The standard deviation is not a good measure of the risk of an individual stock even though it is a good measure of the risk for a well$-$ diversified portfolio. For an individual stock, the good measure of the risk is what we call the beta. Beta is defined as follows.

After looking at the definition, Frodo tells you that $$the increase in the standard deviation of a stock necessarily increases the beta of the stock. Thus, beta is positively correlated with the standard deviation$.$ Comment on this statement.