Mr J$.$ Smith is planning to invest in Asset X and Asset Y which have the following distribution of returns:

Probability Asset X:

Returns in $\%$ Asset Y:

Returns in $\%$

$0\mathrm{.}4011-3$

$0\mathrm{.}35915$

$0\mathrm{.}25252$

REQUIRED

$($a$)$ Calculate the expected return of Asset X and Asset Y$.$

$[6$ Marks$]$

$($b$)$ Calculate the standard deviation of Asset X and Asset Y$.$

$[6$ Marks$]$

$($c$)$ Show that the covariance between Asset X and Asset Y is $-16\mathrm{.}24.$

$($Include all your workings$)$

$[3$ Marks$]$

Page $4$ of $5$

$($d$)$ Given that Mr J$.$ Smith decides to equally invest between Asset X and Y$,$ calculate the expected return and risk of Mr J$.$ Smith$$s portfolio.

$[8$ Marks$]$

$($e$)$ Calculate the weighted standard deviation of the proposed portfolio of Mr J$.$ Smith.

$[2$ Marks$]$

$($f$)$ Explain why the portfolio standard deviation is lower than the weighted standard deviation.