Estimating Corporate Bond Volatility from Duration and Spread Risk

Summary

The document presents a factor decomposition for approximating corporate bond returns and deriving their variance. It starts with the duration approximation, which relates a bond’s return to the negative product of duration and yield change. Yield changes are then separated into interest-rate movements and credit-spread movements. The spread component is expressed using duration times spread (DTS) multiplied by the relative change in spread.

This representation makes return variance depend on the variances of interest-rate changes and relative spread changes, plus their covariance. The author describes estimating that covariance matrix from bond indices, potentially split into groups of similar bonds, and intends to use the resulting bond covariances in portfolio optimization. However, the document does not show the estimation procedure, numerical examples, or validation results; it raises these as open questions. The approach is an approximation, so its usefulness depends on representative index data and estimates that capture the relevant rate-spread relationship for the bonds being analyzed.

Key ideas

• Duration approximates a bond’s return as the negative product of duration and yield change.
• Corporate bond yield changes can be divided into interest-rate changes and credit-spread changes.
• DTS scales relative spread changes to express their contribution to bond returns.
• Return variance depends on rate and spread variances and on the covariance between those factors.
• Index data grouped by similar bonds may help estimate the covariance inputs, though the document gives no worked estimation or validation.

Tags

# How to compute Bonds volatility from Duration and DTS?


# How to compute Bonds volatility from Duration and DTS?












I recently came across article From Ad Hoc Bond-Risk Measures to Variance–Covariance Forecasts from De Jong and Fabozzi, where they show how to infer the variance (and covariance) of Corporate Bonds using their Duration and Duration Times Spread (DTS) properties.

They idea is to decompose the return of a corporate bond starting from the duration approximation:

$$R_{it} \cong -D_{it} \cdot \Delta y_{it}$$

Then, to split the change in yield $\Delta y_{it}$, in two components the interest rate and the spread:

$$R_{it} \cong -D_{it} \cdot \Delta I_{it} - D_{it} \cdot S_{it} \cdot \frac{\Delta S_{it}}{S_{it}}$$

This allows to express the volatility of the returns as a function of the change in interest rate and the relative change of spread:

$$ \text{Var}(R_{it}) = ( D_{it}, D_{it} \cdot S_{it}) \cdot \begin{bmatrix} \text{Var}(\Delta I_{it}) & \text{Cov}\left(\Delta I_{it}, \frac{\Delta S_{it}}{S_{it}}\right) \\ \text{Cov}\left(\Delta I_{it}, \frac{\Delta S_{it}}{S_{it}}\right) & \text{Var}\left(\frac{\Delta S_{it}}{S_{it}}\right) \end{bmatrix} \cdot \begin{pmatrix} D_{it} \\ D_{it} \cdot S_{it} \end{pmatrix} $$

Then, they suggest to estimate this covariance matrix using indices (and splitting across different pockets of similar bonds), but I struggle to see how they proceed with their estimate and then how they test their approach.

Has anyone already used this technique and would be willing to share some numerical examples?

My ultimate goal would be to use this technique to perform a portfolio optimization, using the obtained covariances.

Thanks!

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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