Question

A stock with a beta of 0.5 has an expected rate of return of 10%. If the market return this year turns out to be 9 percentage points below expectations, what is your best guess as to the rate of return on the stock? Stock Return: ___%

Answer 1

since the market return and the risk free rate are unknown, we cannot estimate the expected return using the CAPM model.

Although we can guess the expected return using the stock's beta since beta is an estimate of stock's co-movement with resepct to the market
the formula for beta is:
Covariance (stock's return, market return) / variance (market return)

A beta of 1 indicates that if the market return moves by 1 unit, the stock's return would approximately change by 1 unit as well.

From a beta of 0.5, we can estimate that if the market return was 9 percentage points below expectations, the stock's return would be approximately around 4.5 percentage points below expectations, that is, the stock's return would be around 6.5%