Risk and Credit Analysis · Bonds Explained

Choose the right duration

Macaulay duration is a weighted average time to cash flows. Modified duration translates a small yield change into an approximate percentage price change. Effective duration uses modelled price changes and is useful when cash flows can change with interest rates, as with callable securities.

These measures are related but not interchangeable. A platform displaying duration without identifying the measure leaves an important part of the analysis unspecified.

Estimate a small movement

Suppose a hypothetical bond has modified duration of 4.5. A yield rise of 0.5 percentage points equals 0.005 in decimal form. The approximate price change is minus 4.5 × 0.005, or a decline of 2.25%. On a $10,000 position, that is roughly $225.

This is a local estimate holding other relevant factors constant. It does not include coupon income over a holding period or a change in the borrower’s expected repayment.

Allow for curvature

For a bond with appropriate annual convexity of 25, the convexity adjustment for that same yield change is half × 25 × 0.005 squared. It adds about 0.03125 percentage points to the price estimate, giving a decline of approximately 2.22%.

Ordinary bonds without embedded options generally have positive convexity. Callable securities can behave differently as redemption becomes more likely. The units and compounding convention must match the formula.

Know what the summary hides

A portfolio duration is useful for a small parallel shift. It does not fully describe a curve twist, changing credit spreads or a large move that alters cash flows. Key rate durations measure sensitivity to selected points on the curve and can reveal differences hidden by the same aggregate duration.

Use duration as an exposure measure, then test scenarios. A precise looking estimate is only as useful as the yield change and cash flow assumptions behind it.

Try it yourself

A bond has modified duration 6. If its yield falls by 0.25 percentage points, what is the approximate price effect before convexity?

Show the worked answer

The estimated price rise is 6 × 0.0025 = 1.5%. Actual results can differ because of curvature and other changing risks.

Further reading

Educational material. Examples are hypothetical and do not recommend a security or a personal allocation. Contract terms and market conventions vary.

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