The zero beta form of the CAPM replaces the risk-free rate with the return on a zero beta portfolio. Portfolio Z has zero correlation with the market portfolio. Therefore, the beta for portfolio Z also equals zero. Recall the formula for beta:
where covim is the covariance between any asset i and the market index m, σi is the standard deviation of returns for asset i, σm is the standard deviation of returns for the market index, and ρim is the correlation between asset i and the market index. Therefore, the beta will equal zero if the correlation equals zero.
The equation for the zero-beta CAPM is:
E(R) = E(Rz) + β[E(Rm) – E(Rz)] = 0.08 + 1.50[0.14 – 0.08] = 0.17 = 17%
