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Sizing Bond Exposures to Replicate a Five-Year-Five-Year Forward

Article Quant Q&A · Author: Gumtha
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Summary

The document presents a bond-based approach to creating exposure to a five-year-five-year forward rate. The proposed portfolio is short a five-year bond and long a ten-year bond, with relative weights determined using duration-based interest-rate sensitivity, or DV01. It relates the forward exposure to a ten-year position plus an adjustment through the five-to-ten-year spread, scaled by the ratio of the five-year DV01 to the forward swap DV01.

The answer gives a compact replication relationship rather than a step-by-step derivation of bond weights. The question’s assumptions assign no 5Y-10Y risk to the five-year bond and equal risk across the two periods to the ten-year bond, but the response itself is framed in swap and spread terms. The note does not provide numerical DV01 inputs, quantify residual curve risks, or explain how to translate the swap expression into specific cash bond holdings.

Key ideas

  • A 5Y5Y forward exposure can be approximated with a short five-year bond and a long ten-year bond.
  • Relative sizing depends on the instruments’ DV01 sensitivities.
  • The suggested relationship combines a ten-year exposure with a DV01-scaled five-to-ten-year spread exposure.
  • The source gives a formula outline but no numerical inputs or full bond-weight derivation.

Tags

Fixed incomePosition sizingPortfolio construction
Full text
# How to construct a forward exposure portfolio with bonds?


# How to construct a forward exposure portfolio with bonds?












I was asked in an interview to get an exposure to 5Y5Y forward rate using bonds alone. Essentially it is short 5Y bond and long 10Y bond, and I needed to compute the relative weights. Regarding risk:

- The 5Y bond does not have risk on 5Y-10Y

- The 10Y bond is assumed to have equal risk on 5Y and 10Y.

How to compute the relative weights using this information? I am unclear on the mathematics involved in this sort of question.

## Answer by user68819 (score 1)

https://quant.stackexchange.com/a/76644

In terms of swaps: 5y5y fwd = 10y + (10y-5y) × (dv01 5y/ dv01 5y5y)

So to create a 5y5y fwd for each 1 usd of fwd swap I can pay 1 usd of 10y and (dv01 5y/ dv01 5y5y) USDs of 5s10s spread.

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.