How to calculate the change in bond price with the change in yield
About this lesson
In this video, I will show how a bond’s price changes with the change in yield to maturity. In other words, the calculation will measure the interest rate risk of a bond.
Interest rate risk
When yields rise, bond prices fall, and vice versa. Duration tells you by how much.
Modified duration
Modified duration: D* = D ÷ (1 + y)
where D is the Macaulay duration and y is the yield per period.
The percentage price change is approximately:
ΔP ÷ P ≈ −D* × Δy
Example
The 3-year, 8% coupon bond from the duration lessons: price $950.26 at a 10% yield, Macaulay duration 2.7774 years.
D* = 2.7774 ÷ 1.10 = 2.5249
If the yield rises by 1 percentage point, from 10% to 11%:
ΔP ÷ P ≈ −2.5249 × 0.01 = −2.52%, so the price falls by about $23.99, to about $926.27.
Actual new price at 11%: $926.69, a −2.48% change.
The estimate is close, but not exact. Duration treats the price–yield relationship as a straight line, while the real one is curved. The convexity adjustment closes most of the gap.
Key points
- The longer the duration, the bigger the price change for the same yield move.
- Duration works best for small changes in yield.
- For the change in dollars, multiply by the price: D* × Price × Δy. Here, 2.5249 × $950.26 × 0.01 ≈ $24.
Next: bond portfolio immunization.