Hedge Bond Portfolios with Key Rate Duration

Summary

The document discusses choosing hedges for a vanilla bond portfolio, including bond futures. It suggests that matching a portfolio’s DV01 and maturity to a futures contract is a basic starting point, then points to key rate durations as a way to measure exposure to specific parts of the yield curve. These measures can help assess curve risk that a single duration figure may not capture.

Key rate duration is estimated by repricing a bond after shifting one selected rate upward and downward, then scaling the price difference by the original price and the size of the rate move. The answer recommends a fixed income risk management reference and notes that index data providers may calculate these measures daily. The discussion does not specify a complete auto-hedging algorithm, futures conversion factors, hedge constraints, or execution rules; the pricing model and rate-shock choices are left to the implementer.

Key ideas

• DV01 and maturity can serve as an initial basis for matching a bond exposure to a futures hedge.
• Key rate durations measure a bond portfolio’s sensitivity to selected points on the yield curve.
• Estimate a key rate duration by repricing with an upward and downward shift to one rate.
• A pricing model that can vary individual interest rates is needed for the described calculation.
• The answer discusses risk measurement, but does not provide a complete automated hedge selection procedure.

Tags

# What are some simple algorithms for hedging vanilla bonds?


# What are some simple algorithms for hedging vanilla bonds?












My team will soon be implementing an auto hedger for our bond trading desk which will be integrated tightly with our risk application and I am interested in researching how this may work.

Any advice or information or general thoughts would be appreciated, especially on algorithms used to suggest hedges with bond futures.

I am guessing at the simplest level comparing the DV01 and instrument maturity to find the closest matching bond future would work but I am keen to know what other factors could be taken into account.

Many thanks.

## Answer by Tal Fishman (score 1, accepted)

https://quant.stackexchange.com/a/1596

The top reference for this topic is Risk Management: Approaches for Fixed Income Markets by Golub and Tilman. The main measures you will want to calculate for hedging the yield curve risks of a bond portfolio are the key rate durations. The wikipedia article gives a brief overview. If you have access to Lehman/Barclays data, they calculate key rate durations daily for every bond in their indices. You can also calculate it yourself as

$krd_i=-\frac 1P \frac {P_{i,up}-P_{i,down}} {2\Delta r_i}$

if you have a pricing model for the bonds in which you can vary a set of interest rates $r_i$. See chapter 2 of the book for details.

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