1. Being frustrated about the performance of your portfolio, you decide to verify the benefits of international diversification. You have selected several exchange-traded funds (ETFs) that invest in equity market indices of several world regions. The regions you have selected are the following: Latin America (GML), Middle East & Africa (GAF), Europe (VGK), China (GXC), India (PIN), and U.S. (IWD). You have gathered the monthly returns of these ETFs from January to June 2017. The returns are in the following table:

Date	IWD	GAF	VGK	GXC	GML	PIN
Jan-17	0.86%	3.35%	3.21%	7.51%	8.77%	6.68%
Feb-17	3.65%	2.22%	0.75%	4.04%	3.39%	5.57%
Mar-17	-0.58%	1.24%	4.80%	2.59%	2.98%	6.29%
Apr-17	-0.11%	4.14%	3.98%	2.19%	-0.07%	1.62%
May-17	-0.07%	2.07%	5.01%	4.59%	-2.87%	0.01%
Jun-17	1.82%	-4.30%	-0.36%	2.45%	0.23%	-0.74%

1. Determine the average returns and sample standard deviations of each ETF.
2. What is the expected return and standard deviation for an equally weighted portfolio that includes all ETFs? Create a variance/covariance matrix using the data from the table.
3. Determine the weights for the minimum standard deviation portfolio using Solver. Assume that short sales are allowed and that the proceeds from the shorted securities can be used to purchase more of the long positions.
4. Determine the weights for the maximum expected value portfolio using Solver. Assume that short sales are allowed and that the proceeds from the shorted securities can be used to purchase more of the long positions.
5. Create 3 portfolios using both the minimum standard deviation portfolio and maximum expected value portfolio, and the following weights for the minimum variance portfolio: 35%, 45%, and 55%.