I understand that roll yield = Δforward price – Δspot price and if its positive it means positive carry trade and trade the forward rate bias. But what does it really mean intuitivelly???
I don’t think this is correct. As you pointed out, roll yield refers to forward and spot prices, however I think the carry trade refers to a voilation of interest rate parity where a trader can borrow in a low yield currency and invest in a high yield currency.
The forward rate assumes that the higher yielding currency will depreciate. This is often incorrect, hence one can make a profit by converting at spot, invest in the higher yielding currency, and converting back to spot. This is trading the forward rate bias.
Remember that the formula for roll yield depends on whether you buy or sell the forward. I think of it as taking the spot return out of the change in futures price, so you’re just looking at the gain/loss from the futures moving towards the old/initial spot price.