A contention expressed commonly by academics $($and practitioners$)$ is that international portfolio diversification pushes out the efficient frontier, or$,$ in other words, enables an investor to maintain the same level of expected return with a lower level of risk $($or$,$ alternatively, the same level of risk with a higher expected return$).$

Your assignment is to take historical monthly returns $($the investable market index $$ IMI$)$ for the stock markets in the U$.$S$.,$ Europe, and Asia$/$Pacific and examine the risk vs$.$ return possibilities that can be obtained by combining these markets into $20$ different portfolios $($where the portfolios differ in the weight allocated to each foreign market$).$ Your results should include both the expected return and standard deviation for each of the $20$ portfolios, as well as a graph $($in expected return vs$.$ standard deviation space$)$ that contains the $20$ points $($Note: this is time series data. For your probabilities, assume each observation has a $1/60$th probability of occurring$).($The variance of return for a $3$ asset portfolio consisting of stocks a$,$ b$,$ and c can be calculated as: Wa$2\backslash$sigma a$2+$ Wb$2\backslash$sigma b$2+$ Wc$2\backslash$sigma c$2+2$WaWb$\backslash$sigma a$,$b $+2$WaWc$\backslash$sigma a$,$c $+2$WbWc$\backslash$sigma b$,$c$)$

As part of this assignment, answer the following question: Do you think, over the $60$ month time period, that international diversification was a worthwhile endeavor? Why, or why not?