An international portfolio with a total investment of \($10\) million consists of a US portfolio and a foreign portfolio. The US portfolio requires an investment of \($5\) million and the foreign portfolio requires an investment of \($5\) million. The standard deviations are 4 percent for the US portfolio and 4 percent for the foreign portfolio.

(a) If these two portfolios are perfectly positively correlated, what is the standard deviation of the international portfolio?

(b) If the two portfolios have a correlation coefficient of 0.2, what is the standard deviation of the international portfolio?

(c) If the two portfolios are perfectly negatively correlated, what is the standard deviation of the international portfolio?