Stock Market:

United States Return$($mean$)=1\mathrm{.}26\%$ per month $,$ Risk $($SD$)=4\mathrm{.}43\%$

United Kingdom Return$=1\mathrm{.}23\%$ per month, Risk $($SD$)=5\mathrm{.}55\%$

Suppose you are a financial adviser and your client, who is currently investing only in the U$.$S$.$ stock market, is considering diversifying into the U$.$K$.$ stock market. At the moment, there are neither particular barriers nor restrictions on investing in the U$.$K$.$ stock market. Your client would like to know what kinds of benefits can be expected from doing so$.$ Using this data:

Stock Market:

United States Return$($mean$)=1\mathrm{.}26\%$ per month $,$ Risk $($SD$)=4\mathrm{.}43\%$

United Kingdom Return$=1\mathrm{.}23\%$ per month, Risk $($SD$)=5\mathrm{.}55\%,$ solve the following problems:

$1.$ Graphically illustrate various combinations of portfolio risk and return that can be generated by investing in the U$.$S$.$ and U$.$K$.$ stock markets with different proportions. Two extreme proportions are $($a$)$ investing $100$ percent in the United States with no position in the U$.$K$.$ market, and $($b$)$ investing $100$ percent in the U$.$K$.$ market with no position in the U$.$S$.$ market.

$2.$ Solve for the optimal international portfolio comprising the U$.$S$.$ and U$.$K$.$ markets. Assume that the monthly risk$-$free interest rate is $0\mathrm{.}5$ percent and that investors can take a short $($negative$)$ position in either market. This problem can be solved using the spreadsheet MPTSolver.xIs.

$3.$ What is the extra return that U$.$S$.$ investors can expect to capture at the U$.$S$.-$ equivalent risk level? Also trace out the efficient set.