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, including a world equity index, in an attempt to evaluate a well-diversified international portfolio. The regions you have selected are the following: Latin America (GML), Middle East & Africa (GAF), Europe (VGK), China (GXC), India (PIN), U.S. (IWD), and the entire world (VT). 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	VT
Jan 2017	0.61%	3.10%	2.96%	7.26%	8.52%	6.43%	3.00%
Feb 2017	3.49%	2.06%	0.59%	3.88%	3.23%	5.41%	2.69%
Mar 2017	-0.96%	0.86%	4.42%	2.21%	2.60%	5.91%	1.47%
Apr 2017	-0.19%	4.06%	3.90%	2.11%	-0.15%	1.54%	1.63%
May 2017	-0.17%	1.97%	4.91%	4.49%	-2.97%	-0.09%	1.94%
Jun 2017	1.66%	-4.46%	-0.52%	2.29%	0.07%	-0.90%	0.62%

1. Determine the average returns and standard deviations of each ETF. Also, determine the correlation coefficient and covariance of the American ETF (IWD) with the other ETFs of the rest of the world.
2. Determine the best and worst performer on a risk/return basis during this period. Use the Sharp ratio and assume that the relevant risk-free rate was 3%.
3. What is the expected return and standard deviation for an equally weighted portfolio that includes all ETFs except VT (world index ETF)? Are these results similar to those of VT?
4. Using the Solver, what is the minimum standard deviation that could be achieved by combining these ETFs into a portfolio, with the exception of VT? What are the exact weights of these ETFs? Assume short sales are not allowed.=v