# $0$-beta stock and diversification

If we invest $w$ in the market portfolio and $1 - w$ in the risk-free asset, and observe a $0$-beta asset with expected return greater than the return on the risk-free asset, how can this be used in diversification to reduce risk?

My initial confusion is due to the expected return being greater than the risk-free asset. In equilibrium (i.e., CAPM), this is not possible since the expected returns on the two should be equal?

• It can have $\beta=0$ without $\sigma=0$. The implication is that the risk of this asset is purely idiosyncratic – user25064 May 25 '16 at 13:48