# Effective Duration

## What it is:

**Effective duration** is a calculation used to approximate the actual, modified duration of a callable bond. It takes into account that future interest rate changes will affect the expected cash flows for a callable bond.

## How it works (Example):

The formula for *effective duration* is:

**Effective Duration = (P _{-} - P_{+} ) / [(2)*(P_{0})*(Y_{+} - Y_{-})]**

Where:

P_{0} = the bond's initial price per $100 of par value

P_{-} = the bond's price if its yield falls by x basis points

P_{+} = the bond's price if its yield rises by x basis points

(Y_{+} - Y_{-}) = Change in yield in decimal

For example, let's assume you purchase a Company XYZ bond at 100% of par. The bond currently has an 8% yield. If the bond price increases to 101.5 when yields fall 10 basis points and the price falls to 99.5 when yields rise by 10 basis points, then using the formula above, we could calculate that the bond’s effective duration is:

**(101.5 - 99.5) / [2 *(100) * (.001)] = (2) / (.2) = 10.00**

This bond's effective duration is 10.00.

This means that for every 100 basis point change in rates, the bond's price will change by 10.00%.

Effective duration takes into account what commonly happens to callable bondholders: interest rates change over time and the bond is called away before it matures.

## Why it Matters:

Clearly, the fact that a bond is callable affects its price at certain times. The higher a callable bond's coupon rate is compared to the market's prevailing yield, the more likely it is to be called and, therefore, the lower the bond's effective duration. In contrast, a bond with a coupon rate lower than the prevailing market yield is not likely to be called and will thus have an effective duration similar to a noncallable bond. In turn, the greater duration of the bond, the greater its percentage price volatility.

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Understanding the effective duration formula is not nearly as important as understanding that it is a measure of risk because it demonstrates how sensitive a bond is to changes in market returns for securities of similar risk. By providing a way to estimate the effect of certain market changes on a bond's price, this in turn helps investors use immunization strategies to capitalize on interest rate movements, better meet their future cash needs, and protect their portfolios from interest-rate risk.