FVPV

variance market = mkt std * mkt std

This is because beta measures the sensitivity of the stock's return to market's return (therefore, not mkt std*stock1 std at the bottom), which is the non-diversified risks, the risks that get awarded.

In other words, since the total risk of the stock is measured by its standard deviation, the covariance (stock, market) measures the risk of the stock relative to the market. After standardized for the market covariance, we get the standardized beta to compare across firms in the same industry.

Hope this helps.