Part II: Probl$$mes $(30$ Points Total$)$

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Q$1.(9$ Points$)$ Risk and Return:

Suppose the economy can be in one of the following two states: $($i$)$ Boom or "good" state and $($ii$)$

Recession or "bad" state. Each state can occur with an equal opportunity $(50\%).$ The annual

return on the market and a certain security $x$ in the two states of the economy are as follows:

Market: at the end of the year, the market is expected to yield a return of $30\%$ in the good

state and a return of $(-10\%)$ in the bad state;

Security $x$ : at the end of the year, the security is expected to yield a return of $40\%$ in the

good state and a return of $(-35\%)$ in the bad state;

Furthermore, assume that annual risk$-$free rate of return is $6\%$ in all states of the market.

Assuming CAPM is the correct model:

i$.(7$ points$)$ Calculate the beta of security $x$ relative to the market.

ii$.(2$ points$)$ Calculate the alpha of security $x.$

$($i$)$ of security $x$ is:

Marlat: $E(r_m)=0\mathrm{.}5**0\mathrm{.}3+0\mathrm{.}5(-0\mathrm{.}1)=0\mathrm{.}1=10\%.$

${}_{r_m}^2=0\mathrm{.}5(0\mathrm{.}3-0\mathrm{.}1{)}^2+0\mathrm{.}5(-0\mathrm{.}1-0\mathrm{.}1{)}^2=0\mathrm{.}04$

Secunity $x$ :

$E(r_x)=0\mathrm{.}50\mathrm{.}4+0\mathrm{.}5(-0\mathrm{.}35)=0\mathrm{.}025=2\mathrm{.}5\%.$

Cov$(r_m,r_x)=0\mathrm{.}5(0\mathrm{.}3-0\mathrm{.}1)(0\mathrm{.}4-0\mathrm{.}025)+0\mathrm{.}5(-0\mathrm{.}1-0\mathrm{.}1)(-0\mathrm{.}35-0\mathrm{.}025)$

$=0\mathrm{.}0750$ I DON'T UNDERSTADN WHAT FORMULA IS BEING USED FOR THE EQUATION HIGHLIGHTED IN THE PURPLE