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