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

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 :

Return/Risk graph is below :

b]

Correlation of 1

the

The risk return graph is below :

Correlation of 0

The risk return graph is below :

Correlation of -1

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