I. Efficient Two Asset Portfolios

Assume that the expected return on asset $1$ is $5\%$ and the expected return on asset $2$ is $4\%.$ The standard

deviation of asset $1$ is $3\mathrm{.}0\%$ and $1\mathrm{.}5\%$ for asset $2.$ Assume the correlation of both assets is $0\mathrm{.}5.$

w$1$ w$2$ E$[$Rp$]\backslash$sigma p Sharpe

$1\mathrm{.}000\mathrm{.}00$

$0\mathrm{.}750\mathrm{.}25$

$0\mathrm{.}500\mathrm{.}50$

$0\mathrm{.}250\mathrm{.}75$

$0\mathrm{.}001\mathrm{.}00$

$1.$ The expected portfolio return in the first row is: $($a$)5\mathrm{.}0$; $($b$)4\mathrm{.}0$; $($c$)4\mathrm{.}50$; $($d$)0\mathrm{.}25$;

$2.$ The expected portfolio return in the second row is: $($a$)0\mathrm{.}95$; $($b$)4\mathrm{.}75$; $($c$)0\mathrm{.}12$; $($d$)-5\mathrm{.}00$;

$3.$ The expected portfolio return in the third row is: $($a$)0\mathrm{.}10$; $($b$)0\mathrm{.}20$; $($c$)4\mathrm{.}50$; $($d$)6\mathrm{.}70$;

$4.$ The expected portfolio return in the fourth row is: $($a$)4\mathrm{.}25$; $($b$)0\mathrm{.}25$; $($c$)0\mathrm{.}99$; $($d$)0\mathrm{.}00$;

$5.$ The expected portfolio return in the fifth row is: $($a$)4\mathrm{.}0$; $($b$)-4\mathrm{.}50$; $($c$)0\mathrm{.}33$; $($d$)5\mathrm{.}00$;

$6.$ The portfolio standard deviation in the first row is: $($a$)1\mathrm{.}0$; $($b$)0\mathrm{.}2$; $($c$)3\mathrm{.}0$; $($d$)-1\mathrm{.}0$;

$7.$ The portfolio standard deviation in the second row is: $($a$)5\mathrm{.}12$; $($b$)4\mathrm{.}33$; $($c$)6\mathrm{.}29$; $($d$)2\mathrm{.}09$;

$8.$ The portfolio standard deviation in the third row is: $($a$)1\mathrm{.}30$; $($b$)3\mathrm{.}45$; $($c$)4\mathrm{.}29$; $($d$)5\mathrm{.}67$;

$9.$ The portfolio standard deviation in the fourth row is: $($a$)1\mathrm{.}67$; $($b$)4\mathrm{.}00$; $($c$)3\mathrm{.}97$; $($d$)0\mathrm{.}99$;

$10.$ The portfolio standard deviation in the fifth row is: $($a$)1\mathrm{.}25$; $($b$)3\mathrm{.}59$; $($c$)1\mathrm{.}50$; $($d$)6\mathrm{.}29$;

Assume that the risk free rate of return is $0\%.$

$11.$ The Sharpe ratio in the first row is: $($a$)1\mathrm{.}67$; $($b$)0\mathrm{.}23$; $($c$)3\mathrm{.}01$; $($d$)-1\mathrm{.}00$;

$12.$ The Sharpe ratio in the second row is: $($a$)2\mathrm{.}28$; $($b$)4\mathrm{.}33$; $($c$)6\mathrm{.}29$; $($d$)8\mathrm{.}23$;

$13.$ The Sharpe ratio in the third row is: $($a$)1\mathrm{.}30$; $($b$)3\mathrm{.}46$; $($c$)4\mathrm{.}29$; $($d$)5\mathrm{.}67$;

$14.$ The Sharpe ratio in the fourth row is: $($a$)1\mathrm{.}67$; $($b$)4\mathrm{.}28$; $($c$)3\mathrm{.}97$; $($d$)0\mathrm{.}99$;

$15.$ The Sharpe ratio in the fifth row is: $($a$)1\mathrm{.}50$; $($b$)3\mathrm{.}59$; $($c$)2\mathrm{.}20$; $($d$)2\mathrm{.}67$;

$16.$ What is the weight on asset $1$ in the maximum Sharpe ratio portfolio: $($a$)-0\mathrm{.}50$; $($b$)0\mathrm{.}15$; $($c$)0\mathrm{.}30$;

$($d$)-0\mathrm{.}25$;

$17.$ What is the weight on asset $2$ in the minimum variance portfolio: $($a$)0\mathrm{.}71$; $($b$)0\mathrm{.}25$; $($c$)0\mathrm{.}35$; $($d$)$

$-0\mathrm{.}35$;

$18.$ Why is the point w$2=1\mathrm{.}0$ not on the efficient frontier: $($a$)$ it is never optimal to hold $100\%$ of your

money in a single asset; $($b$)$ all portfolios with negative variances require holdings of both assets; $($c$)$ the

portfolio is stochastically dominated; $($d$)$ it is on the frontier;