A duration of 7 means the bond’s price falls about 7% if yields rise by one percentage point. Effective duration is the right measure for bonds whose cash flows can change, such as callable bonds and mortgage-backed securities.
How to use the Effective Duration Calculator
- Face value
- Annual coupon rate
- Coupon frequency
- Years to maturity
- Yield to maturity (YTM)
- Yield differential (shift)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the bond details, the yield to maturity and the yield shift.
Tips
- Check whether rates are quoted annually, semi-annually or per period.
- Bond prices and yields move in opposite directions – a higher yield means a lower price.
- Use the bond’s clean price (without accrued interest) for yield calculations.
- Credit ratios are most useful when tracked over several years.
Common mistakes to avoid
- Confusing the coupon rate with the yield.
- Using the face value instead of the market price.
- Forgetting that callable bonds may be redeemed before maturity.
Inputs explained
| Field | What to enter |
|---|---|
| Face value | Amount in your currency |
| Annual coupon rate | In % |
| Coupon frequency | Choose one: Annually, Semi-annually, Quarterly, Monthly |
| Years to maturity | A number |
| Yield to maturity (YTM) | In % |
| Yield differential (shift) | In % |
What each result means
- Coupon per period = [Face value]×[Annual coupon rate]÷100÷[Coupon frequency]
- Annual coupon = [Face value]×[Annual coupon rate]÷100
- Bond price = bondpx([Face value], [Annual coupon rate]÷100, [Coupon frequency], [Years to maturity], [Yield to maturity (YTM)]÷100)
- Price if yields fall by the shift = bondpx([Face value], [Annual coupon rate]÷100, [Coupon frequency], [Years to maturity], ([Yield to maturity (YTM)] – [Yield differential (shift)])÷100)
- Price if yields rise by the shift = bondpx([Face value], [Annual coupon rate]÷100, [Coupon frequency], [Years to maturity], ([Yield to maturity (YTM)] + [Yield differential (shift)])÷100)
- Effective duration = ([Price if yields fall by the shift] – [Price if yields rise by the shift])÷(2×[Bond price]×[Yield differential (shift)]÷100)
- Approximate price change for a 1% rise = -[Effective duration]
Example values
How the main result changes when Face value changes and everything else stays at the example values above:
| Face value | Effective duration |
|---|---|
| 500 | 7.677 |
| 750 | 7.677 |
| 1,000 | 7.677 |
| 1,250 | 7.677 |
| 1,500 | 7.677 |
| 2,000 | 7.677 |
Formula
Effective duration = (P₋ − P₊) ÷ (2 × P₀ × Δy)Price change ≈ −duration × Δy × priceWorked example
Inputs — Face value: $1,000; Annual coupon rate: 5 %; Coupon frequency: Semi-annually; Years to maturity: 10; Yield to maturity (YTM): 6 %; Yield differential (shift): 1 %.
Results — Coupon per period = $25.00; Annual coupon = $50.00; Bond price = $925.61; Price if yields fall by the shift = $1,000.00; Price if yields rise by the shift = $857.88; Effective duration = 7.677; Approximate price change for a 1% rise = -7.68 %.
Frequently asked questions
What is effective duration?
A measure of price sensitivity to yield changes, based on re-pricing.
How is it different from modified duration?
It works for bonds with embedded options whose cash flows change with rates.
What does a duration of 5 mean?
About a 5% price change for a 1 percentage point change in yields.
What formula does the Effective Duration Calculator use?
Effective duration = (P₋ − P₊) ÷ (2 × P₀ × Δy).