Question

You have been asked for your advice in selecting a portfolio of assets and have been supplied with the following​ data:

   Projected Return      
Year   Asset A   Asset B   Asset C
2021   13%             17%   13%
2022   15%             15%   15%
2023   17%             13%   17%

You have been told that you can create two portfolio------ one consisting of assets A and B and the other consisting of assets A and C ---------- by investing equal proportions

​(50 %​) in each of the two component assets.

a. What is the average expected​ return,r overbar​, for each asset over the​ 3-year period?

b. What is the standard​ deviation,s​, for each​ asset's expected​ return?

c. What is the average expected​ return,r overbar Subscript p​, for each of the the​ portfolios?

d. How would you characterize the correlations of returns of the two assets making up each of the portfolios identified in part c​?

e. What is the standard deviation of expected​ returns,s Subscript p comma for each​ portfolio?

f. Which portfolio do you​ recommend? Why?

Answer 1

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

L20 A B C D E F Asset B 17.00% Year 2021 2022 2023 Expected return Standard deviation Asset A 13.00% 15.00% 17.00% 15.00% 2.00% 15.00% 13.00% 15.00% 2.00% Asset C 13.00% 15.00% 17.00% 15.00% 2.00% 6 a. 7 b. 8 9c. Expected Return of Portfolio-AB Expected Return of Portfolio AC 15.00% 15.00% 10 11 Correlation (A,B) Correlation (A,C) 12 d. 13 14 15 e. 16 17 18 f Standard deviation of Portfolio-AB Standard deviation of Portfolio-AC 0.00% 2.00% Recommendation Portfolio-AB 19 20 Because Portfolio-AB has same expected return i.e 15% but it has 0% of risk.

Cell reference -

A B DE Asset C -Nm to Year 3 2021 2022 2023 a. Expected return 7 b. Standard deviation Asset A 0.13 0.15 10.17 =AVERAGE(C3:05) ESTDEV.S(C3:05) Asset B 0.17 0.15 0.13 =AVERAGE(D3:05) ESTDEV.S(D3:05) 0.13 0.15 0.17 =AVERAGE(E3:E5) =STDEV.S(E3:E5) 9 c. Expected Return of Portfolio-AB =0.5*C6+0.5*D6 10 Expected Return of Portfolio AC =0.5*C6+0.5*E6 11 12 d. Correlation (A,B) =CORREL(C3:C5,D3:D5) 13 Correlation (A,C) =CORREL(C3:C5, E3:E5) 14 15 e. Standard deviation of Portfolio-AB =SQRT((0.5*C7)^2+(0.5*D7)^2+2*0.5*0.5 16 Standard deviation of Portfolio-AC =SQRT((0.5*C7)^2+(0.5*E7)^2+2*0.5*0.5 17 18 f Recommendation Portfolio-AB Because Portfolio-AB has same expected return i.e 15% but it has 0% of risk.

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