Given a two$-$asset economy comprising assets with the parameters in the following table, and

with covariance of returns between the two assets being $-0\mathrm{.}10$

$($a$)$ Prove that the Markowitz Efficient Frontier in risk$-$return space is given by

${}_P=\sqrt[\phantom{2}]{1750{}_P^2-195{}_P+5\mathrm{.}475}$ provided ${}_{P}0\mathrm{.}055714.$

$($b$)$ If the market portfolio has an expected return of $0\mathrm{.}06$ and standard deviation of returns

of $0\mathrm{.}273861,$ determine the risk$-$free rate of return.