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

Answer 1

Expected Retrun of Portfolio =
Standard Deviation of the Portfolio =

where,
w1 = weight of 1st asset in portfolio
w2 = weight of 2nd asset in portflio
E(r) = Expected return
= Standard Deviation of asset
= coefficient of correlation of asset 1 and asset 2

Part A and B:
As give in the question we have to create different portfolios using 2 assets. We start by assigning 0 weight to Asset1 and remaining weight(1 - weight assigned to asset1) to Asset2, then we keep increasing weight of asset1 by 0.1 each time and weight of asset2 keeps decreasing by 0.1. Hence we get total 11 portfolio.

If we want to analyse at a more granular level we can reduce the step size by 0.1 to 0.05 to give us 21 portfolios.

Expected retrun for a given portfolio will remain same irrespective of correlation of coefficient, but standard deviation will change whenever we change the coef of correlation. So, for every portfolio we calculate 1 expected return and 4 standard deviations corresponding to 4 coef of correl = 0.5, -1, 0, 1.

This can be setup in excel as below -

I have shown you formula for only 1 coeff of correl value = 0.5; but formula will remain same for other 3 coef of correl values as well.

My final values will look like below in excel -

Now, I draw each Expected Return Risk graph by selecting that column and doing "Insert" Scatter plot -

Part C:
Graphs very clearly demonstrate the importance of diversification of the portfolio. Portfolios formed with coeff of correlation as -1, has highest Expected Return/Risk number, specially when weight assigned to the 2 assets is almost same. On the other hand portflio formed with perfectly correlated assets(Coef of Correl = 1) is performing worst and Expected Return/Risk is moving unidirectionally working best when higher return asset is given total 100% weight.

Part D:
Advantage of international diversification - industries in the same country are affected by the same macro-economic policies of the country, so even after being in the different sectors still they move together sometimes in case of common macro-economic factors get affected, in such a scenarion international diversification removes this problem.

Disadvantage - main disadvantage is exposure to foreign currency risk, even if your portfolio is performing well in the foreign currency, advesre movements in the currency exchange rates can eat up all your profit. To hedge this risk additonal cost will be involved.