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Sizing a Yield Curve Flattening Trade with Two Zero-Coupon Bonds

Article Quant Q&A · Author: elchevy
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Summary

The document poses a fixed-income trade-sizing problem: construct a flattening position using two-year and ten-year zero-coupon bonds, with a target profit for a specified change in the yield spread. It asks for each leg’s present-value exposure and whether to buy or sell it.

The questioner expects the shorter yield to rise more than the longer yield and therefore proposes shorting the two-year bond while buying the ten-year bond. A response points out that equal dollar amounts on the two legs do not make the position duration-neutral; if the goal is merely to fund one leg with proceeds from the other, the allocation can be equal in present-value dollars. The exchange does not derive the bond sensitivities or calculate positions that meet the stated profit target, so it leaves the key sizing method unresolved.

Key ideas

  • A yield curve flattening position can combine long and short exposures at different maturities.
  • Equal present-value amounts across bond legs do not create a duration-neutral position.
  • Sizing to a profit target requires accounting for how each bond’s price responds to yield changes.
  • The response discusses funding one leg with the other but does not solve the requested profit-target calculation.

Tags

Fixed incomePosition sizingRisk management
Full text
# Yield Curve Flattening Trade


# Yield Curve Flattening Trade












Relatively simple question, but came upon it in class and have not been able to come up with an answer:

> The two-year bond yield is equal to 4% while the 10-year one is equal to 10%. You want to put on a yield curve flattening trade such that for every 1% flattening you will make a $1000 profit. You can trade 2-year and 10-year 0-coupon bonds at t = 0. For each bond specify, how much you are trading in PV terms and whether you are long or short. (Note: a 1% flattening implies that ∆y10 = ∆y2 - 1%.

My understanding is that since we expect the increase on the 2-year yield to outweigh that of the 10-year yield, we should go long 10-yr while shorting 2-yr. The initial investment would have a net value of 0, since we would fund our investment in the 10-year bond by borrowing at the 2-year rate. But how would we determine the amount allocated to each bond?

## Answer by VanillaCall (score 0)

https://quant.stackexchange.com/a/46594

This is not a duration neutral trade then if you're assuming equal proceeds in on each leg. In that case, why do you need to know how much to allocate to each bond? If you short $100 million on one leg, then you use that to buy the long leg

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