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:

$($a$)$ Given that the expected rate of return of GTS is $12\%,$ calculate its expected return when the

state of the economy is "Bust".

$(4$ marks$)$

$($b$)$ What is the expected return of your portfolio? $[$Hints: Calculate the weight of GTS and NGL

as your first step.$]$

$(5$ marks$)$

$($c$)$ What is the standard deviation of your portfolio?

$(4$ marks$)$