Examine the lowest risk portfolio and the notion of risk and return. Would you include emerging markets into your stock portfolio? Calculate the Sharpe performance measure for each market examined

The historical daily index data for US S&P 500, EAFE (Europe, Australia, Far East) and EM (Emerging Markets) from January 2, 2017 through November 5, 2018. There are 480 points in total.

 After that I computed the daily return for each index using the return formula:

For convenience I keep all in decimal form instead of percentage. So I did not multiple 100 in the above formula. Then I computed the average and standard deviation for each return series, as well as the correlation between them. Suppose the weights of USA S&P 500 index and EAFE index in the international portfolio are a and 1-a respectively

The international portfolio using USA and EAFE is shown in Appendix A. We can see that the standard deviation can be as low as 0.521% although each of USA and EAFE has a higher standard deviation. This effect is called diversification due to the imperfect correlation between the two indices. As long as the correlation coefficient is not 1, we can always have some degree of diversification effect.

The international portfolio using USA and EM is shown in Appendix B. Similar to the above portfolio, we also see diversification effect in this portfolio. The standard deviation can be as low as 0.620% although each of USA and EM has a higher standard deviation.

I computed rp and p for a=weight (0, 0.1, 0.2, 0.3, ..., 1). These weights change in ten percent increments, so there are eleven combinations to compute for the risk and return that can be graphed.

 The international portfolio diversification is way to minimize risk and maximizing the return. The portfolio is created so that the level of risk can be minimized. If the investor is going to invest in only one security than the chances of financial loss are quite higher. Therefore investing in different securities would lead to significant amount of return.