# Key Rate Duration

## What it is:

Key rate duration is not the same as effective duration. Effective duration is an estimate of a security's sensitivity to a parallel shift in interest rates, meaning that it assumes that interest rates change by the same degree for, say, one-year bonds, five-year bonds, 10-year bonds, and 30-year bonds. That's not often the case in the real world, which is why key rate duration is useful -- it measures a security's price sensitivity to shifts at "key" points along the yield curve. Key duration rates are especially useful for securities with embedded options such as call options or prepayment options.

## How it works (Example):

There are 11 maturities along the Treasury spot rate curve, and a key rate duration is calculated for each. The sum of the key rate durations along a portfolio yield curve is equal to the effective duration of the portfolio.

## Why it Matters:

Key rate duration is a measure of how a security's value changes when its yield changes by 1% for a certain maturity.

The formula for key rate duration is:

Key Rate Duration = (P_{-} - P_{+})/(2 * 0.01 * P_{0})

Where P_{-} = the security price after a 1% decrease in yield

P_{+} = the security price after a 1% increase in yield

P_{0} = the original security price