Understanding Key Rate Duration: A Guide for Bond Investors

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 curveYield CurveThe Yield Curve is a graphical representation of the interest rates on debt for a range of maturities. It shows the yield an investor is expecting to earn if he lends his money for a given period of time.  The graph displays a bond's yield on the vertical axis and the time to maturity across the horizontal axis. – 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 durationEffective DurationEffective duration is the sensitivity of a bond's price against the benchmark yield curve. One way to assess the risk of a bond is to estimate the 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 bondCallable BondA callable bond (redeemable bond) is a type of bond that provides the issuer of the bond with the right, but not the obligation, to redeem the bond before its maturity date. The callable bond is a bond with an embedded call option. These bonds generally come with certain restrictions on the call option.. 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

CFI is the official provider of the global Commercial Banking & Credit Analyst (CBCA)™Program Page - CBCAGet CFI's CBCA™ certification and become a Commercial Banking & Credit Analyst. Enroll and advance your career with our certification programs and courses. certification program, designed to help anyone become a world-class financial analyst. To keep advancing your career, the additional resources below will be useful:

• Bond PricingBond PricingBond pricing is the science of calculating a bond's issue price based on the coupon, par value, yield and term to maturity. Bond pricing allows investors
• Non-Callable BondNon-Callable BondA non-callable bond is a bond that is only paid out at maturity. The issuer of a non-callable bond can’t call the bond prior to its date of maturity. It is different from a callable bond, which is a bond where the company or entity that issues the bond owns the right to repay the face value of the bond
• Treasury Bills (T-Bills)Treasury Bills (T-Bills)Treasury Bills (or T-Bills for short) are a short-term financial instrument issued by the US Treasury with maturity periods from a few days up to 52 weeks.
• Yield to Maturity (YTM)Yield to Maturity (YTM)Yield to Maturity (YTM) – otherwise referred to as redemption or book yield – is the speculative rate of return or interest rate of a fixed-rate security.