Your next task is to analyze a proposed portfolio of Chevron, American Airlines, and ExxonMobil stocks. The forecast analyst in your team has provided you with a table that summarizes the distribution of returns for each firm $($Hint: this is an extended version of the $$boom$,$normal$,$ and $$recession$$ problem of slide $3$ in Modern Portfolio Theory$)(15$ points$)$

State of the

Economy

Probability

Chevron

American Airlines

ExxonMobil

State $1$

$5\%$

$-8\mathrm{.}3\%$

$19\mathrm{.}4\%$

$-15\mathrm{.}0\%$

State $2$

$10\%$

$-3\mathrm{.}9\%$

$8\mathrm{.}2\%$

$-10\mathrm{.}0\%$

State $3$

$15\%$

$-1\mathrm{.}3\%$

$5\mathrm{.}0\%$

$-1\mathrm{.}8\%$

State $4$

$20\%$

$0\mathrm{.}9\%$

$3\mathrm{.}2\%$

$0\mathrm{.}8\%$

State $5$

$20\%$

$3\mathrm{.}0\%$

$1\mathrm{.}0\%$

$2\mathrm{.}8\%$

State $6$

$15\%$

$5\mathrm{.}2\%$

$-1\mathrm{.}1\%$

$5\mathrm{.}4\%$

State $7$

$10\%$

$8\mathrm{.}3\%$

$-3\mathrm{.}6\%$

$20\mathrm{.}0\%$

State $8$

$5\%$

$14\mathrm{.}2\%$

$-5\mathrm{.}0\%$

$30\mathrm{.}0\%$

a$)$ Obtain the expected return, variance, and standard deviation of returns for each stock.

b$)$ Obtain the expected return, variance, and standard deviation of returns for a portfolio that invests $-$$$300,000$ in Chevron, $$500,000$ in American Airlines, and $$600,000$ in ExxonMobil.Your next task is to analyze a proposed portfolio of Chevron, American Airlines, and ExxonMobil stocks. The forecast analyst in your team has provided you with a table that summarizes the distribution of returns for each firm $($Hint: this is an extended version of the $$boom$,$normal$,$ and $$recession$$ problem of slide $3$ in Modern Portfolio Theory$)(15$ points$)$

State of the

Economy

Probability

Chevron

American Airlines

ExxonMobil

State $1$

$5\%$

$-8\mathrm{.}3\%$

$19\mathrm{.}4\%$

$-15\mathrm{.}0\%$

State $2$

$10\%$

$-3\mathrm{.}9\%$

$8\mathrm{.}2\%$

$-10\mathrm{.}0\%$

State $3$

$15\%$

$-1\mathrm{.}3\%$

$5\mathrm{.}0\%$

$-1\mathrm{.}8\%$

State $4$

$20\%$

$0\mathrm{.}9\%$

$3\mathrm{.}2\%$

$0\mathrm{.}8\%$

State $5$

$20\%$

$3\mathrm{.}0\%$

$1\mathrm{.}0\%$

$2\mathrm{.}8\%$

State $6$

$15\%$

$5\mathrm{.}2\%$

$-1\mathrm{.}1\%$

$5\mathrm{.}4\%$

State $7$

$10\%$

$8\mathrm{.}3\%$

$-3\mathrm{.}6\%$

$20\mathrm{.}0\%$

State $8$

$5\%$

$14\mathrm{.}2\%$

$-5\mathrm{.}0\%$

$30\mathrm{.}0\%$

a$)$ Obtain the expected return, variance, and standard deviation of returns for each stock.

b$)$ Obtain the expected return, variance, and standard deviation of returns for a portfolio that invests $-$$$300,000$ in Chevron, $$500,000$ in American Airlines, and $$600,000$ in ExxonMobil.