The Japanese stock market has a sigma of 18%, when computed in yen. The U.S. stock market has a sigma of 17% in US$ and the US$/¥ exchange rate has a sigma of 6%. The correlation between the Japanese stock market and $/¥ currency movements is ?0.1; in other words, the Japanese stock market tends to go up when the yen goes down. The correlation between the Japanese and U.S. stock markets is equal to 0.4, measured either in local currency of in dollars.
a. What is the sigma of the Japanese market when expressed in dollars?
b. Using this number, calculate the sigma, in dollars, of a portfolio made up of 50% of Japanese stocks and 50% of U.S. stocks.