# Key Rate Duration

A measure of a bond or bond portfolio’s sensitivity to a 100-basis point change in yield at a specific maturity point

## What is Key Rate Duration?

Key rate duration is a measure of a bond or bond portfolio’s sensitivity to a 100-basis point – 1% – change in yield at a specific maturity point. ### Summary

• The key rate duration is an important metric for determining possible bond value changes resulting from yield changes for the bond’s maturity.
• Key rate duration is considered an improvement over using the effective duration metric, which can only be applied when there are parallel changes in the yield all across the yield curve.
• Using the metric can help investors or financial analysts predict the probable profitability of investing in bonds with various maturities.

### Key Rate Duration vs. Effective Duration

The key rate duration is considered a superior metric to effective duration. It is because the effective duration metric is only applicable to parallel shifts in interest rates and the yield curve – when interest rates for all the various bond maturities simultaneously increase or decrease by the same amount.

In real life, such a phenomenon rarely, if ever, occurs. Interest rate increases or decreases for short-term bonds do not typically parallel rate increases or decreases for long-term or medium-term bonds. In fact, interest rates for different maturities of bonds may even be moving in opposite directions, with, for example, long-term interest rates increasing while the interest rate on short-term bonds is declining.

The key rate duration represents an improvement over the effective duration measure because it indicates predicted changes in price/value when there are shifts in the yield curve that are not parallel across all maturities.

### Formula for Calculating the Key Rate Duration Where:

• P – A bond’s price after a 1% decrease in yield
• P+ – /the bond’s price after a 1% increase in yield
• P0 – The original price of the bond

### Practical Example

Assume that a given bond is originally priced at \$1,000 and that a 1% increase in yield for the bond’s maturity would cause the value of the bond to decline to \$980, while a 1% yield decrease would result in the bond’s value increasing to \$1,030.

Using the formula shown above, the bond’s key rate duration would be calculated as follows:

Key Rate Duration = (1030 – 980) / (2 * 0.01 * 1000) = 2.5

### Significance of the Key Rate Duration

The key rate duration reflects the expected change in value resulting from a yield change for a bond or bond portfolio with a specific maturity. It assumes the yields for all other maturities are kept the same. There are more than ten different bond maturities for U.S. Treasuries, and the investor can calculate the key duration for every different maturity level.

If an investor clearly knows how he or she expects interest rates to move over a given time frame, they can then use the key rate duration metric to figure out which bond maturities are likely to offer the most profitable investment returns (assuming that the investor’s interest rate predictions prove to be correct). Thus, the metric can be used to compare various prospective fixed-income investments.

Another scenario where calculating key rate duration may be useful is when an investor holds a callable bond. They may want to estimate the change in the value of the bond they hold given various basis point changes. Doing so can help them estimate the likelihood of their bond being called for early redemption by the issuer.

More Resources

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• Bond Pricing
• Non-Callable Bond
• Treasury Bills (T-Bills)
• Yield to Maturity (YTM)

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