# Key Rate Duration

## What is 'Key Rate Duration'

Key rate duration measures the duration of a security or portfolio at a specific maturity point along the entirety of the yield curve. When keeping other maturities constant, the key rate duration can be used to measure the sensitivity in a bond's price to a 1% change in yield for a specific maturity.

The calculation is as follows:

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## BREAKING DOWN 'Key Rate Duration'

Key rate duration is an important concept in estimating the expected changes in value for a bond or portfolio of bonds because it does so when the yield curve shifts in a manner that is not perfectly parallel, which occurs often. Effective duration, another important bond metric, is an insightful duration measure that also calculates expected changes in price for a bond or portfolio of bonds given a 1% change in yield, but it is only valid for parallel shifts in the yield curve. This is why key rate duration is such valuable metric.

Key rate duration and effective duration are related. There are 11 maturities along the Treasury spot rate curve, and a key rate duration may be calculated for each. The sum of all the 11 key rate durations along a portfolio yield curve is equal to the effective duration of the portfolio.

## Calculating Key Rate Duration

The formula for calculating key rate duration uses three separate variables. They are:

P(0) = The original price of the bond

P(-) = The bond price with a 1% decrease in price

P(+) = The bond price with a 1% increase in price

The key rate duration formula is:

Key rate duration = (P(-) - P(+)) / (2 x 1% x P(0))

As an example, assume that a bond is originally priced at \$1,000, with a 1% increase in yield would be priced at \$970, and with a 1% decrease in yield would be priced at \$1,040. The key rate duration for this bond would be:

Key rate duration = (\$1,040 - \$970) / (2 x 1% x\$1,000) = \$70 / \$20 = 3.5

## Key Rate Duration Interpretation

It can be difficult to interpret an individual key rate duration because it is very unlikely that a single point on the Treasury yield curve will have a upwards or downwards shift at a single point while all others remain constant. It's useful for looking at key rate durations across the curve and looking at the relative values of key rate durations between two securities.

For example, assume bond X has a one-year key rate duration of 0.5 and a five-year key rate duration of 0.9. Bond Y has key rate durations of 1.2 and 0.3 for these maturity points. It could be said that bond X is half as sensitive as bond Y on the short-term end of the curve, while bond Y is one-third as sensitive to interest rate changes on the intermediate part of the curve.