In plain language — A bond can earn income while time passes, but its price keeps reacting to rates, credit and liquidity. Carry is not free return, and roll-down is not a forecast.
Carry is the economic contribution accrued while holding a position over an interval under a stated definition. It may include coupon or accrual, financing and other cash flows. Roll-down is the price or yield effect of the instrument moving to a shorter residual maturity along a curve assumed to remain unchanged.
“Assumed” is the key word: actual curves and spreads rarely remain identical.
A useful decomposition, not one universal identity
For a short horizon, a teaching approximation is:
Return ≈ carry + roll-down + rate effect + spread effect + convexity − costsThe split depends on model, factor ordering and conventions. Coupon cash, accrued interest and financing must not be counted twice. Currency, hedging, default, options and liquidity may need separate components.
Suppose a five-year bond yields 3.20% while a comparable four-year point on today's curve yields 3.00%. If one year later the curve were unchanged and the bond remained comparable, moving to that lower-yield point could support its price. The observation does not say where the curve will actually be, what the issuer spread will be or how much the position cost to finance.
Operational calculation
Choose start date and horizon, then save a complete snapshot: dirty price, expected cash flows, reference curve, spread, funding curve and option assumptions. Advance the calendar to the horizon and revalue the security under unchanged curve and spread. Reconcile the difference with cash and financing to obtain an estimate of carry plus roll-down.
Separating the two requires a house convention. One method assigns net accrual after funding to carry and the revaluation at the new residual maturity to roll-down. Another includes part of pull-to-par in carry. Either can be coherent when name, formula and reconciliation test remain visible.
The essential control reconstructs realised P&L:
Total P&L = change in value + cash received − costs and financingAttribution components should reconcile to the total, with explained residuals.
From carry to curve risk
Positive carry can be erased by a small adverse yield move. Duration and key-rate duration translate local shocks into price changes; convexity matters for larger moves. Credit securities add spread and CS01 sensitivities.
Roll-down is fragile when slope or curvature changes. Steepening, flattening and a local twist can produce very different results from a parallel shift. A serious review shows at least unchanged-curve, curve-shock, spread-shock and alternative-funding scenarios.
For callable or mortgage-backed securities, cash flows can also change with rates. A simple passage-of-time calculation is then insufficient: the model must update exercise or prepayment assumptions.
Common error — Annualising a few days of carry and roll-down as if they were a stable expected return. That multiplies a local assumption while ignoring curve, spread, costs and events.
Questions this page answers
Which cash flows enter carry? Is funding included? Which curve is held unchanged? Does roll-down use a zero, par or yield curve? Is credit held constant? Do all components reconcile to total return?
Sources
- Federal Reserve Board — H.15 Selected Interest Rates
- U.S. Treasury — Daily Treasury Par Yield Curve Rates
- FINRA — Bonds