What Is Key Rate Duration?
Let me explain key rate duration directly to you: it's a measure of how the value of a debt security or a portfolio of debt instruments, usually bonds, changes at a specific maturity point along the entire yield curve. When you keep other maturities constant, key rate duration shows the sensitivity in a debt security's price to a 1% change in yield for that specific maturity.
Key Takeaways
You need to know that key rate duration calculates the change in a bond's price relative to a 100-basis-point (1%) change in the yield for a given maturity. If the yield curve shifts in a parallel way, effective duration works fine, but for non-parallel shifts, you must use key rate duration to estimate changes in portfolio value. Overall, duration measures like this tell you the price risk in holding fixed income securities when interest rates change.
The Formula for Key Rate Duration
Here's the formula you use for key rate duration: it's (P- - P+) / (2 * 1% * P0), where P- is the security's price after a 1% decrease in its yield, P+ is the price after a 1% increase, and P0 is the original price. I'll skip embedding an image here, but you can visualize it as a standard duration calculation adjusted for key rates.
Calculating Key Rate Duration
Take this example to see how it works: suppose a bond is originally priced at $1,000. If yields increase by 1%, it's priced at $970, and if they decrease by 1%, it's at $1,040. Plugging into the formula, key rate duration is ($1,040 - $970) / (2 * 1% * $1,000) = $70 / $20 = 3.5. That's straightforward for you to apply.
What Does Key Rate Duration Tell You?
Key rate duration helps you estimate expected changes in value for a bond or bond portfolio when the yield curve shifts non-parallelly, which happens frequently. Effective duration, another key metric, calculates price changes for a 1% yield shift but only works for parallel shifts—that's why key rate duration is valuable. Remember, key rate duration relates to effective duration: there are 11 maturities on the Treasury spot rate curve, and the sum of key rate durations for each equals the portfolio's effective duration.
Example of How to Use the Key Rate Duration
Interpreting a single key rate duration can be tricky because it's rare for one point on the Treasury yield curve to shift while others stay put. Instead, look at key rate durations across the curve and compare between securities. For instance, say bond X has a one-year key rate duration of 0.5 and a five-year one of 0.9, while bond Y has 1.2 and 0.3 for those points. You can see bond X is half as sensitive as bond Y on the short end, but bond Y is one-third as sensitive on the intermediate part.
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