Duration gives a straight-line estimate of how a bond’s price changes with yields; convexity corrects for the curve. Higher convexity is valuable: prices rise more when yields fall than they drop when yields rise.
How to use the Bond Convexity 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 face value, coupon rate, frequency, years to maturity, yield to maturity and the yield shift to use.
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)
- Bond convexity = ([Price if yield falls] + [Price if yield rises] – 2×[Bond price])÷([Bond price]×([Yield differential (shift)]÷100)^2)
- Effective duration = ([Price if yield falls] – [Price if yield rises])÷(2×[Bond price]×[Yield differential (shift)]÷100)
Example values
How the main result changes when Face value changes and everything else stays at the example values above:
| Face value | Bond convexity |
|---|---|
| 500 | 71.852 |
| 750 | 71.852 |
| 1,000 | 71.852 |
| 1,250 | 71.852 |
| 1,500 | 71.852 |
| 2,000 | 71.852 |
Formula
Price P = Σ coupon ÷ (1 + y/f)^t + face ÷ (1 + y/f)^NConvexity ≈ (P₋ + P₊ − 2P) ÷ (P × Δy²)Price change ≈ −duration × Δy + ½ × convexity × Δy²Worked 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; Bond convexity = 71.852; Effective duration = 7.677.
Frequently asked questions
What is bond convexity?
A measure of how the duration of a bond changes as yields change.
Is higher convexity good?
Yes, for the holder – prices gain more on falls in yield than they lose on rises.
Which bonds have more convexity?
Long-term, low-coupon bonds.
What formula does the Bond Convexity Calculator use?
Price P = Σ coupon ÷ (1 + y/f)^t + face ÷ (1 + y/f)^N.