Assume you are interested in investing in the stock markets of 7 countries that means France, Canada, Japan, Germany, Switzerland, the United Kingdom, and the United States. Particularly, you would like to solve out for the optimal (tangency) portfolio comprising the above 7 stock markets. To solving out the optimal portfolio, employ the input data (i.e. correlation coefficients, means, and standard deviations) provided .The risk-free interest rate is supposed to be 0.5% per month and you can take short position in any stock market. Describe the optimal weights for each of the 7 stock markets? This problem can be solved via MPTSolver.xls spreadsheet.
Solution: The covariance matrix is calculated and is given below.
CN FR GM JP SW UK US
CN 33.99 15.53 12.97 11.08 14.01 21.88 18.61
FR 15.53 49.14 31.18 21.52 25.88 24.49 14.38
GM 12.97 31.18 45.43 17.74 28.44 21.37 11.37
JP 11.08 21.52 17.74 53.44 16.28 19.86 8.00
SW 14.01 25.88 28.44 16.28 34.34 19.72 12.83
UK 21.88 24.49 21.37 19.86 19.72 41.86 16.82
US 18.61 14.38 11.37 8.00 12.83 16.82 20.79
The optimal weights calculated are -0.7457 for Canada, 0.0237 for Germany, 0.0453 for France, -0.0474 for Switzerland, 0.2435 for Japan, 0.3168 for U.K., and 1.1638 for U.S., respectively.