Bond Roll-Down Return Calculator

The Bond Roll-Down Return Calculator estimates expected total return from yield curve roll-down over a chosen horizon, incorporating carry, price change, and convexity.

About the Bond Roll-Down Return Calculator

This tool focuses on the roll-down effect, a key source of bond returns. When the yield curve is stable, a bond’s remaining maturity shortens over time. Shorter maturities often have lower yields. If yields fall as the bond ages, its price tends to rise. That price drift is the roll-down return.

The calculator isolates roll-down from other forces. It estimates price change from sliding along today’s yield curve, adds coupon carry, and can include convexity for higher accuracy. You can model different holding periods and shape scenarios for the curve. The output gives a simple breakdown by component: coupon, roll-down price change, and optional yield shifts.

Use it to test strategy fit. Compare two bonds across the same horizon. See how steepness and shape matter. Identify when roll-down supports returns and when an inverted curve might work against you.

How to Use Bond Roll-Down Return (Step by Step)

Set up your inputs, choose your horizon, and review the result components. Start with bond terms you can verify. Then test several curve scenarios to see sensitivity. Keep your units consistent and your day count clear.

• Enter bond details: coupon rate, payment frequency, maturity date, and current clean price.
• Choose your holding period in months or years and the day count basis used for accruals.
• Provide the current yield curve data or spot yields at key maturities.
• Include effective duration and convexity if available, or let the tool approximate them.
• Select optional assumptions: reinvestment rate for coupons and expected parallel yield shifts.

Review the breakdown: coupon carry, roll-down price effect, and any extra yield shift impact. If the curve is unchanged, the roll-down piece is the core driver. Adjust the curve shape or horizon to stress test results.

Formulas for Bond Roll-Down Return

Roll-down return comes from the bond’s price revaluation as its maturity shortens, assuming the curve stays the same. We represent yield changes from moving along the curve and translate them into price effects. Coupons add income during the holding period.

• Roll-down yield change: Δy_roll = y(today, T0) − y(today, T0 − h), where T0 is current maturity in years and h is holding period in years.
• Price change from roll-down (duration-only): ΔP_roll ≈ −Duration_eff × Δy_roll × Price_start.
• Price change with convexity: ΔP_roll ≈ [−Duration_eff × Δy_roll + 0.5 × Convexity_eff × (Δy_roll)^2] × Price_start.
• Coupon carry over the holding period: Coupon_income ≈ Clean_coupon_rate × Face_value × (h / year_fraction_base), adjusted for payment frequency.
• Holding period return (simplified): HPR ≈ (Coupon_income + ΔP_roll) / Price_start.
• If including a parallel shift scenario: add ΔP_shift ≈ [−Duration_eff × Δy_shift + 0.5 × Convexity_eff × (Δy_shift)^2] × Price_start.

These are estimates. For higher precision, discount each cash flow at the starting curve and at the rolled-down maturity curve point, then compare clean prices. Duration and convexity give a fast approximation that works well for small yield changes.

Inputs and Assumptions for Bond Roll-Down Return

Roll-down analysis depends on accurate inputs. Confirm your bond terms and yield curve data. Use a consistent day count and compounding basis. Consider the bond type and embedded options, which can change effective duration and convexity.

• Bond terms: coupon rate, payment frequency, maturity date, and current clean price per 100 face value.
• Yield curve: spot or par yields across maturities that bracket T0 and T0 − h.
• Holding period: months or years, matching your analysis horizon.
• Duration and convexity: effective measures that reflect features and expected yield behavior.
• Reinvestment rate: optional rate for coupon cash flows received during the horizon.
• Day count and compounding: Actual/Actual, 30/360, or other, and annual or street compounding conventions.

Set reasonable ranges. Extremely short horizons may make results sensitive to day count choices. Very long horizons increase curve interpolation risk. If the curve is inverted, Δy_roll can be positive, which reduces price. Callable or mortgage-backed bonds require option-adjusted measures to handle edge cases.

Using the Bond Roll-Down Return Calculator: A Walkthrough

Here’s a concise overview before we dive into the key points:

1. Enter the bond’s clean price, coupon rate, payment frequency, and maturity date.
2. Select your holding period and the day count convention used for accruals.
3. Load or paste the current yield curve points that cover your maturities.
4. Input effective duration and convexity, or enable the calculator’s estimate.
5. Choose whether to include a parallel yield shift scenario or keep the curve unchanged.
6. Run the calculation and review the return breakdown by component.

These points provide quick orientation—use them alongside the full explanations in this page.

Case Studies

Normal curve Treasury example: A 5-year Treasury trades at a clean price of 99.20 with a 3% coupon. The curve slopes up. The 5-year yield is 3.4%, and the 4.5-year point implies 3.2%. You plan a 6-month holding period. Δy_roll is 0.20% (3.4% minus 3.2%). With effective duration of 4.6 and convexity of 0.25, the roll-down price change is about [−4.6 × 0.0020 + 0.5 × 0.25 × 0.000004] × 99.20 ≈ +0.91 points. Coupon carry for 6 months adds about 1.50 points per 100 annualized coupon rate, scaled for 6 months and cash timing. With semiannual payments, you receive roughly 1.50 in coupon cash over the period. Holding period return is roughly (1.50 + 0.91) / 99.20 ≈ 2.43% over 6 months, before taxes and fees. What this means: The upward slope supports price drift, and carry compounds the gain.

