Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 30K / b / Solution

For every nonzero-risk portfolio,Equality holds precisely forThe maximum is therefore $\sqrt{q^T{V}^{-1}q}$. For each resulting mean, part (a) shows that this portfolio has the least possible variance, so every maximizer lies on the mean-variance efficient ray.