Suppose that the index model for stocks A and $B$ is estimated from excess returns with the following results:

$R_A=1\mathrm{.}1\%+1\mathrm{.}2R_M+e_A$

$R_B=-0\mathrm{.}9\%+1\mathrm{.}3R_M+e_B$

The $R^2$ of the estimate for stock $A$ is $0\mathrm{.}45$ and the $R^2$ of the estimate for stock $B$ is $0\mathrm{.}55.$ The standard deviation of the market is ${}_M=32\%.$ Assume you create portfolio $P$ with weights of $125\%$ in A and $-25\%$ in B$.$ These weights mean that you go long stock A and short stock B$.$

a$)$ What is the beta of the resulting portfolio?

b$)$ What is the standard deviation of the portfolio? $[$Hint: $R^2=\frac{{}^2{}_M^2}{{}_i^2}].$