DV01 Hedging a Five-Year Bond with Two- and Ten-Year Bonds

Summary

The document explains a curve trade described as buying five-year bonds and hedging with two- and ten-year bonds. The basic idea is to offset the purchased bond’s interest-rate exposure by selling bonds at shorter and longer maturities. It illustrates the approach by matching DV01: the example buys five-year exposure and splits the offset equally between the two- and ten-year maturities.

A second explanation frames a related swap position as paying fixed at five years, paying at two years, and receiving at ten years. It discusses cash flows around the five-year swap rate and links the relative hedge weights to the maturity pattern of convexity. These are conceptual explanations rather than a full construction method: the document does not establish that the position is neutral to all rate movements, and the example does not address curve shifts, convexity risk, or other residual exposures.

Key ideas

• DV01 measures the interest-rate sensitivity used to size the bond hedge.
• Selling two- and ten-year bonds can offset the rate exposure of a five-year bond position.
• A swap version combines fixed-rate positions at two, five, and ten years.
• The described hedge does not establish neutrality to every shape of yield-curve movement.

Tags

# What does Buying 5 year and hedging with 2 year and 10 year mean?


# What does Buying 5 year and hedging with 2 year and 10 year mean?












I hear this during morning meetings where traders are making references to buying the 5 year and hedging with 2 year and 10 year? Does this mean that the position is neutral to overall movements in interest rates? I still don't get the concept of the hedging.

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/36023

Yes this means the trader is selling a combination of 2yr and 10yr bonds to offset the interest rate risk of the purchased 5yr bonds. This is best understood in terms of dv01. For example , you buy 100k dv01 of 5yr notes and sell 50k dv01 each of 2yr and 10yr notes.

## Answer by Daneel Olivaw (score 0)

https://quant.stackexchange.com/a/36022

Assume you're paying (the fixed rate) 5y on a swap. If you then hedge yourself by paying on a 2y swap and receiving on a 10y swap, you are netting a positive cash-flow near the 5y swap rate you pay (assuming a monotonically increasing swap curve). The reason that the receiving swap on the long end of the curve (10y) must be further away from the hedged swap (5y) than the paying swap (2y) is normally due to the decreasing nature of the term-structure of convexity $-$ i.e. the swap curve's slope decreases with maturity.

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