Consider portfolios with positions in the US and Brazilian equity markets. The (annual) expected return and standard deviation of returns for the 2 markets are as follows: US E[r] 5%, Brazil E[r] 10%, US SD[r] 15%, Brazil SD[r] 25%. The correlation between the returns is 0.3, and the (annual) risk-free (T-bill) rate is 2%.

• Calculate the expected returns (in percent), standard deviations (in percent) and Sharpe ratios of the following portfolios:

(i) 50% in the risk-free asset, 50% in the US

(ii) 50% in the risk-free asset, 50% in a portfolio that itself is invested 40% in the US and 60% in Brazil

• What are the portfolio weights in the risk-free asset, the US, and Brazil in the portfolio in part d(ii)
• Find the weights (T-bill, US, Brazil) for a portfolio with the same expected return as Brazil (10%), using only a combination of the risk-free asset and the 40/60 portfolio from d(ii)? What is the standard deviation of this portfolio?