$1$ Portfolio theory $[8$ points$]$

Consider the table below with expected returns, volatilities, and correlations.

$\backslash$table$[[$Stock$,\backslash$table$[[$Expected$],[$Return$]],\backslash$table$[[$Standard$],[$Deviation$]],\backslash$table$[[$Correlation$],[$with Duke$],[$Energy$]],\backslash$table$[[$Correlation$],[$with$],[$Microsoft$]],\backslash$table$[[$Correlation$],[$with$],[$Walmart$]]],[$Duke Energy,$14\%,6\%,1\mathrm{.}0,-1\mathrm{.}0,0\mathrm{.}0],[$Microsoft$,44\%,24\%,-1\mathrm{.}0,1\mathrm{.}0,0\mathrm{.}7],[$Walmart$,23\%,14\%,0\mathrm{.}0,0\mathrm{.}7,1\mathrm{.}0]]$

How can you construct a risk$-$free portfolio, and what is the expected return of that portfolio?

points$]$

Assume that the actual risk$-$free rate is lower than what you found above. Describe what would happen over time to the returns of the stocks in the table. $[2$ points$]$

What are the expected return and volatility of a portfolio that consists of a short position of $$5,000$ in Walmart and a long position of $$10,000$ in Microsoft? $[2$ points$]$