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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.

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    $\begingroup$ "The 10Y bond is assumed to have equal risk on 5Y and 10Y." Please clarify what this means. A fixed coupon bond has most of its interest rate risk in tenor buckets when the principal is repaid. Hence a bullet bond would have most of its IR risk in the maturity tenor bucket. Do you rather mean an amortizing bond repaying 1/2 of the principal in 5Y and the other 1/2 in 10Y? $\endgroup$ Commented Mar 7, 2023 at 13:02
  • $\begingroup$ @DimitriVulis: I was told to assume equal risk on 5Y and 10Y, so I believe it is an amortizing bond. $\endgroup$
    – Bravo
    Commented Mar 10, 2023 at 14:37

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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.

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