Question 4
a) The annualized performance, in U.S. dollars, of the U.S. and European stock indices are:
ReturnUS 10% ?US 16%
ReturnEurope 11% ?Europe 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 (1) with that found in
(2) and explain the difference.
[2.5 marks]
b) Assume that the domestic and foreign assets have standard deviations of ?d = 6% and ?f =
8%, respectively, with a correlation of ?df = 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]
