Use the following information/data to answer the next six questions. Assume the
ID: 2794573 • Letter: U
Question
Use the following information/data to answer the next six questions. Assume the following securities - A, 8, and C-and that there are three possible states of nature that could be realized over the next year Assume that each state has the same probability of occurring and that you have the same amo in each security (thus, make sure you use 1/3 (333 NOTE: YOU MUST GET 333333....) as your weight and don't use just .33). THE RIGHT ANSWER FOR EACH QUESTION BECAUSE SOME OF THE LATTER QUESTIONS PULL FROM WHAT QUESTIONS YOU HAVE DERIVED IN THE EARLIER Security A B C Return (state l): 10.5% 8.0% 6.0% Return (state 2): 7.5% 7.0% 6.0% Return (state 3): 5.0% 5.5% 6.0% 'What are the expected returns for each of the assets? What are the standard deviations for each of the assets? What is the covariance between AB, BC, and AC (in this order)? What is the correlation coefficient for AB, BC, and AC (in this order)? 'What is the overall expected rate of return on the portfolio across all three states? What is the overall expected standard deviation on the portfolio across all three states?Explanation / Answer
a.) Expected Return of A =1/3x10.50 + 1/3x8.0 + 1/3x6.00 =1/3x(10.50 + 8.00 + 6.00) =8.17%
Expected Return of B =1/3x7.50 + 1/3x7.00 + 1/3x6.00 =1/3x(7.50 + 7.00 + 6.00) =6.83%
Expected Return of C =1/3x5.00 + 1/3x5.50 + 1/3x6.00 =1/3x(5.00 + 5.50 + 6.00) =5.50%
b.) Standard Dev of A ={1/3x(10.50-8.17)2 + 1/3x(8.0-8.17)2 + 1/3x(6.00-8.17)2}1/2 =(1.81 + 0.01 + 1.56) =1.84%
Standard Dev of B ={1/3x(7.50-6.83)2 + 1/3x(7.00-6.83)2 + 1/3x(6.00-6.83)2}1/2 =(0.14 + 0.01 + 0.23) =0.62%
Standard Dev of C ={1/3x(5.00-5.50)2 + 1/3x(5.50-5.50)2 + 1/3x(6.00-5.50)2}1/2 =(0.08 + 0.00 + 0.08) =0.40%
c.) Covariance between AB = {1/3x(10.50-8.17)(7.50-6.83) + 1/3x(8.0-8.17)(7.00-6.83) + 1/3x(6.00-8.17)(6.00-6.83)} =(0.52 - 0.01 + 0.60) =1.11
Covariance between BC = {1/3x(7.50-6.83)(5.00-5.50) + 1/3x(7.00-6.83)(5.50-5.50) + 1/3x(6.00-6.83)(6.00-5.50)} =(-0.11 + 0.00 - 0.14) =-0.25
Covariance between AC = {1/3x(10.50-8.17)(5.00-5.50) + 1/3x(8.0-8.17)(5.50-5.50) + 1/3x(6.00-8.17)(6.00-5.50)} =(-0.39 + 0.00 - 0.36) =-0.75
d.) Correlation between AB = Cov(A,B)/SDASDB = 1.11/(1.84x0.62) =0.97
Correlation between BC = Cov(B,C)/SDBSDC = -0.25/(0.62x0.40) = -1.00
Correlation between AC = Cov(A,C)/SDASDC = -0.75/(1.84x0.40) = -1.00