Why Bond Risk Is Measured with Duration and Convexity

Summary

The document considers whether changes in a bond’s yield to maturity should be regressed on changes in a bond index’s yield to estimate a beta. It argues that stock-style beta is not the usual framework for bond risk: interest-rate sensitivity is more directly described by duration and convexity, while bonds also carry risks such as credit spread exposure.

For hedging, it suggests regressing portfolio bond returns against a liquid bond-futures contract to estimate a minimum-variance hedge. The hedge instrument should be comparable in credit quality where possible. Using a government futures contract to hedge corporate bonds can leave the portfolio exposed to widening credit spreads. The answer is brief and does not provide a worked regression, specify a model, or discuss how estimates may vary over time.

Key ideas

• Bond risk is commonly measured through duration and convexity rather than stock-style beta.
• Interest-rate risk is a central driver of bond price sensitivity.
• A return regression against bond futures can help estimate a minimum-variance hedge.
• Mismatch in credit quality between a bond portfolio and hedge can leave credit-spread exposure.
• The document gives conceptual guidance but no detailed estimation procedure.

Tags

# Regress the changes in a bonds YTM against the changes in YTM of a bond index?


# Regress the changes in a bonds YTM against the changes in YTM of a bond index?












does it make sense to regress the changes in a bonds YTM against changes in the YTM of a bond index to get som measure of a bonds beta?

## Answer by Mh Aztec (score 1)

https://quant.stackexchange.com/a/33465

The beta concept is rather easy for stocks, but more complex for bonds. We know that stocks tend to grow long term and rise in price, which compensates investors for their risk. So generally investors want a positive beta to the stock market, to capture this long-run price appreciation tendency. For bonds, there is no long-term appreciation observable and the main source of risk is not a bond index, but interest rate risk, therefore no one uses betas to hedge bonds, but duration and convexitiy. (if its about hedging: Alternatively regress your (portfolio) bond return against the return of a bond-futures contract as they are more liquid to e.g. conduct a minimum variance hedge. Also it is important to note that if you do such a regression to take comparabale bonds in terms of credit rating, i.e. if you hedge a corporate bond portfolio with a gilt futures, you are exposed to an increase in the credit spread.)

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