# Total Interest Rate Risk of a Fixed Income Portfolio

The classic Markowitz risk is $$f=\boldsymbol{x}^{T} \Sigma \boldsymbol{x}$$

Now say I have a duration vector $$\boldsymbol{d}$$ for my assets; and also correlation (of say change of yield) matrix $$\boldsymbol{\text{K}}$$.

The naive approach would be $$f = \boldsymbol{d}^{T} \boldsymbol{x}$$

But is the Markowitz style approach using duration as the measure of risk legit as well? $$\Sigma = \text{diag}(\boldsymbol{d}) \; \boldsymbol{\text{K}} \; \text{diag}(\boldsymbol{d})$$ $$f=\boldsymbol{x}^{T} \Sigma \boldsymbol{x}$$