$(20$points$)$ According to the CAPM, annual return $r$ of an asset can be modeled by a regression

with independent variable of the index $($market portfolio$)$ annual return $r_M$ as follows:

$r-r_f=+(r_M-r_f)+$

where $r_f$ is risk free rate of return, $r_{M}N({}_M,{}_M^2),$ and $N(0,{}^2).$ Here we assume that $r_M$ and

$$ are independent. Suppose that $r_f=0$ and we estimate parameters as follows:

$=0\mathrm{.}002,=0\mathrm{.}9,$ and $=0\mathrm{.}2.$

a$.$ If the expected index annual return is as $0\mathrm{.}1,$ that is ${}_M=0\mathrm{.}1,$ then what is the expected

annual return of the asset?

b$.$ Suppose standard deviation of the index annual return is ${}_M=0\mathrm{.}1.$ Calculate $99\%-$VaR

$(=Va{R}_1\%(r))$ of $r.$ Note that $99\%$ quantile value of the standard normal distribution is $q99\%$

$=2\mathrm{.}326.$

Hint :$r$ is normal distributed and $E(+(r_M-r_f)+)=+E[r_M]$

var$(+(r_M-r_f)+)={}^2$var$(r_M-r_f)+$var$()={}^2$var$(r_M)+$var$()$