Question

% P8-21 (similar to) Is Question Help Expected return and standard deviation. Use the following information to answer the questions: E . 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, 54% in asset K, and 37% in asset L? d. What is the portfolio's variance and standard deviation using the same asset weights from part (c)? 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? i Data Table (Round to four decimal places.) (Click on the following icon in order to copy its contents into a spreadsheet.) State of Economy Boom Growth Stagnant Recession Probability of State 0.28 0.36 0.23 0.13 Return on Asset J in State 0.055 0.055 0.055 0.055 Return on Asset K in State 0.240 0.150 0.060 -0.050 Return on Asset L in State 0.270 0.190 0.070 -0.210 Enter your answer in the answer box and t| 11 parts I remaining

Answer 1

a. Expected Return of Asset J =0.28*0.055+0.36*0.055+0.23*0.055+0.13*0.055 =0.055
Expected Return of Asset K =0.28*0.240+0.36*0.150+0.23*0.060+0.13*-0.050=0.1285
Expected Return of Asset L =0.28*0.270+0.36*0.190+0.23*0.070+0.13*-0.210=0.1328

Variance of asset J =0.28*(0.055-0.055)^2+0.36*(0.055-0.055)^2+0.23*(0.055-0.055)^2+0.13*(0.055-0.055)^2=0
Variance of Asset K =0.28*(0.240-0.1285)^2+0.36*(0.150-0.1285)^2+0.23*(0.060-0.1285)^2+0.13*(-0.050-0.1285)^2=0.008869
Variance of Asset L =0.28*(0.270-0.1328)^2+0.36*(0.190-0.1328)^2+0.23*(0.070-0.1328)^2+0.13*(-0.210-0.1328)^2=0.022632

Standard Deviation of Asset J =0
Standard Deviation of Asset K =0.008869^0.5 =0.04714
Standard Deviation of Asset L =0.022632^0.5 =0.15404

c. Expected Return in case of Boom =9%*0.055+54%*0.240+37%*0.270=23.4450%
Expected Return in case of Growth =9%*0.055+54%*0.150+37%*0.190=15.6250%
Expected Return in case of Stagnant =9%*0.055+54%*0.060+37%*0.070=6.3250%
​​​​​​​Expected Return in case of Recession =9%*0.055+54%*-0.050+37%*-0.210=-9.9750%

Expected Return of Portfolio =0.28*23.4450%+0.36*15.6250%+0.23*6.3250%+0.13*-9.9750% =0.12348

d. Variance of Portfolio =0.28*(23.4450%-0.12348)^2+0.36*(15.6250%-0.12348)^2+0.23*(6.3250%-0.12348)^2+0.13*(-9.9750%-0.12348)^2=0.01115
​​​​​​​Standard Deviation of portfolio =0.01115^0.5 =0.1056

​​​​​​​