Lesson 7 of 8 · All lessons in this module

Lesson 7 of 8 · 15 min

How spread changes move bond prices

A change in spread moves a bond's price exactly like any other yield change: about minus modified duration times the spread change, plus a convexity correction for large moves.

In short

For an option-free bond, the same modified duration and convexity apply whether the yield change comes from the benchmark or from the spread.
Small change: $\%\Delta PV^{\text{Full}} \approx -\text{AnnModDur} \times \Delta\text{Spread}$ .
Large change: add $+\tfrac{1}{2} \times \text{AnnConvexity} \times (\Delta\text{Spread})^2$ . Rescale convexity so it is of the order of duration squared, and enter the spread change as a decimal.
Narrower spreads raise prices and returns; wider spreads lower them. Longer-duration bonds have higher spread sensitivity.
The approximation error grows with duration and with the size of the spread change.

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