Roll-Down Return
Price change from aging along the curve, assuming yields stay constant.
Roll-down return is the price change from the bond getting closer to maturity and 'rolling down' the yield curve, assuming the curve shape stays unchanged. If the curve is upward-sloping (normal), a 10Y bond yielding 4% becomes a 9Y bond yielding 3.5% after a year — price rises even with no yield change. This is 'positive roll-down.' If the curve is flat, roll-down is zero. If inverted, roll-down is negative. Curve dependency is key: steep curves offer more roll-down; flat curves offer none. For premium bonds (price >100), roll-down competes with pull-to-par (negative); for discount bonds, both effects are positive. Roll-down is a 'free lunch' in upward-sloping curves — you earn it just by holding the bond.
Formula
Where
=Bond price at horizon date
=Bond price at purchase
Variables
| R_{rolldown} | Roll-down return (decimal) |
| P_T^{unchanged} | Clean price at horizon with unchanged yield |
| P_0 | Initial clean price |
Assumptions
- Yield to maturity remains constant
- Bond 'rolls down' the curve as maturity shortens
- Premium bonds have negative roll-down (pull to par)
- Discount bonds have positive roll-down (pull to par)
vs. Industry Tools
Bloomberg HRZN — Similar decomposition; may use different interpolation