Question

Here are the expected returns and risks of two portfolios – a domestic and a foreign:

E(r domestic) = 12% σdomestic = 10%

E(r foreign) = 16%   σforeign = 12%

a. Assume a correlation of 0.5 and draw all the portfolios made up of the two assets in

an Expected Return/Risk graph.

b. Repeat the procedure in part (a) assuming a correlation of -1, 0, and +1.

c. Looking at the four graphs, what do you conclude about the importance of correlation

in risk-reduction?

d. Comment on the advantages and disadvantages of international diversification

Please solve in Excel

Please also show how you have graphed

Please teach how to make the graphs however possible

Answer 1

a]

Expected return of two-asset portfolio Rp = w1R1 + w2R2,

where Rp = expected return

w1 = weight of Asset 1

R1 = expected return of Asset 1

w2 = weight of Asset 2

R2 = expected return of Asset 2

Standard deviation for a two-asset portfolio σp = w12σ12 + w22σ22 + 2w1w2Cov1,2

where σp = Standard deviation of the portfolio

w1 = weight of Asset 1

w2 = weight of Asset 2

σ1 = Standard deviation of Asset 1

σ2 = Standard deviation of Asset 2

Cov1,2 = covariance of returns between Asset 1 and Asset 2

Cov1,2 = ρ1,2 * σ1 * σ2, where ρ1,2 = correlation of returns between Asset 1 and Asset 2

The expected return and standard deviation are calculated as below :

ДА В Return 2 Domestic 12% 3 Foreign 16% с Std.Dev 10% 12% 0% 100% Portfolio Portfolio Weight - Weight - expected standard 5 Domestic Foreign return deviation 100% 16.00% 12.00% 10% 90% 15.60% 11.33% 20% 80% 15.20% 10.74% 30% 70% 14.80% 10.24% 40% 60% 14.40% 9.83% 50% 50% 14.00% 9.54% 60% 40% 13.60% 9.37% 70% 30% 13.20% 9.34% 80% 20% 12.80% 9.43% 90% 10% 12.40% 9.66% 100% 0% 12.00% 10.00%

2 Domestic 3 Foreign 4 Return 0.12 0.16 Std.Dev 0.1 0.12 5 Weight - Domestic Weight - Foreign 60 7 0.1 0.9 8 0.2 0.8 9 0.3 0.7 100.4 11 0.5 0.5 12 0.6 13 0.7 0.3 14 0.8 0.2 15 0.9 0.1 16 1 0.6 Portfolio expected return =A6*$B$2)+(B6*$B$3) =(A7*$B$2)+(B7*$B$3) =(A8*$B$2)+(B8*$B$3) =(A9*$B$2)+(B9*$B$3) =(A10*$B$2)+(B10*$B$3) =(A11*$B$2)+(B11*$B$3) =(A12*$B$2)+(B12*$B$3) =(A13*$B$2)+(B13*$B$3) =(A14*$B$2)+(B14*$B$3) =(A15*$B$2)+(B15*$B$3) =(A16*$B$2)+(816"$B$3) Portfolio Standard deviation =((A6^2) *($C$2^2)+(B6^2)*($C$3^2)+(2*A6*16*0.5*$C$2*$C$3))^(1/2) =((A7^2) *($C$2^2)+(3742)*($C$3^2)+(2*A7*B7*0.5*$C$2*$C$3))^(1/2) =((A8^2)*($C$2^2)+(B8^2) *($C$3^2)+(2*A8*B8*0.5*$C$2*$C$3))^(1/2) =((A9^2) *($C$2^2)+(B9^2)*($C$3^2)+(2*A9*39*0.5*$C$2*$C$3))^(1/2) =((A10^2)*($C$2^2)+(B10^2)*($C$3^2)+(2*A10*B10*0.5*$C$2*$C$3))^(1/2) =((A11^2)*($C$2^2)+(B11^2) *($C$3^2)+(2*A11*111*0.5*$C$2*$C$3))^(1/2) =((A12^2)*($C$2^2)+(B12^2)*($C$3^2)+(2*A12*B12*0.5*$C$2*$C$3))^(1/2) =((A1342)*($C$2^2)+(B13-2)*($C$3^2)+(2*A13*B13*0.5*$C$2*$C$3))^(1/2) =((A14^2) *($C$2^2)+(B14^2)*($C$3^2)+(2*A14*B14*0.5*$C$2*$C$3))^(1/2) =((A15^2)*($C$2^2)+(B15^2) *($C$3^2)+(2*A15*B15*0.5*$C$2*$C$3))^(1/2) =((A16^2)*($C$2^2)+(B16^2) *($C$3^2)+(2*A16*B16*0.5*$C$2*$C$3))^(1/2) 0.4

Return/Risk graph is below :

18.00% 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00%

b]

