Bond Carry and Rolldown

Buy a 10-year bond and hold it for a year without the yield curve moving a single basis point, and you still make money two distinct ways: the coupon you collect along the way, and the fact that in a year your "10-year" bond has become a 9-year bond, which — if the curve slopes upward — trades at a lower yield and therefore a higher price than it did as a 10-year. That second effect is rolldown, and together with the coupon it forms a bond's carry — the return you earn purely from the passage of time, holding the curve fixed.

Reading rolldown off the curve

If the curve is upward-sloping, a bond that ages by one year moves left along the curve to a point with a lower yield — and lower yield means higher price, all else equal. The size of that price gain depends on how steep the curve is at that point and the bond's price sensitivity (duration) to a yield change.

$$\text{Rolldown} \approx -D \times (y_{\tau - 1} - y_{\tau})$$

In words: rolldown is approximately the bond's duration times the drop in yield it experiences just from aging one year down an upward-sloping curve — a steeper curve or a longer duration both mean bigger rolldown.

Worked example

A bond currently priced as a 10-year has a yield of 4.60% and duration of 8.2. The curve, held fixed, shows the 9-year point at a yield of 4.45%.

• Yield drop from rolling down: $4.60\% - 4.45\% = 0.15\%$.
• Rolldown price gain: $8.2 \times 0.15\% \approx 1.23\%$ of price.
• Coupon carry: the bond pays a 4.5% annual coupon, so roughly 4.5% over the year (ignoring compounding).
• Total carry + rolldown: approximately $4.5\% + 1.23\% = 5.73\%$ — the return earned over the year if the curve stays exactly where it is.

Compare that to the 1-year forward rate implied for that same horizon. If the market's forward rate implies yields will rise more than what's needed to offset this rolldown, the expected excess return net of the curve's own forecast could be smaller, or even negative, despite the attractive-looking carry number.

What this means in practice

Carry and rolldown are the standard lens for comparing where on the curve to own duration when a trader has no strong view on which way rates will move: positions with high carry-plus-rolldown are preferred, since that's the return earned for simply being patient. It's also the basis for "riding the curve" strategies — repeatedly buying bonds at a steep part of the curve and selling before maturity to capture the rolldown, rather than holding to maturity.