Why might investors require a higher return from one stock than another?

CAPM adds compensation for exposure to broad market movements to the risk-free rate.

Cost of equity = risk-free rate + beta × market risk premium
Beta 1.2 scales the 5% market premium to 6 percentage points. Add the 4% risk-free rate to obtain 10%.
At a 4% risk-free rate, beta 1.2 and a 5% market risk premium, cost of equity is 4% + 1.2 × 5% = 10%.
Beta 1.2 scales the 5% market premium to 6 percentage points. Add the 4% risk-free rate to obtain 10%.

What does the same model require for beta 0.8?