The difference in yield between an on-the-run Treasury security and its when-issued counterpart. For example, if the on-the-run 10-year note is trading at a yield of 6% and the w.i. 10-year note is trading at a yield of 5.95%, the roll is negative 5 basis points, or "give 5" in trader parlance. (You "give" up 5 basis points to own the w.i. note instead of the one-the-run note.) On the other hand, if the w.i. note is trading at a yield of 6.02%, the roll would be 2 basis points, or "pick-up 2."
In any case, the roll is the net of three things:
--The longer maturity of the w.i. security (unless it is a reopening). Normally, investors demand higher yields on longer-maturity issues.
--The better liquidity of the w.i. issue. Normally, investors are willing to sacrifice some yield for liquidity.
--The cost of financing the on-the-run issue in repo. If the financing rate is lower than the issue's yield, an owner of the issue has "positive carry." The owner of a w.i. issue has no carry, so would demand some extra yield for forgoing positive carry. However, if the financing rate is higher than the on-the-run issue's yield, an owner of the issue has "negative carry," and the owner of a w.i. issue would be willing to sacrifice some yield.
Rolls are usually negative, even when on-the-run issues offer positive carry. This attests to the high value placed on liquidity -- it can be worth more than the sum of a longer maturity and positive carry.