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Chrome File Edit View History Bookmarks People Window Help 4 40% Wed Nov 18 7:48:31 PM P Ebadi E c consider The Following cl Can't Figure out The Vari Chapter 13 Graded Home ezto.mheducation.co m/hm.tpx M yahoomail Reddit Facebook youtube soundcloud G orange mail -k D2L okey Account Servi Muscle Matrix: welce other Bookmarks App Consider the following information about three stocks Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock C Stock B -20 46 40 .25 .23 .200 40 03 .25 42 a-1 If your portfolio is invested 35 percent each in A and Band 30 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Portfolio expected return a-2 What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, g., 32.1616 ariance a-3 What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation b. If the expected T-bill rate is 4.50 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected risk premium c-1 If the expected inflation rate is 4.00 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Approximate expected real return Exact expected real return portfolio? (D c-2 What expected intermediate calculations. Enter your answers as a percent rounded to 2 decimal places e 32.16.) Approximate expected real risk premium Exact expected real risk premium Show All RWJ Chapter 11 (1). doc

Explanation / Answer

where

where expected return = sum of weight of stock in portfolio * expected return on portfolio

Variance =

^2 (rp) = w^ 2 a ^2 (ra) + w ^2 b ^2 (rb) + w ^2 c ^2 (rc ) + 2wawb cov(ra,rb) + 2wawc cov(ra,rc ) + 2wbwc cov(rb,rc ),

standard deviation = (variance)^(1/2)

expected risk premium on portfolio = expected return - risk free rate = 9.6 - 4.5 = 5.1%

expected inflation rate = 4%

approximate real return = 9.6 - 4 = 5.6%

exact real return = (1 + nominal return)/( 1 + inflation) -1 = ( 1+ 9.6/100)/( 1 + 4/100) -1 = 5.39%

approximate real premium = approximate real return - t bill rate = 5.6 - 4.5 = 1.1%

exact real premium = exact real return - t bill rate = 5.39 - 4.5 = 0.89%

Stock A Scenario Probability Return =rate of return * probability Actual return -expected return(A) (A)^2* probability Bust 0.4 3 1.2 -15 90 Normal 0.4 25 10 7 19.6 Boom 0.2 34 6.8 16 51.2 Expected return = sum of weighted return = 18 Sum= 160.8 Standard deviation= Standard deviation of stock A =(sum)^(1/2) 12.68069399 Stock B Scenario Probability Return =rate of return * probability Actual return -expected return(B) (B)^2* probability Bust 0.4 -25 -10 -33.4 446.224 Normal 0.4 23 9.2 14.6 85.264 Boom 0.2 46 9.2 37.6 282.752 Expected return = sum of weighted return = 8.4 Sum= 814.24 Standard deviation= Standard deviation of stock B =(sum)^(1/2) 28.53489092 Stock C Scenario Probability Return =rate of return * probability Actual return -expected return(C) (C)^2* probability Bust 0.4 -42 -16.8 -50.4 1016.064 Normal 0.4 20 8 11.6 53.824 Boom 0.2 50 10 41.6 346.112 Expected return = sum of weighted return = 1.2 Sum= 1416 Standard deviation= Standard deviation of stock C =(sum)^(1/2) 37.62977544 Covariance: A and B Probability Actual return -expected return(A) Actual return -expected return(B) (A)*(B)*probability Bust 0.4 -15 -33.4 200.4 Normal 0.4 7 14.6 40.88 Boom 0.2 16 37.6 120.32 Covariance=sum= 361.6 CorrelationAB= Covariance/(std devA*std devB)= 1.00 Covariance: A and C Probability Actual return -expected return(A) Actual return -expected return(C) (A)*(C)*probability Bust 0.4 -15 -50.4 302.4 Normal 0.4 7 11.6 32.48 Boom 0.2 16 41.6 133.12 Covariance=sum= 468 CorrelationAC= Covariance/(std devA*std devC)= 0.980779104 Covariance: B and C Probability Actual return -expected return(B) Actual return -expected return(C) (A)*(B)*probability Bust 0.4 -33.4 -50.4 673.344 Normal 0.4 14.6 11.6 67.744 Boom 0.2 37.6 41.6 312.832 Covariance=sum= 1053.92 Correlation= Covariance/(std devB*std devC)= 0.981521467 weight in portfolio stock A 0.35 Stock B 0.35 Stock C 0.3 Expected return= 9.6 weight in portfolio stock A 0.35 Stock B 0.35 Stock C 0.3 Variance= 605.855228 Standard deviation 24.6141266

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