My understanding is that a flattener trade on a flattish but slightly upwards sloping yield curve has negative carry as we are paying more in the short end than receiving in the long end after accounting for the fact that we need to buy more short end bonds to keep our position DV01 neutral. Does the same apply when the yield curve is in negative territory? Eg if 2y YTM is -2.1% and 10y YTM is -2%, we short N number of 2y bonds (for DV01 hedging where N > 1) meaning we pay -2.1% = receive 2.1% and long 10y bond meaning we receive -2% = pay 2%. Carry = 2.1% * N - 2% which is always >0 If my calculations are correct does that mean that flattener trades are always positive carry assuming interest rates are negative and upwards sloping? On the flip side are steepener trades are always negative carry in the same scenario?