Question

a) “The reason that a high beta stock has a greater expected return than a low beta stock is because the high beta stock must have more volatile returns than the low beta stock." Using the CAPM, critically evaluate this statement and demonstrate the links between betas and stock return variability, using equations and examples where necessary.

Answer 1

CAPM equation is given by

required return = risk-free rate + beta*(market return - risk-free rate).

Beta is a measure of systematic risk which measures how much the stock moves as against the market. As can be seen from the equation, the larger the beta, the greater will be the required return of the stock. This makes intuitive sense because greater the volatility of a stock (greater beta), the riskier it is and investors will demand higher returns to compensate for the higher risk which they take one.

For example, if the risk-free rate is 3%, market return is 8% and beta is 0.8 then

required return = 3% + 0.8*(8%-3%) = 7.00%

Now, if the beta increases to 1.5 then required return becomes 3% + 1.5*(8%-3%) = 10.50%

This is illustrated by plotting the CAPM line (return vs risk) which is a linear equation.