Markowitz portfolio risk with PV01 instead of variance

Question

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?

Answer 1

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

All the dv01 scaling does is change the risk variables from price to yield.