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I have to perform a regression to get an hedge ratio. The dependent variable is the change on day of a swap fixed rate (f.i. 10y) and the independent variable is the change on day of a bond future forward yield (f.i. Bund). How to account for the time decay of the bond? As days pass by, the 10y swap has the same maturity, but the CTD of the bond future has a lower time to maturity.

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You can proxy the dv01 of a bond fut as dv01 of ctd / CF of ctd. Fancier if dv01 of fwd ctd (as of delivery) / CF.

Given your question, I'd assume you aren't thinking about switch options etc.

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