# 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.

• "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? Mar 7 at 13:02
• @DimitriVulis: I was told to assume equal risk on 5Y and 10Y, so I believe it is an amortizing bond. Mar 10 at 14:37