Building Bond Portfolios to Hedge Duration and Convexity

Summary

The answer describes how bond portfolios can immunize a liability or another bond against interest-rate changes using duration and convexity. Given the ability to short, two bonds with different durations can match a target duration, while three non-collinear bonds can match both duration and convexity. It presents bond selection as flexible when short selling is permitted, so the portfolio need not be restricted to a single issuer type or maturity category for the matching exercise itself.

The practical choice depends on the hedging objective and trading constraints. For straightforward immunization, default-free bonds avoid introducing default risk. Long-maturity bonds can reduce rollover risk, but the hedge must be rebalanced regularly as durations change. If short selling is unavailable or limited, the answer recommends searching combinations that achieve the hedge with minimal short positions, often favoring bonds whose durations are close to that of the liability. The document gives conceptual construction guidance but no numerical example, transaction-cost analysis, or specific yield-shock simulation procedure.

Key ideas

• Two bonds with different durations can match a target duration when short selling is available.
• Three non-collinear bonds can be combined to match duration and convexity.
• Default-free bonds avoid adding credit risk to a basic immunization portfolio.
• Long-maturity bonds can reduce rollover risk, but the hedge requires frequent rebalancing.
• Short-sale constraints make portfolio selection harder and favor bonds with durations near the hedged exposure.

Tags

# What's the best way to create a Bond Portfolio for Duration and Convexity hedging?


# What's the best way to create a Bond Portfolio for Duration and Convexity hedging?












I need to create a bond portfolio, hedge it with duration / convexity and simulate yield shocks to . How would you proceed when creating the bond portfolio? Government or Corporate Bonds (or mixed?) Coupon or Zero Coupon Bonds (or mixed?) Short/long term bonds? Bonds from 1 Country / multiple Countries / from 1 Central Bank Area (only US Treasuries) or multiple Central Bank Areas (US Treasuries and European Bonds mixed) ?

## Answer by phdstudent (score 1, accepted)

https://quant.stackexchange.com/a/54931

If you do not have short-selling constraints ... It really does not matter.

With any two bonds with different duration you can match duration of another bond/liability perfectly. With any three non-colinear bonds you can match maturity and convexity of any other bond/liability.

Now 3 things to take into consideration:

- If you really just want immunization, use default free bonds, so that you do not have to worry about default risk;

- You will always have to rebalance your portfolio frequently to keep the immunization at work. Try using long maturity bonds (less rollover risk);

- If you can't short, then it's tricky. Then actually, you just need to brute force which combination of bonds would deliver immunization with the least short-selling possible. Those are usually bonds with duration close you your hedging portfolio.

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.