# Key Rate Duration

Effective duration calculates the approximate change in a bond’s price given a 100 basis point (1%) move in interest rates as part of a parallel shift in the yield curve.

When the yield curve shifts in a non-parallel manner, the portfolio’s effective duration cannot be used to estimate the change in portfolio value.

Key rate duration is the duration at specific maturity point on the yield curve. Keeping all other maturities constant, key rate duration is a measure of the sensitivity of a bond’s price to a 100 basis point change in yield for a given maturity.

When the yield curve changes in a non-parallel manner, key rate durations (and not the portfolio’s effective duration) must be used to estimate the change in portfolio value.

Key rate duration is calculated using the following formula:

$Key\ Rate\ Duration = \frac{P_{-} - P_{+}}{2 \times 1 \% \times P_{0}}$

Where:

P- = Price with a 1% decrease in yield

P+ = Price with a 1% increase in yield

P0 = Original price

On the Treasury spot curve, there are 11 maturities. So, key rate duration can be calculated for each maturity. The sum of all key rate durations on the yield curve will be equal to the effective duration.

In order to estimate a portfolio’s change in value in the event of a non-parallel yield curve shirt, an analyst will need to perform a weighted average calculation utilizing the key rate durations to the portfolio’s weights at different maturities (i.e., the percent invested at two year, five year, ten year, and twenty year bonds).