Question $2(13$ marks$)$

Working as a senior manager at a fast$-$growing technology company, Gold Standard Ltd $($GST$),$ you hold $5,000$ shares of Gold Standard stock $($via employee stock holding scheme$)$ that is currently trading at $$100$ per share. You also have $$750,000$ invested in another $($defensive$)$ stock, Natural Gas Ltd$.($NGL$),$ to balance the risk of your portfolio.

The market information on the two stocks are as follows:

Stock Gold Standard: Expected rate of return $=12\%,$ Standard Deviation $=9\mathrm{.}11\%$

Stock Natural Gas: Expected rate of return $=6\%,$ Standard Deviation $=3\mathrm{.}00\%$

Correlation Coefficient of Stock Gold Standard with Stock Natural Gas $=0\mathrm{.}70$

The probabilities and rate of returns for GTS under different states of the economy are as follows:

$\backslash$table$[[\backslash$table$[[$State of the$],[$Economy$]],$Probability,$\backslash$table$[[$Expected rate of return of$],[$Stock Gold Standard under$],[$various states of the economy$]]],[$Boom$,0\mathrm{.}25,40\%$