recession 0.3 -16
6. 6. Expected Return E(r)14% is the E(r), or mean
7. 7. Equation for meanE(r) = ∑ p(s) r(s)Expected (r)eturn is equal to the sum of the (s)tock’s(p)robabilities multiplied by the (r)eturns
8. 8. Compute State of the Probability HPRRemember:Compute mean and economystandard deviation of the HPR Boom 0.3 44%given: NormalMean = 14 Growth 0.4 14Standard Deviation Recession 0.3 -16
9. 9. σ =standard deviationTo calculate standard deviation, you must first calculatevariance.
10. 10. σ 2= varianceVariance is equal to the square of standard deviation.Calculate variance using E(r) or Expected Return, which we havealready calculated
11. 11. Finding variance - Part 1 State of the Probability HPR economy p(s) r(s)Simply subtract the expected return fromthe HPR for each row, and square that value Boom 0.3 44%[r(s) - E(r)]2 Normal 0.4 14 GrowthRemember: We calculated E(r) = 14 Recession 0.3 -16
12. 12. Compute! HPR r(s) - E(r) [r(s) - E(r)]2 r(s)Subtract E(r) from each HPR to find 44 44-14 = 30 30 2 =900the difference.Then, square this number. 14 14-14 = 0 0 2 =0 -16 -16 - 14 = -32 -32 2 =1024
13. 13. Weight the Variance - Part 2 State of Probability HPR Variance the p(s) r(s) Var(r) economyNow the variance must be weighted as well Boom 0.3 44% 900You’ll use the same probabilities p(s) as Normalbefore 0.4 14 0 Growth Recession 0.3 -16 1024
14. 14. Equation for Varianceσ 2 = ∑ p(s) [r(s) - E(r)]2
15. 15. Compute!Variance = .3 * (900) + .4 * (0) + .3 (1024)Variance = 270 + 0 + 307.2 = 577.2
16. 16. From Variance to Standard DeviationSimply find the square root of the variance.σ 2 = 577.2σ = √577.2σ = 24.0249
17. 17. Final AnswerMean = 14.0%Standard Deviation = 24.0%