# Markowitz portfolio risk with PV01 instead of variance

As the PV01 ($$= dpdy \times notional$$) of a bond is a measure of its risk, as well as its price return variance, could we measure the risk of a bonds portfolio with the Markovitz portfolio variance formula, but substituting variance by the PV01 of each bond?

ie using $$risk = {\sigma}^T \times \rho \times \sigma$$ with $$\sigma$$ the vector of bonds PV01 instead of the vector of bonds variance (and $$\rho$$ the correlation matrix).

Also can the raw PV01 be used, or the PV01 weight ($$= PV01 / \Sigma PV01$$)? If using the weight, how can it differentiate between a small portfolio and a very large portfolio, that would have the same bonds proportion, but obviously not bearing the same risk?

$$\rho$$ needs to be the correlation matrix of bond yields and you also need to scale by the bond yield variances.