a) The annualized performance, in U.S. dollars, of the U.S. and European stock indices are:
Return US Return Europe
10% 16% 11% 18%
i) Calculate the return and the standard deviation of a portfolio invested half in the U.S. index and half in the European index assuming a correlation coefficient of 0.60. Provide all your workings and full calculations when answering this question. [2.5 marks]
ii) Calculate the return and the standard deviation of a portfolio invested half in the U.S. index and half in the European index assuming a correlation coefficient of 0.80. Provide all your workings and full calculations when answering this question. [2.5 marks]
iii) Without doing any further calculations, compare the result found in (i) with that found in (ii) and explain the difference. [2.5 marks]
b) Assume that the domestic and foreign assets have standard deviations of ĆĘa = 6% and ĆĘf = 8%, respectively, with a correlation of ĆĀaf = 0.25. The risk-free rate is equal to 5% in both countries. The expected return of both the domestic assets and foreign assets is 7%.
Calculate the Sharpe ratios for the domestic assets, the foreign assets, and an internationally-diversified portfolio equally invested in the domestic and foreign assets and discuss your answers. Provide all your workings and full calculations when answering this question. [7.5 marks]