# Key Rate Duration Explained: Sensitivity, Calculation & Formula

![Key Rate Duration](https://www.investopedia.com/thmb/SP-UEcGJkPDc9P1OOe0chYmQSdM=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/TermDefinitions_keyrateduration-b04546a8a0124597bdef6226d98ea139.jpg)

*— Investopedia / Tara Anand*

## What Is Key Rate Duration?

Key rate duration is a measure of bond price sensitivity to changes at different points along the yield curve. As opposed to effective duration, which looks at changes in value as a consequence of the yield curve's parallel shifts, key rate duration is used to assess value changes due to non-parallel shifts.

### Key Takeaways

*   Key rate duration specifically measures the sensitivity of a bond or portfolio's price to changes in yield at particular maturity points, unlike effective duration measures that assume parallel shifts in the yield curve.
*   The concept is critical for understanding bond and portfolio value fluctuations when the yield curve changes in a non-parallel manner, which occurs frequently in real-world scenarios.
*   Calculating key rate duration involves comparing a bond's price changes resulting from a 1% increase and decrease in yield, providing an insight into price volatility at distinct maturities.
*   Key rate duration is often used alongside effective duration; while effective duration calculates changes for parallel shifts, the sum of key rate durations aligns with the portfolio's effective duration.

## Key Rate Duration Formula Explained

![Key Rate Duration formula](https://www.investopedia.com/thmb/O1UFnrnk4gWVxk1VBdGMvwkVc3I=/1280x0/filters:no_upscale():max_bytes(150000):strip_icc()/KeyRateDuration-5c6bb05bc9e77c00014764e8.jpg)

*Key Rate Duration formula. — Investopedia *

Where:

*   P\- \= a security's price after a 1% _decrease_ in its yield
*   P\+ \= a security's price after a 1% _increase_ in its yield
*   P0 \= the security's original price

## How to Calculate Key Rate Duration

As an example, assume that a [bond](https://www.investopedia.com/terms/b/bond.asp) is originally priced at $1,000, and with a 1% increase in yield would be priced at $970, and with a 1% decrease in yield would be priced at $1,040. based on the formula above, the key rate duration for this bond would be:

﻿ $\begin{aligned} &\text{KRD}=\left(\$1,040 - \$970\right)/\left(2\times1\%\times\$1,000\right)=\$70/\$20=3.5\\ &\textbf{where:}\\ &\text{KRD = Key rate duration}\\ \end{aligned}$﻿

## Understanding the Implications of Key Rate Duration

Key rate duration helps estimate how bond values change when the [yield curve](https://www.investopedia.com/terms/y/yieldcurve.asp) shifts unevenly rather than as a whole move upward or downward.

Effective duration is another bond metric that shows price changes with a 1% yield shift, but applies only to parallel yield curve shifts. This is why the key rate duration is such a valuable metric.

Key rate duration and effective duration are related. There are 11 maturities along the Treasury [spot rate](https://www.investopedia.com/terms/s/spot_rate.asp) curve, and a key rate duration may be calculated for each. The sum of all the 11 key rate durations along the portfolio's yield curve equal the [effective duration](https://www.investopedia.com/terms/e/effectiveduration.asp) of the portfolio.

## Practical Applications of Key Rate Duration

It’s can be hard to interpret a single key rate duration. It’s unlikely one point on the yield curve shifts while others stay constant. It's useful to look at key rate durations across the curve and at the relative values of key rate durations between two securities.

For example, bond X has a one-year key rate duration of 0.5 and a five-year key rate duration of 0.9. Bond Y’s durations for these maturities are 1.2 and 0.3. Bond X is half as sensitive as bond Y in the short-term and bond Y is less sensitive at the intermediate part of the curve.

## The Bottom Line

Key rate duration is essential to evaluating a bond or portfolio's sensitivity to changes in yield, especially when the yield curve shifts in a non-parallel fashion. It offers a more nuanced view than effective duration, which assesses value changes due to parallel shifts. Investors can utilize key rate duration to compare bond sensitivities at various maturity points. This can help them construct or adjust their investment strategies effectively.