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