Using PV01 in a Bond Portfolio Risk Calculation

Summary

The document asks whether a Markowitz-style portfolio risk calculation can use each bond’s PV01, or dollar value of a basis point, in place of return volatility. It also asks whether to use raw PV01 exposures or normalized PV01 weights, noting that weights alone do not distinguish portfolios with the same composition but different sizes.

The answer clarifies that the correlation matrix should describe bond yield changes and that the calculation must also account for yield variances. PV01 scales yield movements into approximate price changes, so using it changes the risk variables from yield units to price units; it does not replace the variance information required for portfolio risk. The response is concise and does not provide a worked calculation or discuss assumptions such as linearity, but it gives the key distinction between exposure scaling and covariance inputs.

Key ideas

• A bond portfolio risk calculation needs correlations between bond yield changes.
• Yield variances must also be included; PV01 exposures alone do not supply them.
• PV01 translates yield movements into approximate price changes for each bond.
• Normalized PV01 weights describe portfolio proportions but omit overall portfolio scale.

Tags

# Markowitz portfolio risk with PV01 instead of variance


# 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?

## Answer by Ezy (score 3, accepted)

https://quant.stackexchange.com/a/43381

$\rho$ 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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.