The expected rate of return for a stock is $27$ percent, with a standard deviation of $18$ percent. The expected rate of return for another stock is $19$ percent, with a standard deviation of $12$ percent.

a$)$ Which stock would you consider to be riskier? Which stock would you buy?

b$)$ Would you change your answer if you knew that the beta coefficient of the first stock is $1\mathrm{.}4$ and the beta of the second stock is $1\mathrm{.}1?$