Correlation of 1

16% A B C Return Std.Dev 22 Domestic 12% 10% 23 Foreign 12% 24 Portfolio Weight - Weight - expected 25 Domestic Foreign return 0% 100% 16.00% 90% 15.60% 20% 80% 15.20% 30% 70% 14.80% 40% 60% 14.40% 50% 50% 14.00% 60% 40% 13.60% 70% 30% 13.20% 20% 12.80% 10% 12.40% 100% 0% 12.00% 10% Portfolio Standard deviation 12.00% 11.80% 11.60% 11.40% 11.20% 11.00% 10.80% 10.60% 10.40% 10.20% 10.00% 80% 90%

the

22 Domestic 23 Foreign 24 Return 0.12 0.16 Std.Dev 0.1 0.12 25 Weight - Domestic Weight - Foreign Portfolio expected return Portfolio Standard deviation 26 0 =(A26*$B$22)+(B26*$B$23) =((A26^2)*($C$22^2)+(B26^2)*($C$23^2)+(2*A26*B26*1*$C$22*$C$23))^(1/2) 27 0.1 =(A27*$B$22)+(B27*$B$23) =((A2742)*($C$22^2)+(B2742)*($C$23^2)+(2*A27*B27*1*$C$22*$C$23))^(1/2) =(A28*$B$22)+(B28"$B$23) =((A28^2)*($C$22^2)+(B28^2)*($C$23^2)+(2*A28"B28"1"$C$22"$C$23))^(1/2) =(A29*$B$22)+(B29"$B$23) =((A2912)*($C$22^2)+(B2912)*($C$23^2)+(2*A29"B29"1"$C$22*$C$23))^(1/2) =(A30*$B$22)+(B30*$B$23) =((A30^2)*($C$22^2)+(B30^2)*($C$23^2)+(2*A30*B30*1*$C$22*$C$23))^(1/2) =(A31"$B$22)+(B31"$B$23) =((A31^2)*($C$22^2)+(B31^2)*($C$23^2)+(2*A31"131"1"$C$22"$C$23))^(1/2) =(A32*$B$22)+(B32"$B$23) =((A32^2)*($C$22^2)+(B32^2)*($C$23^2)+(2*A32"B32"1"$C$22"$C$23))^(1/2) =(A33*$B$22)+(B33*$B$23) =((A33^2)*($C$22^2)+(B33^2)*($C$23^2)+(2*A33*B33*1*$C$22*$C$23))^(1/2) =(A34*$B$22)+(B34*$B$23) =((A34^2) *($C$22^2)+(B34^2) *($C$23^2)+(2*A34*B34*1*$C$22*$C$23))^(1/2) 35 0.9 =(A35*$B$22)+(B35"$B$23) =((A35^2)*($C$22^2)+(B35^2)*($C$23^2)+(2*A35"335"1"$C$22"$C$23))^(1/2) =(A36*$B$22)+(B36"$B$23) =((A36^2)*($C$22^2)+(B36^2)*($C$23^2)+(2*A36"B36"1"$C$22"$C$23))^(1/2) 27

The risk return graph is below :

| 18.00% 15.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% | 9.50% 10.00% 10.50% 11.00% 11.50% 12.00% 12.50%

Correlation of 0

В 47 Std.Dev Return 48 Domestic 12% 49 Foreign 16% 10% 12% 50 Portfolio Weight - Weight - expected 51 Domestic Foreign return 0% 100% 16.00% 10% 90% 15.60% 20% 80% 15.20% 30% 70% 14.80% 40% 60% 14.40% 50% 50% 14.00% 60% 40% 13.60% 70% 30% 13.20% 80% 20% 12.80% 90% 10% 12.40% 100% 0% 12.00% Portfolio Standard deviation 12.00% 10.85% 9.81% 8.92% 8.24% 7.81% 7.68% 7.87% 8.35% 9.08% 10.00%

46 47 48 Domestic 49 Foreign 50 Return 0.12 0.16 Std.Dev 0.1 0.12 51 Weight - Domestic Weight - Foreign Portfolio expected return Portfolio Standard deviation 52 0 =(A52*$B$48)+(B52*$B$49) =((A52^2)*($C$48^2)+(B52^2)*($C$49^2)+(2*A52*B52*0*$C$48*$C$49))^(1/2) 53 0.1 0.9 =(A53*$B$48)+(B53*$B$49) =((A53^2)*($C$48^2)+(B53^2)*($C$49^2)+(2*A53*B53*0*$C$48*$C$49))^(1/2) 54 0.2 =(A54*$B$48)+(854*$B$49) =((A54^2) *($C$48^2)+(854^2) *($C$49^2)+(2*A54*054*0*$C$48*$C$49))^(1/2) 55 0.3 =(A55*$B$48)+(B55*$B$49) =((A55^2)*($C$48^2)+(B55^2)*($C$49^2)+(2*A55*055*0*$C$48*$C$49))^(1/2) 56 0.4 =(A56*$B$48)+(B56*$B$49) =((A56^2)*($C$48^2)+(B56^2)*($C$49^2)+(2*A56*B56*0*$C$48*$C$49))^(1/2) 57 0.5 =(A57*$B$48)+(B57*$B$49) =((A57^2)*($C$48^2)+(B57^2)*($C$49^2)+(2*A57*B57*0*$C$48*$C$49))^(1/2) 58 0.6 =(A58*$B$48)+(B58*$B$49) =((A58^2)*($C$48^2)+(B58^2)*($C$49^2)+(2*A58*858*0*$C$48*$C$49))^(1/2) =(A59*$B$48)+(B59*$B$49) =((A59^2)*($C$48^2)+(359^2)*($C$49^2)+(2*A59*B59*0*$C$48*$C$49))^(1/2) =(A60*$B$48)+(B60*$B$49) =((A60^2)*($C$48^2)+(B60^2)*($C$49^2)+(2*A60*360*0*$C$48*$C$49))^(1/2) =(A61*$B$48)+(B61*$B$49) =((A61^2)*($C$48^2)+(B61^2)*($C$49^2)+(2*A61*B61*0*$C$48*$C$49))^(1/2) =(A62*$B$48)+(B62*$B$49) =((A62^2)*($C$48^2)+(B62^2)*($C$49^2)+(2*A62*B62*0*$C$48*$C$49))^(1/2) 59 0.7

