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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.

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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.

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    $\begingroup$ By matching up the DV01s in this manner you achieve neutrality against a parallel shift in the yield curve (not against all possible movements). $\endgroup$ – Alex C Sep 13 '17 at 23:27
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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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