Using Key Rate Durations for Nonparallel Yield Curve Shifts

Summary

The note asks how to generalize duration measures when spot rates move nonparallel to one another. It identifies Fisher–Weil duration as a generalization of Macaulay duration for changes expressed through the spot curve, then asks how to represent arbitrary curve movements.

The answer says a single scalar duration is inadequate for arbitrary nonparallel shifts. Instead, use a vector of key rate durations, with a component for each selected maturity, to describe sensitivity to changes at different points on the curve. The note gives no formula, worked example, or guidance on choosing key maturities, so it sketches the representation rather than a full calculation procedure.

Key ideas

• A scalar duration summarizes sensitivity to a parallel yield curve movement.
• For nonparallel curve movements, represent sensitivity with key rate durations across selected maturities.
• The note does not specify formulas or explain how to choose the key maturities.

Tags

# Generalization of Macaulay/modified duration under non-parallel shift of spot curve


# Generalization of Macaulay/modified duration under non-parallel shift of spot curve












The generaliztaion of Macaulay duration (which is defined in terms of yield to maturity) is known as Fisher-Weil duration. How is Fisher-Weil duration or modified duration defined under non-parallel shift in spot curve?

## Answer by Alex C (score 1, accepted)

https://quant.stackexchange.com/a/44851

When you want to consider arbitrary (i.e. non parallel) movements of the yield curve, the duration ( a scalar) is replaced by a vector of 'key rate durations' one for each maturity you wish to consider. investopedia.com/terms/k/keyrateduration.asp

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.