First, the key terms.

Modified duration
A local percentage price sensitivity to a yield change.
Convexity
Curvature in the price-yield relationship under the specified model.

The idea, explained

For a small parallel yield move, percentage price change is approximately negative modified duration times the yield change expressed as a decimal. Larger moves need attention to convexity and the underlying cash flows. Embedded options can alter sensitivity substantially. A portfolio faces changes at different points on the yield curve, not just one uniform rate shift. Duration is a local sensitivity measure, not a complete description of fixed-income risk.

STEP 1

Convert the yield change

A 0.5 percentage-point yield increase is 0.005 in decimal form. Multiplying duration by 0.5 instead creates a hundredfold unit error. Keep basis points, percentage points and decimal rates distinct.

STEP 2

Respect the approximation

The first-order duration estimate holds other assumptions fixed and is most useful for small changes. Larger or nonparallel movements, optionality, credit and liquidity require more analysis. Convexity adds information but does not capture every risk.

Follow a worked example.

A hypothetical bond with modified duration 5 faces a 0.5 percentage-point yield increase, or 0.005. The first-order estimate is −5 × 0.005 = −2.5 percent. The actual change can differ because of convexity and other effects.

Walk it through, one step at a time

  1. A fictional bond has modified duration 4. A 25-basis-point increase is 0.0025.
  2. The estimated percentage price change is −4 × 0.0025 = −0.01, or −1 percent.
  3. For a $1,000 value, this gives an approximate $10 decline before considering convexity and other changes.

Where people get stuck

Use decimal yield changes in the calculation; confusing 0.5 with 0.005 creates a hundredfold error.

Now try it yourself.

Pause before opening each answer. Explain your reasoning in your own words.

1. Check the core idea

Does duration capture credit-default risk or every nonparallel curve movement?

Reveal the answer & reasoning

No. It summarizes a particular interest-rate sensitivity. Credit, liquidity, optionality and curve-shape exposures require additional analysis.

2. Apply what you learned

Would doubling the yield move always exactly double the price move?

Reveal the answer & reasoning

No. Duration is a linear approximation. Curvature and changes in assumptions make actual price responses nonlinear.