Suppose that an American investor is considering investing $10,000 in Japan in the Nikkei index for a year. The current exchange rate is 102 yen per dollar. There is an equal chance that the Nikkei index at the end of the year will go up by 20% or down by 10%. There is also a 60% probability that the dollar in a year will be traded at 90 and a 40% probability that it will be traded at 105 yen. Moreover, the probabilities of changes in the Nikkei index and the exchange rate are independent. (Ignore the interest rates). a a (1) (2 points) Calculate the mean of the investor's portfolio in yen (ii) (3 points) Calculate the mean of the investor's portfolio in dollars. (iii) (3 points) Suppose that the Nikkei index went down by 10% and the exchange rate at the end of the year is 90 yen per dollar. Find your returns in both yen and dollars and explain