Key Rate Duration

What is Key Rate Duration ?

Key Rate Duration is a measure of a bond's sensitivity to changes in interest rates at specific points along the yield curve. It measures the change in the bond's price for a one percent change in the interest rate at a specific point on the yield curve.

The yield curve is a graph that shows the relationship between interest rates and the maturity of fixed income securities. Key rate duration focuses on specific points along the yield curve, known as "key rates." These key rates are typically the interest rates that have the greatest impact on a bond's price

How is Key Rate Duration calculated ?

Key Rate Duration is calculated by first calculating the present value of the bond's cash flows at each key rate point, assuming a one percent change in the interest rate at that point, and then dividing by the bond's price.

The formula for calculating key rate duration is as follows:

Key rate duration for a specific interest rate = (P- - P+)/2 x ∆r

Where:

P- is the bond price when the key interest rate decreases by a small amount (∆r)

P+ is the bond price when the key interest rate increases by the same small amount (∆r)

∆r is the change in the key interest rate

Importance of understanding Key Rate Duration

Here are some reasons why understanding key rate duration is important:

1. Helps manage interest rate risk: By understanding key rate duration, investors and analysts can better manage interest rate risk associated with their bond investments. Key rate duration can help identify which maturities on the yield curve are most sensitive to changes in interest rates, allowing investors to adjust their portfolios accordingly.
2. Provides insight into bond valuation: Key rate duration can also provide insight into how changes in interest rates will affect a bond's value over time. By analyzing key rate duration, investors and analysts can estimate how much a bond's price will change for a given change in interest rates, which is critical for estimating the bond's future value.
3. Assists in portfolio optimization: Understanding key rate duration can also help investors optimize their portfolios by identifying bonds that have low correlation with each other. By selecting bonds with different key rate durations, investors can create a portfolio that is less sensitive to changes in interest rates and more diversified.
4. Helps inform investment decisions: Key rate duration is a critical metric that investors and analysts can use to make informed investment decisions. By analyzing key rate duration, investors can assess the risk and return profile of a bond and determine whether it is a suitable investment for their portfolio.

4 Examples of Key Rate Duration

Here are some examples of key rate duration:

1. 2-year key rate duration: The 2-year key rate duration measures a bond's sensitivity to changes in the 2-year interest rate along the yield curve. If a bond has a 2-year key rate duration of 2, it means that the bond's price will change by 2% for every 1% change in the 2-year interest rate.
2. 5-year key rate duration: The 5-year key rate duration measures a bond's sensitivity to changes in the 5-year interest rate along the yield curve. If a bond has a 5-year key rate duration of 3, it means that the bond's price will change by 3% for every 1% change in the 5-year interest rate.
3. 10-year key rate duration: The 10-year key rate duration measures a bond's sensitivity to changes in the 10-year interest rate along the yield curve. If a bond has a 10-year key rate duration of 4, it means that the bond's price will change by 4% for every 1% change in the 10-year interest rate.
4. Overall key rate duration: The overall key rate duration measures a bond's sensitivity to changes in interest rates across the entire yield curve. It is calculated by summing the key rate durations for each individual interest rate along the yield curve. For example, if a bond has a 2-year key rate duration of 1, a 5-year key rate duration of 2, and a 10-year key rate duration of 3, its overall key rate duration would be 6