Treasury Futures are often used to hedge interest rate risks. Given CtD, a Treasury Futures contract's DV01 is approximately
DV01 of Treasury Futures = DV01 of CtD x Conversion Factor
and thus
Duration of Treasury Futures = Duration of CtD
However, when I estimate the duration by the ratio between daily Treasury Futures log return and CtD yield change, it can be quite different from the duration of CtD and fluctuate by quite a lot as well. Although I understand there is embedded delivery option, I don't feel that is large enough to explain the difference, in particular if the CtD security does not change. Does anyone know the main driver of the difference? Thanks in advance!