The risk return graph is below :

18.00% 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00%

Correlation of -1

69 A Return std.Dev C Std.Dev A B Return 70 Domestic 12% 71 Foreign 16% 10% 12% Portfolio Standard deviation 80% Portfolio Weight - Weight - expected 73 Domestic Foreign return 100% 16.00% 10% 90% 15.60% 20% 15.20% 30% 70% 14.80% 40% 60% 14.40% 50% 14.00% 60% 40% 13.60% 70% 30% 13.20% 80% 20% 12.80% 90% 10% 12.40% 84 100% 0% 12.00% 50% 12.00% 9.80% 7.60% 5.40% 3.20% 1.00% 1.20% 3.40% 5.60% 7.80% 10.00%

A 69 70 Domestic 71 Foreign B Return 0.12 0.16 Std.Dev 0.1 0.12 72 Weight - Weight - 73 Domestic Foreign 74 0 75 0.1 0.9 76 0.2 77 0.3 78 0.4 "1: 11-222333333 79 0.5 Portfolio expected return Portfolio Standard deviation =(A74*$B$70)+(374*$B$71) =((A74^2) *($C$70^2)+(374^2) *($C$71^2)+(2*A74*B74*-1*$C$70*$C$71))^(1/2) =(A75*$B$70)+(B75*$B$71) =((A75^2) *($C$70^2)+(B75^2) *($C$71^2)+(2*A75*175*-1*$C$70*$C$71))^(1/2) =(A76*$B$70)+(B76*$B$71) =((A76^2)*($C$70^2)+(B76^2)*($C$71^2)+(2*A76*B76*-1*$C$70*$C$71))^(1/2) =(A77*$B$70)+(B77*$B$71) =((A77^2) *($C$70^2)+(377^2) *($C$71^2)+(2*A77*B77*-1*$C$70*$C$71))^(1/2) =(A78*$B$70)+(B78*$B$71) =((A78^2) *($C$70^2)+(378^2)*($C$71^2)+(2*A78*878*-1*$C$70*$C$71))^(1/2) =(A79*$B$70)+(B79*$B$71) =((A7942)*($C$70^2)+(B7942)*($C$71^2)+(2*A79*B79*-1*$C$70*$C$71))^(1/2) =(A80*$B$70)+(B80*$B$71) =((A80^2)*($C$70^2)+(B80^2)*($C$71^2)+(2*A80*380*-1*$C$70*$C$71))^(1/2) =(A81*$B$70)+(881*$B$71) =((A81^2)*($C$70^2)+(881^2)*($C$71^2)+(2*A81*381*-1*$C$70*$C$71))^(1/2) =(A82*$B$70)+(B82*$B$71) =((A8242)*($C$70^2)+(B8242)*($C$71^2)+(2*A82*882*-1*$C$70*$C$71))^(1/2) =(A83*$B$70)+(B83*$B$71) =((A83^2)*($C$70^2)+(B83^2)*($C$71^2)+(2*A83*B83*-1*$C$70*$C$71))^(1/2) =(A84*$B$70)+(B84*$B$71) =((A84^2)*($C$70^2)+(B84^2)*($C$71^2)+(2*A84B84*-1*$C$70*$C$71)^(1/2) 80 0.6 81 0.7 82 0.8 83 0.9 84 1

18.00% 16.00% 14.00% 12.00% 0 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% | 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00%

The graphs are done using with these steps :

• Select (using the mouse) the table containing the data expected return and standard deviation only. For example, for the first graph, C5 : D16 is selected
• Click on "Insert" Tab on the top
• In "Charts", select the last option --> "Scatter" Charts and then the first option --> "Scatter"
• This should display the graph

c]

It can be concluded that lower the correlation, lower the portfolio risk

d]

Advantages of international diversification are :

• More opportunities for growth
• Provides diversification benefit to portfolio
• Reduces country specific risk of home country

Disadvantages of international diversification are :

• Exposes the portfolio to foreign exchange risk
• Exposes the portfolio to country specific risk of foreign country
• Liquidity may be lower in foreign markets