Use the information in Table $1$ below to answer questions $1\mathrm{.}1$ to $1\mathrm{.}2\mathrm{.}7.$ Note that the correlation matrix merely shows the correlations between the four assets in the table $($e$.$g$.$ correlation between asset A and asset C is $0\mathrm{.}60)$ Portfolio E$($r$)$ Standard deviation Correlation with Portfolio A Correlation with Portfolio B Correlation with Portfolio C Correlation with Portfolio DA

$11\mathrm{.}55\%$

$9\mathrm{.}65\%$

$1$

$0\mathrm{.}75$

$0\mathrm{.}6$

$0\mathrm{.}45$

B

$14\mathrm{.}65\%$

$19\mathrm{.}55\%$

$0\mathrm{.}75$

$1$

$0\mathrm{.}85$

$0\mathrm{.}55$

C

$15\mathrm{.}25\%$

$22\mathrm{.}64\%$

$0\mathrm{.}6$

$0\mathrm{.}85$

$1$

$-0\mathrm{.}25$

D

$11\mathrm{.}51\%$

$16\mathrm{.}55\%$

$0\mathrm{.}45$

$0\mathrm{.}55$

$-0\mathrm{.}25$

$1$

Risk free rate $($rf$)$

$7\mathrm{.}50\%$

$0\mathrm{.}00\%$

$1\mathrm{.}1$

Which of the four portfolio$($s$)$ in Table $1$ is$($are$)$ on the best$-$possible CAL? Also include an Illustration $($i$.$e$.$ draw separate CALs for each portfolio$)$ to help explain your answer. $[8$ marks$]$

$1\mathrm{.}2$

Use the information in Table $1$ to calculate the following:

$1\mathrm{.}2\mathrm{.}1$

Covariance between portfolios A and B$.[2$ marks$]$

$1\mathrm{.}2\mathrm{.}2$

Covariance between portfolios C and D$.[2$ marks$]$

$1\mathrm{.}2\mathrm{.}3$

Historical return of a portfolio consisting of $60\%$ Portfolio A and $40\%$ in portfolio B$.[2$ marks$]$

$2$

$1\mathrm{.}2\mathrm{.}4$

Historical return of a portfolio consisting of $30\%$ Portfolio C and $70\%$ in portfolio D$.[2$ marks$]$

$1\mathrm{.}2\mathrm{.}5$

Use the $$Markowitz formula$$ to calculate the historical standard deviation of a portfolio consisting of $60\%$ in Portfolio A and $40\%$ in Portfolio B$.$ Call it portfolio X$.[4$ marks$]$

$1\mathrm{.}2\mathrm{.}6$

Use the $$Markowitz formula$$ to calculate the historical standard deviation of a portfolio consisting of $30\%$ in Portfolio C and $70\%$ in Portfolio D$.$ Call it portfolio Y$.[4$ marks$]$

$1\mathrm{.}2\mathrm{.}7$

Would portfolio X or portfolio Y be the better investment choice based on the historical data used? Explain in detail. $[4$ marks$]$

$1\mathrm{.}3$

Suppose you have a $3-$asset portfolio $($portfolio P$)$ that is invested $25\%$ in Asset $1,60\%$ in Asset $2$ and $15\%$ in Asset $3.$ Use the table below to calculate the expected return, expected standard deviation and expected coefficient of variation of your portfolio P$.[12$ marks$]$ State of economy

Probability of state of economy

Rate of return if state occurs Asset $1$ Asset $2$ Asset $3$ Economic boom

$10\%$

$28\%$

$40\%$

$15\%$ Good growth

$25\%$

$22\%$

$25\%$

$10\%$ Poor growth

$45\%$

$-7\%$

$0\%$

$5\%$ Recession

$20\%$

$2\%$

$-15\%$

$0\%$