Question Three

XYZ Ltd has placed its short$-$term investments in two securities A and $B$ as detailed below;

$\backslash$table$[[$Portfolio $(\%),$Expected returns,Standard deviation,Proportion$],[$A $(\%),12,16,0\mathrm{.}5],[$B $(\%),16,20,0\mathrm{.}5]]$

Required;

a$)$ Determine the correlation coefficient to derive a portfolio standard deviation of $18\%$

b$)$ If the weights of the two securities A and $B$ is modified to $75$:$25$ what would portfolio risk be$?$

c$)$ What would the correlation be if the desired portfolio standard deviation is $16\%$ and the assets are combined in equal proportion?