How do you calculate the roll-down return for a bond, and what assumptions does it require?

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AcadiFi · Accepted Answer

Roll-down return is the price appreciation a bond experiences as it ages along an unchanged yield curve. On a positively sloped curve, a 5-year bond that becomes a 4-year bond moves to a lower yield — and lower yields mean higher prices.

**The Key Assumption**

Roll-down return requires the assumption that the **yield curve does not change** over the holding period. This is the "unchanged yield curve" scenario. It does not predict what will happen — it asks: what would the return be if yields stay exactly where they are today?

**Calculation Framework**

Total Return (1-year horizon) = Coupon Return + Roll-Down Return + Pull-to-Par

**Worked Example — Fenwick Capital, 5-year Treasury:**

Current yield curve (government bonds):

| Maturity | Yield |
|---|---|
| 3-year | 3.90% |
| 4-year | 4.15% |
| 5-year | 4.40% |
| 6-year | 4.58% |

Fenwick holds a 5-year Treasury, coupon 4.25%, currently priced at **$99.34** (yield = 4.40%, semi-annual).

After 1 year (unchanged curve), the bond has 4 years remaining and rolls to the 4-year yield of 4.15%. New price: **$100.37**.

| Component | Calculation | Return |
|---|---|---|
| Coupon return | $4.25 / $99.34 | +4.28% |
| Roll-down return | ($100.37 - $99.34) / $99.34 | +1.04% |
| **Total horizon return** | | **+5.32%** |

The roll-down return of +1.04% comes entirely from the yield curve slope — the 25 bps decline from 4.40% to 4.15% as the bond ages one year.

**Roll-Down Return Approximation**

For quick calculations:

Roll-Down Return ≈ (Yield at Current Maturity - Yield at Horizon Maturity) x Duration at Horizon

= (4.40% - 4.15%) x 3.7 = 0.25% x 3.7 = **0.93%**

(The approximation is close to the exact 1.04% — the gap is due to convexity and the linear duration approximation.)

**When Roll-Down Is Highest:**

1. **Steep yield curve** — larger yield drop per year of aging
2. **Intermediate maturities** — the 3-7 year segment often has the steepest slope
3. **Longer duration** — amplifies the price impact of the yield change

**When Roll-Down Disappears:**

- **Flat yield curve** — no yield decline from aging
- **Inverted yield curve** — negative roll-down (price declines as bond ages to higher yields)
- **If yields actually shift** — the unchanged curve assumption is violated

**Exam Application:**

Candidates are often asked to compare horizon returns across bonds with different maturities on the same curve. The bond with the highest carry + roll-down combination is the optimal position under the unchanged curve assumption.

Practice roll-down calculations in our CFA Level II fixed income modules.

How do you calculate the roll-down return for a bond, and what assumptions does it require?

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