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 Brazil

E[r] 5% 10%

SD[r] 15% 25%

The correlation between the returns is 0.3, and the (annual) risk-free (T-bill) rate is 2%.

Find the weights in the US and Brazil for a portfolio with an expected return of 15%. What is the standard deviation of this portfolio (in percent)?

What are the approximate weights (to the nearest 1%) in the US and Brazil in the maximum Sharpe ratio portfolio, i.e., the tangency portfolio? What is the expected return (in percent), standard deviation (in percent), and Sharpe ratio of this portfolio?

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?