Suppose that many stocks are traded in the market and that it is possible to borrow at the risk$-$free rate, r$.$ The characteristics of two of the stocks are as follows:

Stock Expected Return Standard Deviation

A $8\%55\%$

B $4\%45\%$

Correlation $=1$

Required:

a$.$ Calculate the expected rate of return on this risk$-$free portfolio? $($Hint: Can a particular stock portfolio be formed to create a $$synthetic$$ risk$-$free asset?$)($Round your answer to $2$ decimal places.$)$

b$.$ Could the equilibrium r$$ be greater than rate of return?