Bond Duration Calculator

Measuring Interest Rate Sensitivity

Bond duration quantifies how much a bond's price changes when interest rates move—essential knowledge for fixed income investors. The calculator computes duration metrics that predict price volatility, helping manage interest rate risk in bond portfolios.

Longer duration means greater sensitivity to rate changes. Understanding duration enables constructing portfolios that match your risk tolerance and investment horizon, avoiding nasty surprises when rates move.

Know your rate risk.

What Duration Measures

Duration represents approximate percentage price change for 1% rate change:

Duration of 5 years: Price moves ~5% for 1% rate change Duration of 10 years: Price moves ~10% for 1% rate change

Higher duration = more interest rate risk.

Macaulay Duration

Weighted average time until cash flows received:

Bond: $1,000 face, 5% coupon, 5 years, 4% yield

Cash flow timing weights: Year 1: $50 coupon Year 2: $50 coupon Year 3: $50 coupon Year 4: $50 coupon Year 5: $50 coupon + $1,000 principal

Weighted average considering present values = Macaulay Duration

Modified Duration

Macaulay Duration adjusted for yield:

Modified Duration = Macaulay Duration / (1 + Yield/periods)

This directly estimates percentage price change for yield changes.

5-year Macaulay Duration at 4% yield: Modified Duration = 5 / 1.04 = 4.81

Price changes ~4.81% per 1% rate move.

Duration Calculation Example

10-year bond, 6% coupon, 5% yield:

Present value of each coupon and principal Weight by time received Sum weighted times / bond price = Macaulay Duration

Result: ~7.8 years Macaulay Duration Modified Duration: ~7.4 years

Factors Affecting Duration

Duration increases with:

Longer maturity: More time to receive cash flows Lower coupon: Less early cash return Lower yield: Future cash flows worth more

Zero-coupon bonds have duration equal to maturity (no early payments).

Duration by Bond Type

Price Change Approximation

Using duration to estimate price impact:

Bond with modified duration 6 Interest rates rise 0.5% Estimated price change: -6 × 0.5% = -3%

Rates fall 0.5% Estimated price change: +6 × 0.5% = +3%

Duration provides linear approximation of price change.

Convexity Adjustment

Duration is linear; bonds actually have curved price/yield relationship:

Convexity: Measures curvature Positive convexity: Price rises more than duration predicts when rates fall

Price Change ≈ -Duration × ΔYield + 0.5 × Convexity × (ΔYield)²

Convexity matters more for larger rate changes.

Duration vs. Maturity

Not the same thing:

30-year Treasury: 30-year maturity, ~18-year duration 30-year zero-coupon: 30-year maturity, 30-year duration 10-year high-coupon: 10-year maturity, ~7-year duration

Maturity is final payment date; duration is weighted average timing.

Portfolio Duration

Weighted average of holdings:

Bond A: $50,000, duration 3 years Bond B: $30,000, duration 7 years Bond C: $20,000, duration 12 years

Portfolio duration: (50×3 + 30×7 + 20×12) / 100 = 6.0 years

Portfolio moves ~6% per 1% rate change.

Duration Matching Strategy

Match portfolio duration to investment horizon:

Investment horizon: 5 years Target portfolio duration: 5 years

If rates rise: Bond prices fall, but reinvestment earns more If rates fall: Bond prices rise, but reinvestment earns less

Effects offset at the horizon date.

Interest Rate Risk Management

Reducing rate sensitivity:

Shorten duration: Sell long bonds, buy short bonds Ladder maturities: Spread duration across time Use floating rate: Zero duration on rate resets Hedge with derivatives: Interest rate swaps

Duration and Rising Rates

When rates rise, duration determines damage:

2% rate increase: Bond with 2-year duration: ~4% price decline Bond with 10-year duration: ~20% price decline

Long-duration bonds devastated in rising rate environments.

Duration and Falling Rates

When rates fall, duration determines gain:

2% rate decrease: Bond with 2-year duration: ~4% price gain Bond with 10-year duration: ~20%+ price gain

Long-duration bonds benefit most from falling rates.

Duration for Income Investors

Income focus suggests shorter duration:

Goal: Stable income, principal preservation Approach: Shorter duration reduces price volatility Trade-off: Lower yields than long bonds

Principal safety vs. yield trade-off.

Duration for Total Return

Total return investors may accept more duration:

Goal: Maximum total return Approach: Longer duration when expecting rate declines Risk: Significant losses if rates rise unexpectedly

Duration bet is interest rate bet.

Dollar Duration

Duration in dollar terms:

Bond value: $100,000 Modified duration: 6

Dollar duration = $100,000 × 6 / 100 = $6,000

Price changes ~$6,000 per 1% rate move.

Using the Calculator

Enter bond face value, coupon rate, years to maturity, and yield to maturity.

The calculator shows:

• Macaulay Duration
• Modified Duration
• Convexity
• Dollar Duration
• Price change estimates for various rate scenarios

Model scenarios: How does duration change with different coupons? What's my portfolio duration? How much will my bond drop if rates rise 1%?

Use results to understand and manage interest rate sensitivity in your fixed income investments.

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Bond duration quantifies interest rate risk—how much prices move when rates change. The calculator computes duration metrics that enable informed portfolio construction and risk management. In volatile rate environments, understanding duration protects against unexpected losses and positions for potential gains. Know your duration; manage your risk.