Suppose that sixteen stocks have been identified whose rates of return satisfy

\[\overline{r_{i}}= \pm \alpha+f+\varepsilon_{i}\]

where $\alpha>0$. Eight of the stocks use the + sign and the other eight use the - sign. The factor $f$ is common to all sixteen stocks. It has mean equal to 1 , and its standard deviationis $15 %$. Each $\varepsilon_{i}$ represents firm specific error, in the sense that each has zero mean, zero covariance with $f$, and zero covariance with other stocks. Each $\varepsilon_{i}$ has a standard deviation of $24 %$. Now assume that a portfolio consists of all of these stocks, with equal weight given to each one of them. What is the expected rate of return and the corresponding standard deviation of that rate?