Question

GLUL. UU HW P8-21 (similar to) Expected return and standard deviation. Use the following Information to answer the questions: a. What is the expected return of each asset? b. What is the variance and the standard deviation of each asset? c. What is the expected return of a portfolio with 9% in asset J. 55% in asset K, and 36% in asset L? d. What is the portfolio's variance and standard deviation using the same asset weights from part (e)? Hint: Make sure to round all intermediate calculations to at least seven (7) decimal places. The input instructions, phrases in parenthesis after each answer box, only apply for the answers you will type a. What is the expected return of asset J? Data Table 0651 (Round to four decimal places.) What is the expected return of asset ? 0.0994 (Round to four decimal places.) (Click on the following icon in order to copy its contents into a spreadneet.) What is the expected return of asset L? (Round to four decimal places.) State of Economy Boom Growth Stagnant Recession Probability of State 0.26 0.37 0.22 0.15 Return on Asset Jin State 0.065 0.065 0.065 0.065 Return on Asset Kin State 0.200 0.130 0.085 -0.100 Return on Asset Lin State 0.290 0.230 0.060 -0.220 Print Done Enter your answer in the answer box and then click Check Answer. Clear All parts remaining MacBook Pro

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

A B с D E F Probability Asset J Asset L 0.065 1 2 3 4 5 6 0.26 0.37 0.22 State of Economy Boom Growth Stagnant Recession a. Expected return b. Variance Standard Deviation Asset K 0.200 0.130 0.065 -0.100 0.0994 0.009202 0.0959 0.065 0.065 0.065 0.0650 0.000000 0.0000 0.15 0.290 0.230 0.060 -0.220 0.1407 0.029695 0.1723 7 8 9 10 c. Portfolio's Stock Asset) Weight Asset K 9% 55% 36% Asset L Expected return of Portfolio 0.1112 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Covariance(UK) Covariance (JL) Covariance (KL) 0.000000 0.000000 0.016315 d. Variance of Portfolio 0.013093 Standard deviation of Portfolio 0.1144

Cell reference -

7 А B C D E F 1 2 State of Economy Probability Asset Asset K Asset L 3 Boom 0.26 0.065 0.2 0.29 4 Growth 0.37 0.065 0.13 0.23 5 Stagnant 0.22 0.065 0.065 0.06 6 Recession 0.15 0.065 -0.1 -0.22 a. Expected return =SUMPRODUCT($C$3:$C$6,D3:D6) =SUMPRODUCT($C$3:$C$6,E3:E6) =SUMPRODUCT($C$3:$C$6,F3:F6) 8 b. Variance =SUMPRODUCT((D7-D3:06)^2,$C$3:$C$6) =SUMPRODUCT((E7-E3:E6)^2,$C$3:$C$6) =SUMPRODUCT((F7-F3:F6)^2,$C$3:$C$6) 9 Standard Deviation =SQRT(D8) =SQRT(E8) =SQRT(F8) 10 11 c. Portfolio's Stock Weight 12 Asset) 0.09 13 Asset K 0.55 14 Asset L 0.36 15 16 Expected return of Portfolio =C12*D7+C13*E7+C14*F7 17 18 Covariance(U,K) =SUMPRODUCT((D7-D3:06),(E7-E3:E6),C3:06) 19 Covariance (JL) =SUMPRODUCT((D7-D3:D6),(F7-F3:F6),C3:06) 20 Covariance (KL) =SUMPRODUCT((E7-E3:E6), (F7-F3:F6),C3:C6) 21 22 d. Variance of Portfolio =(C12*D9)^2+(C13*E9)^2+(C14*F9)^2+2*C12*C13*C18+2*C12*C14*C19+2*C13*C14*C20 23 24 Standard deviation of Portfolio =SQRT(C22) 25 26

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.