II$.$ Mean Variance Analysis

Provide step$-$by $-$ step explanations.

Consider the following time series of returns for ABC stock and the S&P$500$ Index

What is the mean return of ABC stock: $($a$)-0\mathrm{.}2$ ; $($b$)1\mathrm{.}4$ ; $($c$)5\mathrm{.}2$ ; $($d$)17\mathrm{.}3$ ;

What is the mean return of the S&P index: $($a$)-0\mathrm{.}2$ ; $($b$)-0\mathrm{.}8$ ; $($c$)4\mathrm{.}3$ ; $($d$)1\mathrm{.}8$ ;

What is the covariance between ABC and S&P: $($a$)52\mathrm{.}3$ ; $($b$)29\mathrm{.}7$ ; $($c$)18\mathrm{.}6$ ; $($d$)70\mathrm{.}3$ ;

What is the variance of ABC stock: $($a$)74\mathrm{.}3$ ; $($b$)109\mathrm{.}7$ ; $($c$)31\mathrm{.}4$ ; $($d$)47\mathrm{.}3$ ;

What is the variance of the S&P index: $($a$)45\mathrm{.}7$ ; $($b$)67\mathrm{.}3$ ; $($c$)29\mathrm{.}9$ ; $($d$)102\mathrm{.}3$ ;

What is the correlation between ABC and $S$&$P$; $($a$)0\mathrm{.}99$ ; $($b$)-0\mathrm{.}45$ ; $($c$)-0\mathrm{.}27$ ; $($d$)-0\mathrm{.}82$ ;

What is the minimum variance portfolio weight for ABC stock: $($a$)-0\mathrm{.}55$ ; $($b$)0\mathrm{.}91$ ; $($c$)0\mathrm{.}36$; $($d$)-1\mathrm{.}66$ ;

What is the Beta of ABC stock: $($a$)-0\mathrm{.}68$ ; $($b$)0\mathrm{.}33$ ; $($c$)1\mathrm{.}54$ ; $($d$)-0\mathrm{.}23$ ;

HINT: Use the portfolio weights for the minimum variance portfolio and construct a series of returns to

answer $13-16.$

What is the mean return on the minimum variance portfolio: $($a$)-1\mathrm{.}80$ ; $($b$)-2\mathrm{.}20$ ; $($c$)1\mathrm{.}5$ ; $($d$)2\mathrm{.}3$ ;

What is the covariance of the minimum variance portfolio with the S&P index: $($a$)-3\mathrm{.}22$ ; $($b$)4\mathrm{.}81$;

$($c$)9\mathrm{.}32$ ; $($d$)5\mathrm{.}67$ ;

What is the variance of the minimum variance portfolio: $($a$)2\mathrm{.}63$ ; $($b$)-12\mathrm{.}19$ ; $($c$)4\mathrm{.}81$ ; $($d$)6\mathrm{.}74$ ;

What is the Beta of the minimum variance portfolio: $($a$)-0\mathrm{.}32$ ; $($b$)-2\mathrm{.}96$ ; $($c$)1\mathrm{.}0$ ; $($d$)0\mathrm{.}11$ ;