In an attempt to diversify your portfolio internationally, you must decide how to invest in Brazil. You can invest in an index fund that replicates the Brazilian stock market, or you can buy shares of the Brazil Fund traded on the New York Stock Exchange. The covariance of dollar returns on the  index with the S&P 500 is 0.02; the covariance of dollar returns on the Brazil Fund with the S&P 500 is 0.03; the variance of the S&P 500 index is 0.035; and the beta of the Brazil Fund with respect to the Brazilian index is 0.90. In addition, the Brazil Fund and the Brazilian index are expected to yield annual dollar returns of 21% and 19%, respectively, in contrast to expected annual returns of 18% from investing in the S&P 500.

a. Ignoring other considerations, should you buy the Brazil Fund or the Brazilian index fund?

b. Suppose the U.S. Treasury bill rate is 5%. Assuming the S&P 500 has a beta of 1, plot the capital market line and show the positions of the Brazil Fund and the Brazilian stock index relative to the capital market line.