Hi! Equity beta measures sensitivity of a stock to market risk. By its definition, usually we have % change in stock = beta of the stock * % change in index.
However, from CAPM perspective, we have E[R(stock)] = beta * E[R(market)] + (1-beta) * Rf.
If we compare two formula above and consider the % change as return, it looks like there are more items, i.e. (1-beta)*Rf, in the second formula when considering return on stock.
Does “realized” return vs “expected” return make the difference above?
If I take expected value on the both sides of the first formula, would it be contradictory to the second formula?
Thanks in advance!
Assuming (as CAPM does) that β and rf are constant, their percentage change is zero.