Rates Carry and Roll-Down

Ask a bond investor what they earn if yields simply sit still for a year, and many people guess "nothing — nothing moved." That is wrong. A bond earns its coupon regardless, and if the yield curve is upward sloping, the bond also gets more valuable over the year for a second reason that has nothing to do with any change in market conditions: it becomes a shorter-maturity bond, and shorter maturities on an upward-sloping curve carry lower yields.

Two separate sources of "doing nothing"

Carry is the coupon (or repo-adjusted financing cost, for a futures or swap position) collected simply by holding the position — it is what you'd earn if the yield curve were frozen in place forever. Roll-down is different: as a 10-year bond becomes, six months later, a 9.5-year bond, its yield should fall to match wherever 9.5-year bonds trade today if the curve shape is unchanged, and a falling yield means a rising price. On a flat curve, roll-down is roughly zero. On a steep, upward-sloping curve, roll-down can be a large share of a bond's expected return, which is why steepness itself is a signal traders trade.

Steepen the curve above and picture a bond starting at the 10-year point: as time passes it moves left along the curve toward shorter maturities, and the steeper the curve, the further it drops in yield for a given amount of time elapsed — that vertical drop is roll-down.

Worked example

A 10-year government bond yields 4.50%. The 9-year point on today's curve yields 4.30%, a 20 basis point gap purely from the curve's slope. Approximate the price gain from a yield change using duration of about 8.5 years:

$$\Delta P \approx -\text{Duration} \times \Delta y = -8.5 \times (-0.0020) = 0.017$$

In words: dropping 20 basis points in yield as the bond rolls down the curve is worth roughly 1.7% in price appreciation over the year, on top of the coupon itself. If the coupon is 4.50%, the total "curve stays put" return is approximately 4.50% + 1.70% = 6.20% — a meaningful return earned with zero change in the level of interest rates.

What this means in practice

Rates desks routinely compare bonds and futures contracts on carry-plus-roll-down rather than on yield alone, because two bonds with identical yields can offer very different total returns if one sits on a steep part of the curve and the other on a flat stretch. This is also why a curve can be attractive to hold even when a trader has no directional view: a flattening trade that is long the steep, high-roll-down end and short the flat end can earn a positive expected return purely from time passing, assuming the curve shape persists.