Inverted curve corporate example: A 7-year A-rated corporate bond trades at 101.00 with a 5% coupon and an OAS of 120 bp. The 7-year government yield is 4.0%, and the 6.5-year point is 4.2%. Over 6 months, Δy_roll is −0.20% plus any spread roll behavior. If spread stays constant in OAS terms, the higher government yield at 6.5 years leads to a small price loss from roll-down. With duration 6.0 and convexity 0.35, ΔP_roll ≈ [−6.0 × (−0.0020) + 0.5 × 0.35 × 0.000004] × 101.00 ≈ −1.21 points because the curve is inverted around this segment once OAS effects are applied. Coupon income is about 2.50 points for half a year. Net holding period return is about (2.50 − 1.21) / 101.00 ≈ 1.28% over 6 months. What this means: Inversion can offset carry; coupon income dominates the result.

Limits of the Bond Roll-Down Return Approach

Roll-down return assumes the yield curve is stable. Markets rarely hold still. Credit spreads move. Liquidity changes. Optionality can alter effective duration. Use this method as a planning tool, not a guarantee.

• Curve shape risk: Level, slope, and curvature can shift in ways that overwhelm roll-down.
• Credit events: Downgrades or upgrades change spreads and duration behavior.
• Optionality: Calls, prepayments, or sinking funds require option-adjusted measures.
• Reinvestment risk: Coupons may reinvest at different rates than expected.
• Transaction costs: Bid-ask and taxes reduce realized returns.

Combine roll-down analysis with scenario testing. Check bear and bull curve shifts. Review liquidity and spread history. If the bond is complex, prefer full cash flow models with option-adjusted spread methods.

Disclaimer: This tool is for educational estimates. Consider professional advice for decisions.

Units Reference

Units matter because small yield changes drive price changes. A few bp can move price by many ticks. Keep your inputs aligned so the calculator handles scaling correctly and reports a clear breakdown.

Read the table as a quick checklist. If your yield is in percent, convert to decimals before applying formulas. Keep duration and convexity in effective terms to reflect curve and cash flow nuances.

Tips If Results Look Off

If the output surprises you, check basics first. Small unit errors can drive big mistakes. Confirm your curve points and ensure the horizon matches your day count and coupon schedule.

• Verify that yields at T0 and T0 − h are from the same curve and basis.
• Ensure duration is effective, not Macaulay, for price sensitivity.
• Confirm clean vs dirty price handling and accrued coupon timing.
• Test a tiny horizon to see if the sign and magnitude behave as expected.

Still unsure? Run multiple scenarios: unchanged curve, +50 bp, and −50 bp. The pattern should match your bond’s duration and convexity. If not, revisit inputs and assumptions.

FAQ about Bond Roll-Down Return Calculator

What is roll-down return in plain terms?

It is the price gain or loss that happens as a bond “ages” along a stable yield curve. The change occurs because shorter maturities often carry different yields than longer ones.

How is roll-down different from carry?

Carry is income you earn by holding the bond, mostly coupon and any financing spread. Roll-down is the price drift from moving along the yield curve with time.

Do I need convexity for a good estimate?

For small yield changes and short horizons, duration may be enough. Convexity improves accuracy when the curve is steep, the horizon is longer, or yields are volatile.

Can I use this for callable or mortgage bonds?

Yes, but use option-adjusted duration and convexity. Plain measures can misstate sensitivity when cash flows change with rates.

Glossary for Bond Roll-Down Return

Roll-Down

The price effect from a bond’s maturity shortening along an assumed unchanged yield curve over the holding period.

Yield Curve

A graph of yields by maturity for a set of similar bonds, often government securities used as a curve benchmark.

Duration

A measure of price sensitivity to small yield changes, expressed in years. Effective duration reflects curve and option effects.

Convexity

A second-order measure of curvature in the price-yield relationship. It adjusts duration estimates for larger yield moves.

Clean Price

The bond price excluding accrued interest. Dirty price includes accrued and reflects the cash amount exchanged.

Carry

The income from holding a bond, including coupon and any financing benefit, before price changes from yield shifts.

Basis Point

One hundredth of a percent, equal to 0.01%. There are 100 basis points in one percent.

Holding Period Return

The total return earned over a specified time, including coupon income and price change, divided by the starting price.

References

Here’s a concise overview before we dive into the key points:

• Investopedia: Rolldown Return Definition
• Bank of England: What is the yield curve?
• U.S. Treasury: Daily Treasury Yield Curve Rates
• Wikipedia: Duration (finance)
• Investopedia: Convexity Explained
• Investor.gov: Bonds and Interest Rate Risk

These points provide quick orientation—use them alongside the full explanations in this page.