The Japanese market is on the verge of rising again, and the UK market is doing better than the US market in the

current economic recovery. Therefore, as a US investor, John is contemplating investing in the Japanese and UK

stock markets. Using the historical data, John has estimated the means, volatilities, and correlation of the US,

UK, and Japanese stock markets as the following:

US UK Japan

Means 0.120 0.150 0.084

St. Dev. 0.150 0.240 0.220

Correlation matrix:

US UK Japan

US 1.000 0.500 0.266

UK 0.500 1.000 0.358

Japan 0.266 0.358 1.000

Assume that the risk-free rate is 4%. .

(a) Given the data above, what are the Sharpe ratios on the US portfolio and the UK portfolio? Given the

correlation between US and UK above, should John add the UK portfolio to his US only portfolio?

(b) To see how robust his conclusion is on the issue of adding UK stocks to his portfolio, John wants to know

the lowest expected return on UK stock can be in order to improve his Sharpe ratio from holding the two

country stocks, given the correlations, volatilities and US Sharpe ratio. What is it? Show your reasoning

and computations.

(c) What is the Sharpe ratio for the Japanese equity? Similar to (b), compute the lowest expected return for the

Japanese equity. Are the differences between your answers to (b) and (c) surprising? Why or why not?