Question $5$

$In$ this problem you need $to$ construct the diagram $of$ a portfolio similar $to$ figure $6\mathrm{.}8(Luenberger,$ page $153).$

Consider a portfolio $of$ two assets with the following mean rates $of$ return and standard deviation $of$ the rates

$of$ return:

$5\mathrm{.}1$ Express the mean and standard deviation $of$ the portfolio $in$ terms $ofand{}_{12}.$

$5\mathrm{.}2$ Let $=0$;$0\mathrm{.}1$;$0\mathrm{.}2$;dots;$1$ and determine the mean and standard deviation for the following portfolios:

Portfolio $P_1$ with the correlation coefficient $=1=\frac{{}_{12}}{{}_1{}_2}{P}_2$ with $=-1.$

Portfolio $P_3$ with ${}_{12}=0\mathrm{.}01\frac{\text{;}}{b}ar(r)$ A when $=+-1,$ and the

curve formed when $is$ not equal $to+-1(see$ Luenberger, figure $6\mathrm{.}8).$