Consider the following market portfolios from the US, UK, and Japan.
US UK Japan
μ 0.12 0.15 0.14
σ 0.15 0.24 0.22
We also know that the correlation coefficient between US and UK market portfolios is ρUS,UK = 0.5 and the correlation coefficient between US and Japan is ρUS, Japan = 0.266. Suppose that the risk-free rate is Rf = 5%. You currently hold a portfolio with 100% invested in the US market portfolio.
(a) What are the Sharpe ratios for the US, UK, and Japanese market portfolios?
(b) You are thinking about diversifying your existing portfolio with the UK market. Should you include the UK market portfolio in your new optimal portfolio?
(c) You are thinking about diversifying your existing portfolio with Japanese market. Should you include the Japanese market portfolio in your new optimal portfolio?