d$)$ Consider two assets, Asset X and Asset Y$,$ with expected returns of $6\%$ p$.$a and $9\%$ p$.$a

and standard deviation of returns of $3\%$ and $5\%,$ respectively and correlation ${}_{xY}=0\mathrm{.}7.$

Let ${}_i$ denote the proportion of the portfolio invested in Asset $i.$

i$)$ Determine the portfolio expected return and standard deviation for an equally

weighted portfolio consisting of assets $x$ and $Y$ only. $(3$ marks$)$

ii$)$ If only Assets $x$ and $Y$ are available, determine the optimal portfolio weights that

would minimize the portfolio risk. $(3$ marks$)$

iii$)$ A third Asset, Asset Z$,$ is risk$-$free and has an expected return of $4\%$ p$.$a$.$ Assume

that the market capitalization for the risky assets $x$ and $Y$ are $$15,000$ and $$35,000$

respectively. Determine the equation of the capital market line. $(4$ marks$)$

e$)$ You are given a set of prices for $N$ risky securities $P_1,P_2,$dots,$P_N$ for the trading period

$t=1,$dots,$T.$ Using a pseudo$-$code, outline how the expected mean return for the Global

Minimum Variance portfolio $($GMVP$)$ can be determined. $(5$ marks$)$